101F90050
THE APPLICATION OF UTILITY THEORY TO
              THE VALUING OF
AIR POLLUTION-RELATED HEALTH EFFECTS:

     Three Proposed Pilot Studies on Subjective
              Judgments of Asthma
                 Prepared for

              Harvey M. Richmond
        Environmental Protection Specialist
    Office of Air Quality Planning and Standards
       U.S. Environmental Protection Agency
           Research Triangle Park, NC
                  Prepared by

               Adam C. Johnston
       EPA NNEMS Graduate Student Intern
      University of North Carolina, Chapel Hill
    Dept Environmental Science and Engineering
                December 1990       y g  Environmental Protection Agency
                                    Region 5.Library (PL-12J)
                                    77 West Jackson Boulevard, I2trt FJoof
                                    Chicago, IL  60604-3590

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                           DISCLAIMER

This report was  furnished to the U.S. Environmental Protection
Agency by  the student identified on the cover page,  under a National
Network for Environmental Management Studies  fellowship.

The contents are essentially as  received from  the  author.  The
opinions, findings,  and conclusions  expressed  are  those of the author
and  not necessarily those of the U.S. Environmental  Protection
Agency.  Mention,  if any, of company, process, or product names  is
not to be considered as an endorsement  by the U.S.  Environmental
Protection  Agency.

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                         ACKNOWLEDGMENTS
     This National Network for Environmental Studies fellowship
was conducted for Harvey Richmond, Environmental Protection
Specialist, Office of Air Quality Planning and Standards, U.S.
EPA, Research Triangle Park, NC.

     I would like to recognize several contacts and reviewers who
have assisted greatly on this project.  This includes Leland
Deck, David McKee, Thomas Feagans, Ron Whitfield, Robert Winkler,
Howard Kehrl, Deborah Amaral, and Tom Wallsten.

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                        EXECUTIVE SUMMARY








     Utility under uncertainty is a field of decision theory that



has received increasing attention in the field of public health.



This report reviews its uses during the past decade and suggests



its possible use in national ambient air quality standard setting



procedures.  It is common practice in standard setting to assess



the likelihood of air pollution effects on sensitive populations.



One such population, asthmatics,  is selected in this report and



the relationship between air pollution and asthma is reviewed.



In addition, three possible pilot studies are suggested which use



aspects of utility under uncertainty theory to elicit values



concerning asthma health effects.  The results of such studies



would provide U.S. EPA with information for their ambient air



quality standard setting and increase the awareness of the



possible uses of utility theory in such applications.

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                           INTRODUCTION







     During the past twenty years significant efforts have been



made to create a method of measuring health status on a single



scale for comparisons over time, and between individuals-and



groups in an attempt to overcome what Bergner (1) calls the



"single-continuum dilemma."  This dilemma has arisen in the past



because of the diverse and complex nature of many health states,



making it difficult to make comparisons between individuals in



the same or different health conditions.  Such a means of



measurement would be useful in making decisions, creating health



indices, setting priorities, and developing a basis for



regulatory standards.  One area which has been suggested for this



purpose is utility theory.  Spitzer (2) in his keynote address to



the Portugal Conference on the measurement of quality of life



stressed the importance of utility theory in such applications by



stating that "utilities and trade-off methods hold enormous



promise in the field of public health,  [and] there is a strict



discordance between the logical strength of the utility strategy



for the assessment of quality of life or health status and the



extent to which the methods have been demonstrated."



      As Spitzer has stated, the health field appears to be an



excellent area for the application of utility theory and its



methods.  In many fields, when an individual is making a decision



or comparing a series of possible outcomes, comparable units



representing the worth of each outcome, such as dollars, lives

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 saved,  or  cases  of  disease  averted  are clear.   In the health
 field,  however,  effects  are often refered to in  intangible  terms
 such as pain  and suffering  (3).  These outcomes  do not have
 obvious, uni-dimensiona.l measurable values which can serve  as  a
 single  unit of comparison.  This may frequently  cause
 difficulties.  In addition, in policy or regulatory environments
 it is desirable  to  compare  these intangibles with each other or
 with more  concrete  ideas of money or time.  To overcome this
 problem, it is possible to  employ some aspects of utility theory
 as a means of valuing outcomes which have varying likelihoods  of
 occurrance, but  do  not have inherent quantifiable measurements.
 This area  of utility theory is referred to as utility under
 conditions of uncertainty and is considered a specific
 application of the  broader  theory.  Within this  specific
 application it is common to use various assessment techniques  to
 elicit  subjective values from an individual for  any number  of
 different  outcomes.  These  values, or utility levels, can then be
 compared on a single scale.  Utility, therefore, can be thought
 of as a subjective  measurement whereas money and lives saved are
 uni-dimensional,   objective  measurements (4).   For this reason,
 utility has become  particularly useful in the health field; it is
 often used in the field of  medical decision making to compare
possible health outcomes, treatments, or health  states.   In this
 case,  utility theory is used to provide a means of comparison
through the assignment of probabilities and preference weights to
the various possible outcomes.

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     Only a small volume of workin the field,  however,  has been



associated with health-related environmental decisions.  Keeney,



a major contributor to the field of utility under uncertainty,



and collegues have done, some work related to environmental



decisions, especially in the area of air pollution control and



regulations (5,6).  There is,  however, much room for additional



work to be done.



     This report, therefore, reviews the theory, biases, and



various methods of assessment of utility under uncertainty, and



its applications to health-related outcomes.  In addition, the



specific health state of asthma and its association with air



pollution is discussed and a series of possible studies applying



utility analysis techniques to air pollution health effects



valuing are suggested.  Specifically,  three pilot studies are



outlined which attempt to provide information to the U.S. EPA on



the valuing by asthmatics of air pollution-related health



effects.  These studies are intended as a means of displaying the



ease of use of utility assessment and to provide specific



information on subjective valuing of asthma and its symptoms by



asthmatics.  Furthermore, such studies may provide valuable input



during the assessment of effects on sensitive populations as a



part of national ambient air quality standard setting.

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                          UTILITY  THEORY








     Utility theory has its roots in more than two hundred years



of economic thought.  Qne of the early developers of the idea of



utility was Daniel Bernoulli.  In 1738 he developed the  .



St.Petersburg Paradox which provided a source for early



discussions about utility.  The paradox involves a game in which



a coin is tossed n times until it comes up heads at which time



the player of the game is paid $2n.  The question that must be



asked , therefore, is how much should an individual be willing to



pay to play this game?  It would be reasonable to predict the



amount by calculating the expected payoff of the game by summing



the products of all the possible payoff outcomes and their



respective probabilities of occurance.  As it turns out, the



expected payoff for this game is an infinite sum.  The player,



therefore, should be willing to pay anything to participate in



this game.  Intuitively, however,  this does not make sense.



Bernoulli, therefore, stated that one should consider the "moral



worth"  of an alternative and not just its expected monetary



value.  In other words it could be said that in the process of



gaining an item, a point is reached where an additional item is



not worth as much as the item preceeding it.  For example,  if you



receive a pizza you place some value on that pizza.  The second



and third pizza that you receive you may also value equally;



however,  you will quickly reach a point where an additional pizza



is not worth as much to you as those previously received.  Money

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can be considered similarly.  The value or utility of money  (or



pizzas) will decrease as more is gained.  If this idea can be



accepted then a finite solution to the above game may result.



     The St. Petersburg Paradox showed a need for the idea of



utility.  It wasn't until the 1940's, however, when von Neumann



and Morgenstern published Theory of Games and Economic Behavior



(7) that utility theory under uncertainty became established.



Watson and Beude  (8) state that von Neumann and Morgenstern



developed utility "to prescribe how people should evaluate



options about which they were uncertain."  Specifically, von



Neumann and Morgenstern thought that individuals should assign



utility values to possible outcomes.  Then,  when faced with



decisions which include risky alternatives,  the individual should



select the outcome with the highest expected utility.  The



expected utility is the product of the assigned utility level and



the probability that the outcome will occur.



     The theory is justified by a series of axioms.  These axioms



include assumptions about how an individual ought to behave while



making a decision under uncertainty, and, therefore,  are



normative.  They do not, however,  describe how individuals



actually behave.  If a subject accepts these axioms,  then his



only rational action during decision making is to select an



outcome with the maximum expected utility.  This point,  however,



is considered somewhat controversial.  It is often argued whether



individuals should even necessarily conform to the axioms.



Furthermore, when they do not behave consistently with the

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axioms, it is often out of choice and not because they are "being



fooled by cognitive illusions-" or not considering all the



dimensions (9) .



     Certain specific decisions which are often cited by scholars



are the various paradoxes that go against the axioms.  The axioms



of utility theory assume that the value of an outcome and the



probability of its occurance are independent.  This assumption,



however, may not always be true in real decision making as shown



by the results of the Allais Paradox.  The paradox involves



several choices between gambles.  In the first an individual is



offered a choice between  (A) a guaranteed payoff or  (B) a chance



at a higher payoff that also involves a very small risk of



receiving nothing.  In the second decision the individual must



choose between (C) a chance at receiving a moderate payoff with



some risk of receiving nothing or (D) a much greater prize at a



slightly higher probability of receiving nothing.  If the



expected payoffs are calculated for each case, it appears that



the best choices are (B) and (C).  When this problem is actually



presented to people the predominant choices by far are (A) and



(C).  The problem involved here is that most people overweigh the



very small probability that exists in (B) and would rather



receive a moderate guaranteed payoff than risk getting nothing



for a chance at a much higher payoff.  Furthermore, even when the



inconsistency of their choice is pointed out, many people stay



with their original choice.  This is a case in which the axioms



are clearly violated by choice.  The original idea of utility and

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the modern von Neumann-Morgenstern uncertainty utility therory



still have not resolved this-paradox; however, it should be



remember that axioms do not attempt to describe decisions exactly



but instead provide a target for rational behavior.  For the



purpose of this paper these controversies are set aside, but it



should be noted that the field of utility under uncertainty is



still under development and its validity is often questioned and



discussed by both its critics and proponents.



     The following is a list of axioms compiled from three



sources (9-11) and should not be considered exhaustive.  These



axioms are not all equally important.  Hershey and Baron (12)



state, for example, that the two most important axioms are



transitivity and independence and Bell and Farquhar (9) include



continuity as a basic axiom also.  Each of the axioms, however,



is necessary at least in some specific case.



     Transitivity - given the outcomes A, B, and C, in a



preference relationship such that A is preferred to B and B is



preferred to C,  then it is assumed that A is preferred to C.



     Independence - if A is preferred to B then a gamble where A



is the prize is preferred to a gamble where B is the prize if the



two gambles have equivalent alternatives to the prize and equal



probabilities of outcomes.



     Continuity - it must be possible for indifference to exist



between a certain outcome, C, and a pair of uncertain outcomes, A



and B, given that C is preferred to B and A is preferred to C.

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     Reduction of Compound Uncertain Events - a mixture of



gambles may be reduced or simplified using standard probability



manipulations without affecting preferences.



     Connectivity - an individual is able to make judgments about



preferences when faced with a gamble (i.e. preferences exist).



     Sure Thing - preferences for gamble A over gamble B should



not depend on events for which A and B have identical outcomes.



     Substitutability - indifference exists between a certain



outcome, C, and one formed by substituting for C with an outcome



which may be a lottery judged equivalent to C.



     Monotonicity - given a choice between two gambles with



equivalent outcomes, A and B, the gamble with the higher



probability of winning the better outcome is preferred.



     Completeness - outcome values and probabilities are required



to determine preferences between uncertain outcomes.



     Boundedness - outcomes cannot be infinitely bad or



infinitely good.



     The validity or strength of a number of these axioms is



often questioned.  Further, as mentioned above, the axioms are



considered controversial because individuals in their usual



decision making process do not necessarily adhere to these axioms



and it is also argued whether an individual even ought to conform



when able.  There may, in fact,  be very rational reasons for



violating an axiom.  A brief discussion of the psychology and



biases which cause these differences is presented later in this



paper.

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     The usually intended result of the application of the theory

and the axioms is the assignment -of utility levels or

measurements to specific outcomes.  If it is assumed that an

individual's choices in simple cases obey the axioms then one may

infer from these choices the individual's utility levels.-.  These

utilities may then be used in more complex cases  (12) .

Similarly, von Neumann and Morgenstern state that the utility of

an outcome is equal to the probability of winning a gamble such

that an individual is indifferent between accepting the gamble

and receiving an outcome with certainty.  In other words, an

individual may be confronted with two possibilities, A and B,

and, in addition, there exists a third possibility, C, which is

preferred to B but not to A  (i.e. C is preferred to B and A is

preferred to C).  It is possible under these conditions to find a

level of C for which the individual is indifferent between

receiving C with absolute certainty or taking a gamble between

the two extremes, A and B.  It is common to represent such a

decision with a following decision tree (Figure 1).

                             FIGURE  1
        	Basic  Decision  Tree	
                                       outcome
                                          B


                                          C
                                10

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where the box  (decision  node)  represents  a  choice  between C and
the A/B gamble and the circle  (chance  node)  represents  possible
outcomes of a decision.   Furthermore,  numerical  measures can be
introduced by assigning  probabilities  to  the two possible
outcomes  (Figure 2).  Again, C can be  found for  which the
individual is indifferent to receiving outcome C or  taking the
gamble of A with probability,  p,  and B with probability,  1-p.

                             Figure 2
     	Decision Tree  with Outcomes  and Probabilities	
                                  outcome  probability
                                    A        p
                                    B        1-p
                             	   C         1
     It is often true in utility assessment that the values  of A
and B are the maximum and minimum  (most preferred and least
preferred) of a range of possible outcomes.  When this is true, A
and B are assigned utility values of 1 and 0, respectively,  to
facilitate the measurement of the utility levels of intermediate
outcomes. This can be written as u(A) =1 and u(B) =0.  The
utility value of C, therefore, should fall between these values
as would be expected given the preference relationship: B is less
preferred than C which is less preferred than A.  Using simple
algebra and utility theory the value of p (the probability of A
occurring) is defined as being equivalent to the utility of C if
                                11

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indifference between the options exists.  According to utility



theory, A, B, and C can be represented by utilities, and because



A has been assigned a value of 1 and B a value of zero, the



following equation holds true:





               u(A)p + u(B) (1-p) = u(C)



and simplifies to:



                    P = u(C)





where u(C) is the utility of outcome C.  Utility, therefore,



provides a means of assessing the strength of preference for an



outcome relative to other possible outcomes. In fact, it is



possible to take any number of intermediate outcomes and assess



their individual utility values.  Further coverage of the



principles of utility theory can be found in a number of works



(5,7,8,10,11,13-15) .



     In summary, it is useful to outline an application which



incorporates the theory discussed above.  First,  the outcomes



which are to be assigned utilities must be clearly defined.



Next, a scale is constructed which is based on the outcomes of



interest.  Often this is an arbitrary scale of zero to 1 with the



most appealing option assigned the maximum value and the least



preferred option the minimum value of zero.  A final step may be



the elicitation of utilities for the various intermediate



outcomes on the specified scale using utility assessment methods.



Several of these methods are described in the following section.
                                12

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                    UTILITY ASSESSMENT METHODS

Single-attribute Utility Assessment Methods
     Many different methods of directly estimating utility  levels
exist; some are based on the indifference gambles of uncertainty
utility theory, whereas others have been developed as  the need
for different methods has  arisen.
     Standard Gamble Methods
     The group of methods  that is most often used are  called
standard gamble methods  (SG).  These techniques  are based on the
utility theory relationship between various outcomes,  outlined in
the previous section.  The general form of the decision  tree as
described earlier is shown in Figure 3.

                             Figure 3
        	Standard Gamble Decision Tree	
                             outcome  probability  utility
                                B       1-p
                                              unknown
     According to utility theory the utility of outcome  C  is
equivalent to the probability, p, of the occurrence  of outcome  A
under indifference conditions.  In the above relationship  there
are four possible variables: A, B, C, and p.   In utility
assessment, three of the four variables are held constant  while

                                13

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the final one is varied until indifference exists between the two



choices. Consequently, three-main types of standard gamble



elicitation procedures have been developed.



     Certainty Equivalence Method



     The first technique is called the certainty equivalence



method  (CE).  This is employed when the outcomes, A, B, C, are



continuous variables, such as money or time.  It is common in



this method to set p at 0.5  (50%), therefore, giving equal



probability to A and B in the gamble.  A and B are generally the



extreme values of the entire possible range of outcomes and C is



an intermediate whose value is varied until indifference exists



between the options.  The outcome value of C is then given a



utility of p, or in this case, 0.5.  The analyst continues in



this manner, but replaces outcome B with C.  The 0.5 utility



value of the bisection of the C to A outcome range is assessed



and can be called D.  Using the same equation as before, but



replacing B with C:



               u(A)p + u(C) (1-p)  = u(D)



The utility of A, u(A), has already been set at 1, u(C) has been



previously assessed at 0.5, and the probability remains at 0.5,



therefore:



                    u(D)  = 0.75



On the overall utility scale between B (0)  and A  (1) this second



assessed point,  therefore, has a utility of 0.75.  The analyst



continues this process, assessing as many bisecting utilities as



is desired until a smooth utility function is determined.  The





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utility function or curve is commonly represented  by  a  graph of

utility on the y-axis  (0 -  1). and outcomes  on the  x-axis  (B - A),

This provides a graphical representation  for all outcomes  within

the range of B to A.

                             Figure 4
            	Basic Utility Curve	
          Utility
          Level
                       Outcome Range  (B to A)
     Probability Equivalence Method

     In some cases the outcomes are discrete, such as  objects  or

health states. In these cases a different method must  be used.

This second technique is called the probability equivalence

method (PE).  In this method, the analyst sets A and B as  the

most and least preferable options, respectively, and selects and

intermediate option C.  This is represented in Figure  5.

                             Figure  5
         	Probability Equivalence Decision Tree	

                             outcome probabI I Ity utI I Ity
                                       1-p
0
                                              unknown
                                15

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The value of p is varied until the decision maker is indifferent

between the certain outcome C. and the gamble over A and B.  This

method may also be used when the outcomes are continuous and is

often used as a consistency check for the CE method.  Just as

before the utility of C is equivalent to the elicited

probability, p, and a utility curve for the various discrete

outcomes between A and B is drawn.

     Value Equivalence Method

     A third method of standard gamble techniques is the value

equivalence method (VE).   In this technique the values of B, C,

and p are held constant and A is varied.  This method, however,

is rarely used in the literature and will not be discussed

further.  There are also equivalent versions of the PE and VE

methods which involve the comparison of two gambles (Figure 6)

                             Figure  6
            	'Gamble Comparison Decision Tree	
                                          B    l-p

                                          c    q



                                          D    l-q
These are also not popularly used because it often believed that

many people have difficulty comparing gambles.  Further

information is available concerning standard gamble methods

(5,8,10,11,13,16).
                                16

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     Utility Curves

     In using each of these standard gamble methods it is

possible to create a utility curve.  A number of points should be

made, however, concerning the shape of the resulting curve.  If,

for example, the midpoint of the outcome range is given a.utility

value of 0.5 the individual is said to be risk neutral.  A series

of such risk neutral utility elicitations would result in a

linear utility curve from (B,0), the origin,  to the point  (A,l).

Similarly,  if the intermediate outcomes are given utility values

greater than those expected from risk neutrality then the

resulting curve will be concave downward and the decision maker

is said to be risk averse.  Conversely, if the curve is convex

downward then the decision maker is said to be risk seeking.

These types of risk attitudes are shown graphically in Figures 7

and 8.
                            Figure  7
                   Utility  Curve Representing
            	Risk Seeking Behavior	
     Utility
     Level
                    Outcome Range (B to A)
                               17

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     Utility
     Level
                             Figure 8
                    Utility Curve Representing
                       Risk Averse Behavior
                    Outcome Range  (B to A)
     Category Scaling Method

     A second type of single attribute utility assessment method

is category scaling  (CS).  This technique generally involves the

use of a visual analogue or "feeling thermometer".  First, the

individual ranks the outcomes from worst to best. The worst is

given a value of zero and the best a value of 1.   The remaining

outcomes are rated, relative to the extremes, on the visual

scale.  Torrance (17), for example, suggests a 100 unit scale, 10

cm in length. In addition, small arrows are provided to the

individual to be used as indicators to identify his relative

positioning of outcomes on the scale.  Further explanation and

discussion on the use of category scaling is provided by  (18-23).

Some studies have shown that category scaling is best for

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obtaining ordinal rankings only and should not be employed to



elicit cardinal utility values  (22,23) and is not grounded in the



principles of von Neumann-Morgenstern utility theory.







Multiattribute Utility Assessment Methods



     In the example of single attribute analyses the outcomes



(A,B,C) are each at different levels of one attribute, and are



compared, therefore, on a single utility scale.  In many cases,



however, an outcome will have several different attributes



associated with it, each at a different level.  When faced with



comparing such outcomes with multiple value dimensions,



difficulty may arise because of the presence of conflicting



goals.  The best possible option may involve maximizing one



attribute while minimizing another.  In such instances the



application of multiattribute utility theory  (MAUT) may be



employed for the comparison or valuing of outcomes.  Basically,



the outcome being valued must be broken down into its component



parts - the different single attributes.  Each individual



attribute may then be assessed as described previously.  A model



to reaggregate the single attribute utility functions, which



generally includes weights or scaling factors that also must be



assessed, is necessary.



     There are three main types of aggregation models: additive,



multiplicative, and multilinear.  Each is progressively more



complex but requires a less restrictive independence condition



than the previous one.  Associated with each model is a utility





                                19

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independence condition that must be met for the model to be

applicable.  The three types of independence conditions are

called: additive independence, mutual utility independence, and

order-one utility independence.  They correspond, respectively,

to the three models listed above.

     Additive Model

     The additive model is the easiest to use but its additive

independence restriction is the most difficult to meet.  For

every attribute, x^, additive independence must hold between it

and all other attributes (y, z, etc).  Additive independence

holds if changing the values of one attribute does not alter the

preference for the attribute being assessed. For example, in a

two attribute system, where x and y are the attributes, the

individual must be indifferent between the following pair of

choices shown in Figure 9 if each branch has an equal probability

of occurrence.

                             Figure  9
         	Requirement for Additive Independence	
                      <(Xi ,YO         D// CXl 'Yz)
                                   cxT

                 u'3   (X2,Y2)         °'5   CX2,Yi)
where Xj and yj are different levels of attributes x and y,

Changing the value of attribute y should have no effect on

preferences for attribute x.
                                20

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     Once additive independence  is  found to exist between  all

attributes or groups of attributes, the additive model  may then

be applied.

The form of the model is quite simple, but requires  a lot  of time

to assess.


                          U(X) = E kiui (x,)
where,
     U(X)      = the multiattribute utility
     kj        = weight or scaling factor
     u-j(x-j)    = utility of level x of attribute  j
     n         = number of attributes
and,
     Multiplicative Model

     To use the multiplicative model of utility aggregation,

mutual utility independence must hold.  Mutual utility

independence exists when preferences for uncertain choices
         i
involving different levels of attribute x are independent of the

level of attribute y.  For example, if x-^ is a minimum value, x.-$

is the maximum, and X2 is an intermediate value then the

indifference (~)  relationship  shown in Figure  10  must  hold for


utility independence to exist in this two attribute system:

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                            Figure 10
           Requirement for Mutual Utility Independence
                          (Xz.Yi)
For more than two attributes, mutual utility independence holds

if there is "no interaction between preferences for lotteries  on

some attribute and the fixed level on the other attributes" (11) .

If this condition is met, the following multiplicative model

equation can be used:


                      l+JcZ7(.x)=n
where,
and,
     U(X)      = the multiattribute utility
     Uj (Xj)    = utility of level x of attribute j
     n         = number of attributes
     k and k_i are scaling factors where
          kj is a scaling factor that makes single attribute
          assessments consistent with overall assessment,  and
          k is a scaling factor that is a solution to:
                                22

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     Multilinear Model



     The third model type is -called 'multilinear .  It is the most



complicated to use, but requires the least restrictive



independence condition, order-one utility independence.  This is



simply met by insuring that each single attribute is independent



of all other attributes (i.e. pairs or groups of attributes need



not be independent of remaining attributes) .  The multilinear



model is superficially similar to the multiplicative model, but



has a series of interaction parameters, k.  In most cases,



however, the multilinear model is complicated and one study has



shown that generally the simplest model, the additive, is



sufficient  (24) .  This, of course, cannot be accepted as a



general rule.



     Assessing Independence and MAU Functions



     For each of the three models discussed above the method for



assessing the multiattribute utility function is quite similar.



First, the single attribute utility functions for each of the



attributes are assessed using single attribute methods.  Next,



the k-:S are assessed by eliciting the utility of setting one



attribute at its best level while the others are at their worst.



For example, in a three attribute system:
                         (b) ,x2 (w) ,x3 (w) ]



               k2 = utx-L (w) ,x2 (b) ,x3 (w) ]



               k3 = utx-L (w) ,x2 (w) ,x3 (b) ]
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where,



               Xj(b) = best possible level of attribute j



               xj (w) = worst possible, level of attribute j







Finally, when using the multiplicative and the multilinear



models, the scaling constants, k.^, are calculated iteratively.



In addition, Klein et al.  (25) have developed a method of



assessing multiattribute utility models with mathematical



programming.



     It is also necessary to demonstrate that the specific



independence condition holds for the model being used.  Because



it is very difficult and time consuming to demonstrate additive



or mutual utility independence, Keeney and Raiffa (5) have



developed a number of simpler methods to demonstrate



independence.  Torrance  (17) also outlines some of these.  For



example, Torrance states that additive independence can be



determined by first demonstrating that mutual utility



independence exists.  It is then necessary to establish additive



independence for only any two attributes with all other



attributes held constant.  Similarly, the demonstration of mutual



utility independence can be simplified by showing that utility



independence, as described above, holds between one attribute and



the others, and then showing that the remaining pairs of



attributes which involve the one tested for utility independence



are preferentially independent.  Preferential independence exists



when an individual is indifferent to outcomes involving one or





                                24

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more attributes regardless of the level of the  remaining

attributes.  In a three attribute system, for example,  with x-j_,

x2, anc* x? as attributes, mutual utility independence  can be

shown by demonstrating .the following:

               is utility independent of  (Xo,x3)
              x2) is preferentially independent of  (x3)
              x3) is preferentially independent of  (x2)
                                25

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              UTILITY ASSESSMENT of HEALTH OUTCOMES







     The basic concepts and methods of utility theory remain



unchanged when applied .to the field of health; however, it has



been necessary in some cases for new or slightly altered -methods



to be employed. These changes are generally considered valid if



the axioms of utility theory still hold.  In fact,  Torrance  (26)



restates the axioms to fit in the context of health states and



comments on their validity.  He states that the axiom of



continuity has been empirically tested and appears to be



applicable while the others seem to be reasonable,  but none has



been rigorously tested.



     The use of uncertainty utility theory in the health field



has grown dramatically in the past two decades.  Many of the



medical applications of single and multiattribute utility



analysis prior to 1980 are reviewed by Krischer (27).   Since that



time the use of utility and its traditional methods has continued



to expand and new methods have been created.







     Single-attribute Approaches to Health Status Assessment



     Single attribute utility analysis has been used



significantly to assign values to health states for the purpose



of clinical, technological, and health program decision making.



Also,  it has been widely used in the creation of health indexes



as a way of prioritizing health states.  There are many examples



of such uses in the literature.  Utility values have been





                                26

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 assessed  for various types  of  cancer  including  ovarian  (28),
 gastric  (29), rectal  (30),  laryngeal  (31), endometrial  (32),  lung
 (33,34),  and various other  cancer  states  (35,36).   It has  also
 been used with such chronic conditions as prostatic hypertrophy
 (37), Hodgkin's lymphoma  (38), arthritis  (39,40), kidney-disease
 (41), osteoporosis  (32),  and generally poor health  or disability
 (41-43).  It has also been  applied to other areas including
 outcomes  from coronary artery  bypass  surgery  (23),  menopausal
 symptoms  (32), childbirth (44), genetic counseling  (45-47)  and
 drug effects  (48,49).
     In most of these cases, an expert, physician,  or patient was
 asked to  rate these conditions on  a single attribute utility
 scale of  quality-of-life  using one of the elicitation methods
 described earlier.  For example, category scaling was employed by
 Llewellyn-Thomas et al  (31)  when they asked subjects to indicate
 on a 100  mm line the relative  desirability of several health
 state scenarios.  Similarly, Boyd  et al.  (30) utilized a standard
 gamble method to elicit the  value  of living with colostomy.
Various groups of subjects  were presented with the  choice between
 two alternatives: A - living a full lifetime with a colostomy
 (certain  outcome) or B -  taking a  gamble of perfect health  for a
 lifetime  with probability p  or immediate death with probability
 1-p.  The value for p was elicited from the subjects until  there
was indifference between the choices,  A and B.
                                27

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This is represented schematically  in  Figure 11.


                            Figure ll

           	Decision Tree with Health Outcomes
                              outcome probability  utility


                               perfect

                               health     H




                               death     1-P      0
                               llfewlth    1     unknown
                               co I ostotny
This is equivalent to the PE method described earlier.  In



examples such as this the CE method cannot be used because it



requires a continuous variable,  whereas the PE method can


accommodate discrete values such as health states.






     Multiattribute Approaches  to Health Status Assessment



     Single-attribute utility assessment has been used


significantly in the health field;  however, some groups have


found it necessary to decompose quality-of-life into several


attributes.  Consequently, in assessing a subject's utility


function for the quality-of-life in a health state, a


multiattribute utility  (MAU) model must be used.  An excellent



review of the application MAU theory to health state evaluation



is found in  (50).  Torrance et  al.  (51) have created a four


attribute classification system to categorize various levels of



health.  The four attributes each represent a different facet of



health which must be considered in determining value.  In their



                                 28

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opinion, the value of health states depends upon:  (1) physical
function  (mobility and physical activity);  (2) role  function
 (self care and role activity);  (3) social-emotional  function
 (emotional well-being and social activity); and  (4)  health
problems.  As is done in traditional MAU analysis, each of  the
utility functions for these attributes must be assessed
individually and then aggregated using one of the models.
     Keeney and Ozernoy  (6) employed an additive multiattribute
model to assess the relative values of the possible  health
impacts of several carbon monoxide (CO) standards.   Judgments
about the utility function and scaling factors for four
attributes were elicited from an EPA staff person.   These
attributes concerned four possible health effects of CO exposure:
heart attacks, angina attacks, peripheral vascular attacks, and
vigilance impairment.
     The MAU method has also been used in the creation of health
status indices (52).  Gustafson et al. (53) have used the
additive model to develop a severity index.  In this case the
attributes are various indicators of the severity of heart
disease.  Similarly, Gustafson's model has been applied by Choi
et al. (54)  to assess the severity of non-traumatic chest pain.
     Other methods of valuing health effects have been developed,
such as the index of well-being (55).   This index is based on an
ordinal ranking of various health states from which scores
similar to utility are derived.
                               29

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Incorporating Health State Quality and Duration



     In both the single and multiattribute methods described



above the main purpose was to value specific health states



independent of any other factors.  It has been suggested by Dowie



(56), however, that this may not be an accurate representation.



He argues that it is not appropriate to value life and health



directly, but instead each should be seen as a demand for time



(i.e. nothing is consumed independent of time).  Dowie suggests,



therefore, that it is time that should be valued  (in terms of



utility).



     Single Attribute Approaches



     Torrance (57) also felt that incorporating time was



important and devised the single attribute time trade-off method



(TTO) which evaluates the value of health states in the context



of time.  This method has been used extensively and was developed



specifically for health outcomes.  The technique was created



because many people have difficulty understanding and working



with probabilities.  The method is not based on von Neumann-



Morgenstern utility axioms and requires an additional assumption



that the subject's utility function for additional healthy years



be linear over time  (39) .  This assumption has been a serious



point of controversy.



     In the TTO method the subject is provided with two



alternatives.  The first alternative is living the rest of one's



lifetime  (t) in a specified health state, such as arthritis.  The



second alternative is living in perfect health but for a shorter





                                30

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period of time  (x).   The number of years of perfect health are



varied until the subject is indifferent between the two



alternatives.  The preference or utility value is defined then as



x/t.  This method has been used and described by Torrance and



other researchers (21,22,29,37,38,40,57-60).  For example.,



Krumins et al.  (37)  used the TTO method to value the possible



outcome of prostate surgery.  In a situation such as this, TTO is



very good because patients and physicians must often try to



balance between quality of life and prospects for survival.



     The balancing of the duration and quality of life is a



common goal in the health field.  In fact, a unit of measurement



has been devised which incorporates these two values and has been



called quality-adjusted life years (QALY).  QALY is basically a



measure of expected time of survival adjusted for varying states



of health.  For example, living ten years with a disability or



disease is worth only a fraction of living ten years in good



health.  QALYs provide a means, therefore, of comparing survival



in two states of health.  A review of QALYs is presented in



(60,61) .



     QALYs are not necessarily used when time and quality are



being accounted for.  For example, McNeil et al. (62)  studied the



differences in the utility of survival with artificial and normal



speech.  First, the CE method was used to determine a utility



curve for duration of survival. In the next step the TTO method



was employed to create a graph of years of survival with normal



speech (y-axis) and years of survival with artificial





                                31

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speech  (x-axis).   If  the  two were 'valued equally then a linear
relationship with  a slope of 1 would result.  In this manner
utility values  for varying years with artificial speech were
determined based on the CE and TTO utility curves.  Consequently,
two curves were drawn which compared the utility for years  of
life in each of these two states.  The effect of a poorer health
state over time, therefore, could be observed graphically.  The
curves produced by this method are shown in Figure 12  (62).  This
procedure, however, does  not produce the QALY measure that  is
often desired.
                             Figure 12
Utilitv Curve  Construction for Survival with Artificial Speech
  100
       5 f 10  15  20 25
       YEARS OF SURVIVAL
       (NORMAL SPEECH)
                                10  15  20 25
YEARS OF SURVIVAL
(ARTIFICIAL SPEECH)
                       5   10  15  20  25
                       YEARS OF SURVIVAL
           Note: above graphs taken fron reference  (62)
      When such a measure is required the utility  level for a
 specific health state is multiplied by the  average duration of
 the health state to get QALYs.  Utility measures  for health
 states derived from TTO, SG, or CS methods  may  be used for
 calculating QALYs but only the TTO method  considers quality in
 the context of time.  This simple single attribute method of
                                 32

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is used only to obtain weights and does not fully incorporate

preferences for time  (63).  This controversy is discussed later

in this report.

     Multiattribute Approaches

     In an attempt to compensate for the weaknesses of the single

attribute approach to quality of life and health status duration

incorporation, a number of different models have been developed

to calculate functional equivalents to QALYs using multiattribute

utility (MAU) or MAU-like methods.  Pliskin et al.  (64,65)

developed a MAU model for this purpose which is based on several

assumptions.  First, it is assumed that mutual utility

independence exists between survival time and health status.  The

resulting model they use is a "quasi-additive" form of a MAU

function:


          U(Y,Q) = au(Y) + bu(Q) +  (l-a-b)u(Y)u(Q)

where,
          u(Y) = utility for survival time
          u(Q) = utility for health status
          and a and b are weights.


     It is also assumed that "constant proportional tradeoff" is

valid.  This means that an individual is willing to give up the

same proportion of his remaining life for an improvement in

health regardless of how many years remain in his lifetime.  For

example, if an individual is willing to give up 3 of 15 remaining

years of expected lifetime for an improvement in health, then he

must also be willing to give up 4 of 20 remaining years for the

same improvement.

                                33

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     The second assumption implies that the utility function,

U(Y,Q), exhibits constant proportional risk aversion.  It will,

according to Pliskin et al.,  therefore, take one of three general

forms  (concave, convex,, or linear) of which the linear form is

selected.  Miyamoto and Eraker (66) develop further this•model

and state the following relationship between the QALY-like

measure, U(Y,Q), and a bivariate utility function:


                    U(Y,Q) = bYrH(Q)

where,

     Y  .  = survival time
     H(Q) = utility of survival in a health state, Q
     b    = scaling constant
     r    = risk attitude factor with respect to survival
            duration

     Using the PE or the CE method the value for r is determined

and the TTO method is employed to determine the utility function

for health status, H(Q).  Extensive examples and proofs are

provided in (64-66).

     Loomes and McKenzie  (67) criticize this method for

determining QALYs.  They first attack the constant proportional

time trade-off assumption on the grounds of empirical evidence

from (41,43,62), which show that individual's preferences change

depending on the expected time in the health state.  Furthermore,

the above model does not account for individual preference for

present consumption over future consumption; this is called time

preference  (68).  Loomes and McKenzie  (67) suggest alternative

methods that do not involve traditional utility analysis.
                                34

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     Other Methods



     Other alternatives to QALYs have been suggested in response



to criticisms of QALYs  (63,67,69-71).  One of these alternatives



to QALYs is Healthy-Years Equivalents  (HYE), suggested by Mehrez



and Gafni  (63).  HYEs cannot be assumed to be equivalent to QALYs



and Mehrez and Gafni warn that it may not be possible to



construct conversion curves.  They support HYEs because even



though they are more difficult to elicit, they include



preferences for both time and quality of survival.  In addition,



they provide several examples where QALYs would incorrectly



describe a subject's true preferences and they provide a full



description of the method for eliciting HYEs in the appendix of



(63) .



     A final method that should be mentioned briefly is the DEALE



method (Declining exponential approximation of life expectancy).



Several groups have used this method to assess what they call



utilities  (72-78).  This method assumes that life expectancy can



be approximated by a simple exponential function.  Therefore,



survival is calculated using the reciprocal of the age, sex, and



race specific mortality rate combined with the reciprocal of the



rate of disease in question.  Quality adjustments for long and



short term morbidity are then made to the calculated life



expectancy.  This value is used as a "utility".  The result is a



measure of quality adjusted life expectancy.
                                35

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            COMMENTS ON UTILITY ASSESSMENT AND QUALYs







     As mentioned above, both utility assessment and QALYs are



often criticized for various reasons.  Included in these



criticisms are general comments concerning decision analysis



overall, perception, and the psychology behind stating



preferences (79-81).  In the following section, the specific



criticisms concerning utility analysis and QALYs are discussed.







Utility Assessment



     The advantages and disadvantages of utility assessment are



frequently enumerated.  There appear to be some points that are



repeatedly stressed.  For example, Albert  (3) comments that



"utility functions  for one individual cannot be carried over to



another individual  or group" while Kassirer  (82)  states the



opposite, but qualifies it by saying that comparing utilities is



only acceptable in  a non-rigorous analysis.  Furthermore,  Albert



states that utilities cannot be associated with a monetary amount



because different individuals have differing utilities for money.



Feeny and Torrance  (39), however, clearly state that an advantage



of utilities is their ability to be integrated into economic



evaluations.



     Other pros and cons of utility assessment have been stressed



by a number of authors  (39,83,84).  Utility can be a very



comprehensive measure, taking into account all the many



attributes and tradeoffs presented by a problem and aggregating





                                36

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them on one scale.  Furthermore, various evaluators or raters can

be elicited.  These may include experts, patients, policy makers,

or even the general public.  There has been some discussion as to

whether an individual c.an truly give a value  (or disvalue) to

something he has not experienced. Drummond  (84) states that the
                                             V
issue of "whose values" may depend upon the purpose of the study,

as some have stated  (58,83), but says that further investigation

is required.  If such a variability in raters can exist it allows

utility assessments to be applied to hypothetical situations

which greatly increases the applicability of the method.

Finally, utility can be combined with outcome probabilities to

get expected utilities with which comparisons with other possible

outcomes can be made.

     The advantages are, of course, balanced by a number of

disadvantages.  There is complaint of a lack of precision in that

the same rater's utility levels may change greatly from one

measurement to the next.  In addition, the elicitation process

consumes a lot of time and labor, and requires trained

professionals to attain the best results.  It is also common to

find that the results^ of utility studies are not easily

interpretable, and there have even been suggestions that the

method of decomposing a problem as utility analysis does, may

change an individual's preferences (28).

     Sources of Bias in Utility Assessment

     When performing a specific study there are significant

sources of bias or error which may greatly affect the results.


                                37

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There have been quite a few studies which have pointed to the



fact that significant differences may result from the various



methods of utility elicitation.  Again, this is a source of



controversy and there are studies which support both sides



(14,19,53,80-88) .



     Much of the discussion in the literature on the



comparability of assessment methods concerns the three methods:



SG,CS, and TTO.  Read et al.  (23) found that the three methods



produce significantly different results, with SG resulting in the



highest utility and CS, the lowest.  Large differences between CS



and SG were also noted in (18,89,90).  In one of these studies,



however, Torrance did not find statistical differences between SG



and TTO (89).  Wolfson et_al  (18) found that TTO results were



close to those found using CS.  Conversely, the SG method has



been shown to agree with direct evaluation  (CS) results  (55,91).



     Other comparisons have been made between the different types



of SG methods.  For example, Hershey et al. (12,92)  cite several



studies that show differences in the shape of utility curves



created by CE and PE methods.  CE resulted in more risk seeking



behavior and PE resulted in aversion to risk.



     The ability to point out differences between methodological



results, however,  does not provide judgment of which method is



best.  Economists generally support the use of SG techniques



because they have the strongest foundation in utility theory



axioms  (21,23) and they involve risk.  Psychologists and



regulators argue,  however, that visual scales are superior





                                38

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because of their ease of use and because risk is not always a



factor in a decision.  These strong'preferences for specific



methods and the obvious differences in results from these methods



may restrict the use of certain methods to specific areas or



studies.  In an attempt to explain some of the discrepancies and



provide assistance in selecting a method, much work has been done



on the psychology of utility assessment and the factors that



affect decision making abilities.



     One area that has received significant attention is the



effect of time on an individual's utility values



(21,31,34,41,43,68,93).  Time preference is very important



because of its potential effects on utility values.  Time



preference is the desire for gains at the present as opposed to



equal gains at some point in the future.  Some utility assessment



methods assume that time preference does not exist. This is not



supported by empirical studies (21,34,68); however, there are



methods of accounting for or measuring time preference.  Most



commonly,  the CE standard gamble method is employed.  Using this



technique the utility of varying years of survival can be



measured.



     Utilities have also been shown to be affected by the length



of time that an individual is in a specific health state.  As the



length of time increases,  the utility for being in that health



state decreases (31,41,93).   Furthermore,  it has been found that



in very disabling states,  individuals often reach a point of
                               39

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"maximum endurable time" after which death becomes more



preferable  (43).             .       "



     Another factor that has been investigated for its effects on



utility is personal position or context.  Christensen-Szalanski



has shown that utilities of women in childbirth change with



regard to preferences for anesthesia (44).  It has not been



proven, however, that age, sex, social position, or professional



status have any effect on the utility values elicited for



specific health states (36,41).



     It has also been shown that individuals in specific health



states value the health state differently than objective



observers or medical experts (30,41).  The question arises,



therefore, of which group of people should be used to elicit



utility levels.  Studies have been done which employed medical



experts (18,23), patients (18,35,41,42,94), and objective raters



(41,55,95).  It can be argued that "the choice of raters should



be influenced by who are the stakeholders" (83) , but it can also



be argued whether these "stakeholding" raters can really provide



an informed judgment.  Many opinions exist on this question, but



there may be no right or wrong answer.   This topic, however, must



still be considered when conducting a utility assessment.



     A final area that has received significant attention is the



psychology behind the assessment of utilities.  It is often



believed that individuals allow biases to affect their decision



making (79) , therefore, it should be no different in the



assessment of utilities.   Extensive work in this area has exposed





                                40

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a number of psychological  factors that affect the valuing  of
outcomes.  The factors include framing, regret, outcome bias,  and
range and probability effects among others.  The factor that
receives the most attention is framing or context bias
 (33,36,92,93,95-98).  This type of bias can be controlled.by the
analyst because it is caused by the way in which questions or
elicitations are posed to the subject.  For example, Llewellyn-
Thomas et al.  (97) have shown that the form of the health  state
description affects utility values being elicited.  They found
that assessed utilities for health states described in the first
person narrative form were significantly different from utilities
assessed for the same condition described in standard point form.
Furthermore, the tone of the health state description, whether it
is framed in positive or negative terms, can affect the outcome
(33,36).  Regret  (12,32,92,93) is the tendency to shy away from
or devalue outcomes that could cause the decision maker to regret
making a wrong decision.  This is especially common in the field
of medical decision making where physicians must value possible
outcomes or treatment options.  For example,  treatments or
therapies that have some potential for disabling effects may be
devalued because of regret bias even though they may be highly
unlikely.  Outcome bias refers to the shifting of risk attitude
(risk aversion or risk seeking)  depending on the whether the
outcome is a pure loss,  pure gain or mixed situation (49,92,96).
The range of the outcomes has also been shown to affect the
assessment of health state utilities.   Sutherland et al.  (42)

                               41

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found differences in utility values depending on whether perfect



health and death were used as anchors or a smaller range



including an intermediate effect and perfect health were used.



Others have also described the occurrence of this bias



(87,94,96).



     Other biases which have been identified include aversion to



gambles over health outcomes (89),  the spreading of responses



across entire utility scales (23) (especially with CS technique);



the overweighting of low probability events (32,79,92); thinking



in only one dimension (i.e. not including all attributes)  (92);



and overweighting the value of past events because they are



easily recalled or remembered (23,96).  There are, of course,



many other sources of error or bias and not all those listed



above apply in all situations.   Each one, however, should be



considered and accounted for, if possible, during any elicitation



process.








Quality Adjusted Life Years  (QALYs)



     The use of QALYs as a decision making tool has increased



significantly during the past decade; consequently, so have the



criticisms of this method of measurement.  As stated earlier,



QALYs have been attacked because of the restrictive assumptions



(67): utility independence, risk neutrality for time, and



constant proportion trade-off;  and because of their simplicity:



utility used only as a quality weight for life years (63).



Several authors have brought up ethical questions in addition to





                                42

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the problems with validity.  They have even gone as far as



stating that QALYs are unjust  (69-71).   They complain that QALYs



value time over individual lives, too narrowly define the meaning



of quality of life, and do not treat all age groups equally.



Conversely, equally strong arguments are made in support of QALYs



(100-103).   These authors argue that even though some problems



may exist with QALYs, they are usually successful in their goal



of comparing specific health states or treatment programs.  More



time,  they state, should be spent on standardizing the methods



and measuring sensitivity.
                               43

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               ASTHMA. AS A HEALTH STATE OF CONCERN







     Many varied diseases and physical conditions have been the



object of research using the utility under uncertainty



techniques.  One health state, however, which apparently.has not



been addressed in this manner is asthma.  Asthma is a condition



that may be characterized by many different attributes,



therefore, it should lend itself to the use of utility assessment



methods.  Furthermore, the valuing of these various attributes by



asthmatics should be given some importance considering the



significance of asthmatics in air pollution research and standard



setting.








Definition of Asthma








     Asthma, in its many and varied forms, is a condition that



affects at one time or another approximately 20 million



individuals in the United States and accounts for over 6 million



doctors visits, nearly 2 million emergency room visits, and 1



million work days lost in a single year (104).   Often assumed to



be a specific disease, the term asthma, in fact, "encompasses



many patterns of response to a variety of stimuli,  which find



common expression in variable airflow obstruction" (105).



     Many attempts have been made to formulate an accurate and



all-encompassing definition for this disease, yet discussion and



controversy concerning the true description of asthma have





                                44

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continued for decades.  A frequently accepted definition is that



of the American Thoracic Society (1962)  which states that asthma



is a "disease characterized by an increased responsiveness of the



trachea and bronchi to .a variety of stimuli and manifested by



narrowing of the airways that changes in severity either•.



spontaneously or as a result of therapy" (106) .   This definition



was rejected by a study 'group  in 1971 because it allegedly was



not a definition of a "disease".  Furthermore,  in 1980, Gross,



following the philosophy of Karl Popper, suggested that asthma



should remain undefined  (107) .



     Because of the lack of agreement over a specific definition



it may be useful, instead, to provide a simple broad definition,



but include defining characteristics in an explanatory paragraph.



Scadding does just this by defining asthma as "a disease



characterized by wide variations over short periods of time in



resistance to flow in the airways of the lungs"  (108).  To this



definition one may add various symptoms and causes to better



characterize the disease.  For example,  the airways of asthmatics



are often referred to as being hypersensitive to various stimuli



or environmental factors in concentrations that would not be



expected to affect non-asthmatics.  The disease may also be



episodic or persistent and may or may not be associated with



atopy, an Immunoglobulin-E  (IgE) mediated allergic response.  IgE



refers to a specific antibody that reacts to inhaled allergens.



Furthermore, the symptoms may be augmented by the swelling of



airway tissue or the collection of mucus in addition to the





                                45

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 constricting  of the  smooth muscle of the air pathways.



     The causes for  the narrowing of the airways  is  somewhat



 unclear.   It  appears, however, that asthmatics are genetically



 predisposed and that various humoral, neurogenic, and



 environmental factors exaggerate the effect  (109).   These, include



 such physical, chemical, pharmacological, and immunological



 stimuli as allergens, infectious agents, cold air, exercise,



 emotional  stress, laughter, inhaled substances such  as



 methacholine  and histamine, and atmospheric pollution.  It is



 this latter one that is of particular interest to regulators and



 environmental scientists.  Many studies have been performed on



 the effects of air pollutants on the lung function of asthmatics;



 several of these will be discussed later in this report.







Asthma Severity Measurement



     The broad definition and many variations of asthma have led



to several attempts at categorizing asthmatics.  Dawson and Simon



 (109),  for example, divide asthmatics into several groups



 including those that have no bronchial obstruction but react



abnormally to inhalation challenge testing with stimuli,



individuals who are acutely episodic,  and those that are chronic.



Scadding (108) suggests that separate categories should also be



made for those whose asthma is and is not affected by inhaled



allergens  (IgE mediated),  and asthmatics whose condition is only



brought on by heavy exercise.



      A more common method of categorization has been to use some





                               46

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sort of severity scale.  In this manner, those that are mildly,
moderately, or severely affected can be identified for routine
medical and emergency purposes.  It has been estimated that a
majority of asthmatics .are only mildly affected, 25% are
moderately affected, and as many as 15% are severely affected
(110).  Many of the symptoms of asthma, such as airways
narrowing, cannot be quantified without the use of clinical
measurements.  Several of these objective means of measurement
have been developed in an attempt to reflect the degree of
severity of a patient's asthma.  The forced expiratory volume in
one second (FEV^) is the volume of air that an individual can
expire in one second.  This is a good measure for asthma because
the narrowed airways of an asthmatic do not allow for rapid
expiration.  A second measure is the forced vital capacity  (FVC
or VC)  which is the total volume of air that can be expelled from
the lungs.  Each of these measures can be used independently or
as a ratio FEV1/FVC.  The ratio has the advantage of allowing for
better comparison between individuals because it will not be
dependent on body size as FVC may be.  It is also common to
measure the flow rate of expired air using a spirometer and note
the peak expiratory flow rate (PEFR).  In measuring both the flow
and the volume it is helpful to portray the measurements
graphically (Figure 13):
                                47

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                             Figure 13
    Graphical  Representation, of Peak Expiratory Flow Rate and
               Forced Expiratory Volume Measurements
                                         FVC
  Expiratory
    Flow
               Volume Expired
An additional measure that  is  used is  the  specific resistance of
the airways  (SRAW).  This value,  however,  is  not  as easily
attainable because of the need for a body  plethysmograph,  a
complex piece of equipment,  and is less  reproducible than  those
described above.  Several other measurements  exist which are
slight variations of those  described.
     It is often the case that ranges  of these measurements are
used to indicate the presence  of asthma.   For example,  an  FEV-^ to
FVC ratio of greater than 0.7  is often considered the normal
range.  Similarly, a PEFR of 400 - 600 1/min  is considered
normal, whereas 200 - 400 1/min may indicate  the  presence  of
asthma.  Bateman et al.  (Ill)  proposes bounds that roughly
identify healthy or asthmatic  individuals.  An example is  shown
below.
     FEV-,  (% predicted)
     FEV-L/FVC
     PEFR  (% predicted)
Asthmatic
  85 ± 6
0.74 ± 0.4
  76 + 5
 Healthy
 119 i 4
0.88 ± 0.2
  99 + 3
                                48

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     These objective clinical measures used in conjunction with



frequency and degree of asthmatic attacks have been used to



determine asthma severity in patients.  Often these are presented



in the form of severity scales.  A rather simple scale, commonly



called the Aas scale (112), is based primarily on the number and



duration of asthmatic episodes in a year, but it also considers



drug consumption and clinical evaluation.  Godard et al. (113)



claim to increase the correlation between severity and this scale



by including the objective FEVj measurement.  Juji et al.  (114)



attempted to find what measures best correlate with asthma



severity. They found that low respiration threshold to



acetylcholine, high maximal histidine release by anti-IgE,  high



serum IgE, and high eosinophil counts in the blood all correspond



well with severity.  Pereira et al. (115) examined the



coefficient of variation  (COV) of PEFR in asthmatics.  It was



found that the COV of PEFR has a bimodal distribution which was



interpreted as a natural separation between mild and severe



asthmatics.  Those individuals with severe asthma had greater



variations in their expiatory flow rate than mild or non-



asthmatics.



     In many cases a more subjective aspect is included in the



severity scale.  Scadding  (108) bases a severity categorization



on necessary treatment and lifestyle interferences.  Mild asthma,



according to Scadding,  is controllable with a bronchodilator and



there is no interference with normal activities.  Moderate



severity causes occasional interferences and necessitates the use





                                49

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of systemic corticosteroids, and severe asthma is defined as



seriously interfering lifestyle and' may include life threatening



episodes.  Similarly, Jones  (116) uses effects to lifestyle and



the ability to perform housework or one's job as a part of a



severity scale.



     A broad and encompassing scale was developed by Brooks et



al. (117) to estimate the clinical status of asthmatic subjects.



Included were ratings of frequency and degree of four symptoms:



cough, wheeze, chest tightness, and shortness of breath.  In



addition, frequency of attacks and therapy use were considered.



Scores were given to various levels within each of these



categories to indicate asthma severity.  Similarly,  Donnelly et



al. (118) identified variables which could be used to rate



patients severity.  In their study multivariate cluster analysis



was used to select eight variables which correlated well with



severity from a group of 256 seasonal and environmental factors



gleaned from patient questionnaires.  The selected variables



included four symptoms and four lifestyle interferences.  The



symptoms included cough, chest tightness, wheeze,  and shortness



of breath, and the lifestyle interferences were hospitalizations,



days of school missed, nights of sleep missed, and degree of



physical activity tolerated.  Several other severity scales have



been developed which are also based on degree and frequency of



asthmatic attacks and clinical evaluations (119,120).



     Often,  patients are asked to rate their own severity or



subjective feeling about a specific asthma symptom.   One commonly





                                50

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used scale was developed by Hackney (121).   On this scale,

specific symptoms are rated on a scale of zero to 40 on the basis

of lifestyle interferences and meication use.  Various levels are

shown below.

                    Hackney Scale

     0    Symptoms not present
     5    Minimal (not noticeable unless asked about)
     10   Mild (noticeable but not bothersome)
     20   Moderate (bothersome, consider taking medication to
                    alleviate)
     30   Severe  (interferes with activities)
     40   Incapacitating


Other subjective scales have been developed using visual analog

scales  (VAS) on which various symptoms are rated on a scale of

zero to 100 where zero represented no breathing problems and 100

represented total disability.  For example, shortness of breath

was rated by patients on a VAS scale and the VAS score was then

correlated with PEFR measurements.  In three studies  (122-124)

the r values were found to range between -0.7 and -0.85 showing a

negative correlation between the two.  This implies that

individuals who had greater difficulty in breathing and felt more

disabled also had lower PEFRs.  Similar symptom rating techniques

have been used by patients as a part of more encompassing

severity scales which also included other criteria such as

clinical examination information and drug consumption  (125-127).



Air Pollution Effects on Asthamtics

     As stated earlier, many diiferent airborne contaminants can

adversely effect the functioning of an asthmatic's lungs and may

                                51

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even bring on an attack.  There has been a significant amount of
research in this area by environmental scientists, especially
with regard to air pollutants such as sulfur dioxide and ozone.
Regulators are also concerned with the results of such studies
because of the need to consider the effects of pollutants, on
sensitive groups in the ppulation during standard setting.  The
Environmental Protection Agency (EPA) does just this by reviewing
all pertinent studies in order set national ambient air quality
standards  (NAAQS).
     The importance of regulating these pollutants in the
atmosphere becomes obvious when one examines reports of severe
exposure episodes.  In London in 1952 a brief period of S02-
polluted fog was blamed for hundreds, perhaps thousands of deaths
of sensitive individuals.  Similarly, 88% of the asthmatic
patients in Donora, Pennsylvania experienced exacerbations during
a period of high S02 concentrations in 1948 (128).  These are
isolated incidents; however, high S02 concentrations have been
reported near S02 point sources,  in indoor air of kerosene-heated
homes,  and in industrial plants such as paper-pulp mills,
smelters,  and food processing plants (128) .
     Sulfur dioxide (S02) is one such atmospheric pollutant which
has received significant attention.  EPA, in an assessment of
available health S02 health effects data (129)  states that
asthmatics as a group are more sensitive to S02 than non-
asthmatic individuals.  Furthermore they state that moderate to
heavy execise with exposure to S02 is likely to cause

                               52

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bronchoconstriction within 5 minute at concentrations of less



than 1 ppm.  These assertions are based on the results of various



inhalation studies which measured several objective, clinical



lung function criteria .including SRAW, FEV-^, and PEFR as a means



of quantifying the observed decreased lung function and  •.



bronchoconstriction (130-133).



     Similarly, studies on the inhalation of ozone  (03)  by



asthmatics were reviewed by EPA during an assessment of effects



on sensitive individuals (134).   Recent studies were pointed out



as reporting airway resistance after Og exposure (135-136).  EPA



concluded that the lungs and airways of asthmatics are more



responsive to 63 than are those of normal subjects.
                               53

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                     SUGGESTED PILOT STUDIES








     The final part of this project is the design of a number of



pilot studies that apply utility under uncertainty techniques to



the valuing of asthma health states associated with air .



pollution.  Specifically, three pilot studies have been developed



to accomplish two main objectives. The first is to evaluate the



possible uses of utility assessment for common problems faced by



the EPA. The second is to collect subjective data about how



asthmatics value  (or disvalue)  asthma and its associated



symptoms.  These two main areas are discussed individually in the



following sections.







Evaluation of Utility Assessment



     Utility assessment has been shown to be useful in many



different fields and even as a possible application to



environmental standard setting procedures (6).   To further the



study of the applicability and ease of use in areas such as this,



three pilot studies have been designed to test several



methodological variables (which I will call "utility assessment



variables") that may affect the results of such tests. Three



variables in particular have been selected:  subject group,



elicitation method, and elicitation format,  and each is



elaborated upon below.
                                54

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     Subject Group
     As mentioned earlier there is much debate about what group
should be the decision makers in a utility assessment problem.
Some have said that it should be the stakeholders that should be
elicited, while others think that the general public or ..
regulators should also have a say.  It would be interesting,
therefore, to compare the results of studies using one or the
other of these general groups.  The questions being pursued in
this report concern the elicitation of various uncertainty
utility levels of asthma and its symptoms.  Severe asthmatics are
used in the present studies as the stakeholders and non-
asthmatics familiar with utility assessment as the other group.
This provides a good basis of comparison as to which is more
important, to experience a health state first hand or to be
knowledgeable about the assessment techniques.
     Elicitation Method
     There are several types of elicitation methods that are used
commonly in the literature.  Two of these, the standard gamble
method and the time trade-off technique, however,  receive much of
the attention and appear to have been well accepted.  The purpose
of the pilot tests is not to compare the results from each method
quantitatively but more to weigh their individual advantages and
disadvantages.  For example, the ease with which subjects can
comprehend the technique or the difficulty for the interviewer in
performing the elicitation would provide valuable information for
later studies.

                                55

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     Elicitation Format



     There has been much discussion in the literature concerning



biases or errors that may be associated with the format of the



study.  The pilot studies attempt to test two different format



methods: interview and questionnaire.  It is expected that a well



designed interview should provide more valid results than a



questionnaire.  For an agency such as the EPA,  however, where



time and money are often important criteria, it may be helpful to



know whether a questionnaire format is a possible option and what



limitations may be associated with it.








Subjective Information on Asthma



     The second area of interest is information on how various



aspects of asthma are judged (i.e., the utility of changes in a



health state which may be brought on by exposure to air



pollution).  From discussions with members of EPA who are



associated with the study of asthma and air pollution it appears



that there are several areas of primary interest concerning



asthma and subjective judgment.  These include the severity of



asthma, the severity of its symptoms, and the frequency of asthma



attacks.  Each of these health state variables may be adversely



affected by exposure to air pollutants, therefore, subjective



judgment concerning them may prove valuable.
                                56

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     Asthma Severity



     There is much discussion, in the literature about the



severity of asthma and the various methods of placing asthmatics



in such levels.  It may be useful, therefore, to elicit



uncertainty utility curves for changes in severity which.may be



expected to occur upon exposure to air pollutants.  For example,



this could quantify the difference in effects between mild and



moderate  (or severe) asthmatics.  Or, studies may be designed to



elicit judgments of how undesirable it is to remain a severe



asthmatic for a certain period of time as compared to a moderate



or mild asthmatic over that same duration.







     As t hma S ympt oms



     A second area of interest concerns the various symptoms



associated with asthma.  Because asthma varies greatly from



person to person, it is difficult to pinpoint only a few defining



symptoms.  Studies which were discussed earlier, however, have



shown that several symptoms correlated well with asthma severity.



In controlled human exposure studies these included cough,



wheeze, chest tightness, and shortness of breath (dyspnea).  It



is expected that each of these symptoms is of greater or less



concern than the others.  It would be helpful,  therefore, to use



utility under uncertainty methods to elicit the severity



relationships that exist between them.
                                57

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     Frequency of Attacks

     The use of utility assessment under uncertainty would also

appear to be a good vehicle to elicit subjective valuing of

additional asthma attacks.  It is possible, for example, to find

what range of asthma attack frequency is relatively acceptable to

an asthmatic or at what point one additional attack would become

intolerable.



Pilot Study Protocols

     Three pilot studies have been designed to test the effects

of each of the various utility assessment variables discussed

above and listed in Table 1.
                             Table 1
          	Utility Assessment Variables	

          Subject Group:      Asthmatics
                              Non-asthmatics

          Elicitation Method: Time Trade-Off  (TTO)
                              Standard Gamble (SG)

          Elicitation Format: Interview
                              Questionnaire
Each of the pilot studies also addresses one of the three areas

concerning asthma with different combinations from Table 1.
                                58

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     Pilot Study 1
     The first study attempts- to elicit the preference
relationship of three severity levels of asthma  (severe,
moderate, mild) over differing periods of time.  The order is
expected to remain the same; however, it is anticipated that the
relative differences on a quantifiable scale may change over
time.
          Elicitation Method
     Of the two elicitation methods that have been discussed, the
TTO method is better suited for the type of test in which time is
involved.  In fact, it was specifically designed for this type of
application.  The time trade-off technique is used to elicit
preferences for various lengths of time in a specific health
state.  It involves presenting the subject with a choice of two
options, and in the case of severe asthma, for example, the
options would appear as follows:

                A                             B
          A guarantee                    A guarantee
          of x years of       or         of y years of
          good health                    severe asthma

     The number of years in option A is varied until the subject
is indifferent between A and B.  In each of the two options the
health state is guaranteed for only the time indicated.  After
that period, what might happen is unknown; it may be asthma,  good
health, or immediate death.  It is expected that the subject will
prefer fewer years of guaranteed good health to a greater number
of years with asthma.  The process is repeated for various time
                                59

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 periods  (y^), and in each case a corresponding good health

 duration  (x^) is elicited from the individual.  The resulting

 values may be plotted on an x - y axis.

      The  same process may also be performed for the various

 severity  levels of asthma, therefore creating a comparison of the

 three.  It is hoped that a comparison of the curves would

 indicate  whether the preference relationship of the three

 severity  levels would remain in equal ratios over time or if the

 more severe levels become disvalued at the greater durations.

      For  the sake of clarity the subject is provided with a

 written description of the various health states being considered

' in the study.  Good health is defined as the lack of any major

 illnesses and each of the severity levels by changes in lifestyle

 caused by the asthma.  These lifestyle effects are listed in

 Table 2.

                              Table 2
 	Criteria Used to Define Asthma Severity	

      Symptom Frequency:  wheeze
                          cough
                          chest tightness
                          dyspnea

      Frequency of Attacks

      Number of hospital/doctor visits per year

      Necessary Treatment  (frequency, type, possible side effects)

      Lifestyle Changes:  work or school missed
                          physical activity tolerated
                          avoidance of precipitating factors



 For each  of the three levels of asthma a different description is


                                 60

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provided to the subject using the terms in Table 2 to define it.







          Subject Group



     Because this is only a pilot study and only very general



trends are of interest, it is possible to select a small. .sample



size of subjects.  Consequently, it is expected that the number



of participants will be kept between three and ten.  This first



pilot study is designed to compare responses for asthmatics and



non-asthmatics; therefore, a group of each must be selected.  The



asthmatic group will consist of several asthmatics who will be



contacted through their physician and will be interviewed during



a regular hospital clinic visit.  The non-asthmatics consist of a



similar sized group of EPA staff members and other individuals



who are familiar with the methods of utility under uncertainty.








          Elicitation Format



     This test also compares the two types of elicitation



formats: interview and questionnaire.  The interview consists of



a series of questions in which the subject is presented with



options (A or B) as described above.  For example, the subject is



asked whether y years of asthma or x years of good health are



preferred.  The interviewer reduces the number of years of good



health until indifference between the two exists.  To control



bias,  however, it is necessary that this not be done in a



stepwise manner.  The interviewer, therefore,  must alter the



years of asthma  (y)  for each question.  To assist in this, a





                                61

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tally sheet is provided to the interviewer which consists of a



grid with the years of asthma  (y) oh the y-axis and the years of



good health (x) on the x-axis.  Each box in the grid represents a



comparison of an x with a y.  The interviewer may easily select



any box and ask the preference of the subject.  Once the..



preference is recorded, the interviewer chooses another box in a



predetermined random order.  A different tally sheet is necessary



for each of the three asthma severity levels and, switching



between the three levels is also necessary during the random



sequence.



     The questionnaire does not involve the tally sheet; however,



it does involve the presentation of a random sequence of options



for which the subject must indicate a preference or indifference.







     Pilot Study 2



     The second of the three pilot tests investigates the



preference relationships of four symptoms: wheeze,  cough, chest



tightness, and dyspnea.  Once again, both asthmatics and non-



asthmatics are interviewed.  The questionnaire format, however,



is not used in this test.  In addition, this test only uses the



standard gamble technique.  To explain its use in this



application one symptom, dyspnea, is discussed as an example.



     The severity of dyspnea is best described by discrete levels



as shown in Table 3.
                                62

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                             Table 3
                        Severity of Dyspnea
     None      no shortness of breath at any time

     Mild      shortness of breath with strenuous exertion

     Moderate  shortness of breath with moderate exertion
                (e.g., climbing one to two flights of stairs or
               walking four or five blocks)

     Severe    shortness of breath with minimal exertion
                (e.g., climbing one-half to one flight of stairs
               or walking half a block or performing housework)

     Dyspnea
     at rest   shortness of breath without any physical activity

                                        Source: reference  (117)


     Because of the lack of continuity it is possible to use only

the probability equivalence method.  This involves presenting the

subject with a pair of options to elicit a preference of

indifference.  For example, the subject may be asked to choose

between two options, A and B:

                A                             B
          A guarantee of                 A chance of no
          moderate dyspnea      or       dyspnea with a
          for the remainder              probability of p
          of one's life                  and dyspnea at rest
                                         with probability 1-p


The value of p is altered by the interviewer until indifference

between the two options exists.  This may be done in much the

same manner as in pilot test 1 (i.e., using a tally sheet).  This

process should produce utility levels for each of the various

severities of dyspnea.

     The other three symptoms are also tested in a similar

manner.  In some cases,  however,  it is possible to use the

                               63

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certainty equivalence method as well.  The severity of wheeze and

chest tightness, for example,-can be considered continuous

variables if frequency of occurrence is used to determine the

severity of the symptom.



     Pilot Study 3

     The final pilot study attempts to elicit utility curves of

the frequency of asthma attacks.  Because it may be difficult to

accurately describe to a non-asthmatic what an asthma attack is

like, this test is restricted to asthmatics.  Furthermore, the

information of interest lends itself better to standard gamble

methods, and because the variable being tested is continuous (#

of attacks)  both the certainty equivalence and probability

equivalence methods may be used.

     As in pilot test 2 , the subjects are presented with two

options, A and B.  For example,


                A                             B
          z attacks per                  An equal chance of
          year with             or       the maximum possible
          certainty                      imaginable attacks in
                                         one year or no attacks
                                         during the year



The value of z is altered by the interviewer in much the same

manner as in pilot test 1 and 2 using a tally sheet as an aid.  A

utility curve is drawn from the resulting data.
                                64

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                           CONCLUSIONS



     The assessment of the likelihood of effects of air pollution

on sensitive populations, such as asthmatics, plays an important

role in the regulatory process and standard setting by the EPA.

The subjective judgments of the nature and value of these effects

by the individuals affected may also add valuable input to these

processes.  It is useful, therefore, to attempt to elicit utility

under uncertainty judgments from such populations.  To do this

several possible pilot tests have been suggested.  It is

anticipated that the results of these pilot tests will provide

information to the EPA concerning how asthmatics value

effects.   Furthermore, performing such valuations will also

increase the awareness of EPA about the use of utility under
                                        i
uncertainty, its advantages,  disadvantages, and areas for further

study.
                               65

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                        REFERENCES  CITED
 1.   Bergner,  M.   Measurement of health status.  Med. Care, 1985,
     23,  5,  696-704.

 2.   Spitzer,  W.O.  State of science 1986:  Quality of life
     and functional status as target variables for research.  J.
     Chron.  Dis.,  1986,  40,  465.

 3.   Albert, D.A.   Decision theory in medicine:  A review and
     critique.  Milbank Mem. Fund Quarterly / Health and Society.
     1978,  56, 3,  362-401.

 4.   Clarke, J.R.   Decision making in surgical practice. World J.
     Surg.,  1989,  13,  245-251.

 5.   Keeney/ R.L., and Raiffa, H.  Decisions with Multiple
     Objectives:   Preferences and Value Tradeoffs, Wiley, New
     York,  1976.

 6.   Keeney, R.L., Ozernoy,  V.M. An illustrative analysis of
     ambient carbon monoxide standards. J. Opl. Res. Soc. 1982,
     33,  365-375.

 7.   von Neumann,  J.,  and Morgenstern,  0.  Theory of Games  and
     Economic Behavior,  2nd edition, Princeton Univ. Press,
     Princeton, NJ, 1947.

 8.   Watson, S.R., and Buede, D.M.  Decision Synthesis, Cambridge
     Univ.  Press,  Cambridge, U.K., 1987.

 9.   Bell,  D., P.  Farquhar.  Perspectives on utility theory. Oper.
     Res. 1986. 34,1,179-183.

10.   Clemen, R. Making Hard Decisions.  An Introduction to
     Decision Analysis (In publication)

11.   von Winterfeldt,  D., and Edwards,  W.  Decision Analysis and
     Behavioral Research, Cambridge Univ. Press,  Cambridge,
     U.K.,  1986.

12.   Hershey,  J.C., and Baron, J.  Clinical reasoning and
     cognitive process.   Med. Dec. Mak., 1987, 7, 203-211.

13.   Raiffa, H. Decision Analysis. Introductory Lectures on
     Choice Under Uncertainty. Addison-Wesley, Reading, MA,
     1968.
                                66

-------
14.  French, S.  Decision Theory:  An  Introduction  to  the
     Mathematics of Rationality, Ellis Horwood,  Ltd.,Chichester,
     U.K., 1968.

15.  Fisburn, P.C. Utility Theory for Decision Making.  Wiley,  New
     York, New York, 1970.

16.  Farquhar, P.  Utility assessment methods.   Management   Sci.,
     1984, 30, 11, 1283-1300.

17.  Torrance, G.W.  "Multiattribute Utility Theory as  a Method
     of Measuring Social Preferences for Health  Status  in Long-
     term Care" in Values and Long-term Care. Robert L. Kane and
     Rosalie A. Kane, eds., Lexington Books D.C.  Heath and  Co.,
     Lexington MA, 1982.

18.  Wolfson, A.D., Sinclair, A.J., Bombardier,  C.,  and
     McGreer,  A.  "Preference Measurement for Functional Status
     in Stroke Patients" in Values and Long-term Care,  Robert L.
     Kane and Rosalie A. Kane, eds., Lexington Books D.C. Heath
     and Co., Lexington, MA, 1982.

19.  Kaplan, R.M., Bush, L.W., Berry, C.C., et.  al.  Health
     status index:  Category rating versus magnitude estimation
     for measuring levels of well-being.  Med. Care, 27, 5,
     1979

20.  Patrick, D.L., Bush, J.W., and Chen, M.M.   Methods for
     measuring levels of well-being for a health status index.
     Health Serv. Res., 8, 3, 1973.

21.  McNutt, R.A.  Measuring patient preference  for health
     outcomes:  A decision analytic approach.  Patient  Educ.
     and Counseling, 1989, 13, 271-279.

22.  Feeny, D., Labelle, R., and Torrance, G.W.  Integrating
     economic evaluations and quality of life assessments.   in
     Quality of Life Assessments in Clinical Trials, B. Spiker,
     ed.,  Raven Press,  Ltd., NY, 1990.

23.  Read, J.L.,  Quinn, R.J., Berwick, D.M., et. al. Preferences
     for health outcomes:  Comparisons of assessment methods.
     Med.  Dec. Mak., 1984, 4, 3, 315-329.

24.  Leung, P.  Sensitivity analysis of the effect  of variations
     in the form and parameters of a multivariate attribute
     utility model:  A survey.  Behav. Sci., 1978,  23,  478-485.

25.  Klein, G., Moskowitz, H., Mahesh, S., et. al. Assessments  of
     multiattribute measuring value and utility  functions via
     mathematical programming.  Decision Sciences,  1985, 16,  309-
     324.

                                67

-------
26.  Torrance, G.W.  Toward a utility theory foundation for
     health status index models.  Health Serv. Res., 1976, 11,
     349-369.

27.  Krischer, J.P.  An annotated bibliography of decision
     analytic application to health care.  Oper. Res., 1979,
     28, 1, 97-113.

28.  Simes, R.J.  Treatment selection for cancer patients:
     Application of statistical decision theory to the treatment
     of advanced ovarian cancer.  J. Chron. Dis., 1985, 38, 2,
     171-186.

29.  Lane, D.A.  Utility, decision and quality of life.  J.
     Chron. Dis., 1987, 40, 6, 585-591.

30.  Boyd, N.F., Sutherland, H.J., Heasmann, K.Z., et. al. Whose
     utilities for decision analysis?  Med. Dec. Mak., 1990,  10,
     1, 58-67.

31.  Llewellyn-Thomas, H.A., Sutherland, H.J., Ciampi, A.,  et.
     al.  The assessment of values in laryngeal cancer:
     Reliability of measurement methods.  J. Chron. Dis.,   1984,
     37, 4, 283-291.

32.  Einstein, A.S., Holzman, G.B., Ravitch, M.M., et. al.
     Comparison of physicians decisions regarding estrogen
     replacement therapy for menopausal women and decisions
     derived from a decision analytic model.  Am. J. Med.,  1986,
     80, 246-258.

33.  McNeil, B.J., Pauker, S.G., Sox, H.C., et. al.  On the
     elicitation of preferences for alternative therapies.  N.
     Eng. J. Med., 1982, 306, 21, 1259-1262.

34.  McNeil, B.J., Weichselbaum, R., and Pauker, S.G.  Fallacy  of
     the five-year survival in lung cancer.  N. Eng. J. Med.,
     1978, 299, 25, 1387-1401.

35.  Llewellyn-Thomas, H.A., Sutherland, H.J., Tibshivani,R., et.
     al.  Describing health states:  Methodologic issues in
     obtaining values for health states.  Med. Care, 1984,  22,
     6, 543-552.

36.  O'Connor, A.M.C., Boyd, N.F., Tritchler, D.L., et. al.
     Eliciting preferences for alternative cancer drug
     treatments:  The influence of framing, medium, and rate
     variables.  Med. Dec. Mak., 1985, 5, 4, 453-463.
                                68

-------
37.   Krumins,  P.E., Finn, S.D., and Kent, D.L.  Symptom
     severity  and patients' values in the decision to perform a
     transurethral resection of the prostate.  Med. Dec. Mak.,
     1988,  8,  1-8.

38.   Corder,  M.P., and Ellwein, L.B.  A decision-analysis
     methodology for consideration of morbidity factors in
     clinical decision making.  Am. J. Clin. Oncol., 1984, 6,
     19-32.

39.   Feeny, D.H., and Torrance, G.W.  Incorporating utility-
     based quality-of-life assessment measures in clinical
     trials.   Med. Care, 1989, 27, 3, S190-S204.

40.   Bombardier, C., Ware, J., Russell, I.J., et. al.  Auranofine
     therapy and quality of life in patients with rheumatoid
     arthritis.  Am. J. Med., 1986, 81, 4, 565-578.

41.   Sackett,  D.L., and Torrance, G.W.  The utility of different
     health states as perceived by the general public.  J. Chron.
     Dis.,  1978, 31, 697-704.

42.   Sutherland, H.J., Dunn, V., and Boyd, N.F.  Measurement  of
     values for state of health with linear analog scales,  ed.
     Dec. Mak., 1983, 3, 4, 477-487.

43.   Sutherland, H.J., Llewellyn-Thomas, H., Boyd, N.F., et.  al.
     Attitudes toward quality of survival:  The concept of
     maximum endurable time.  Med. Dec. Mak., 1982, 2, 3,   299-
     309.

44.   Christensen-Szalanski, J.J.J.  Discount functions and  the
     measurement of patients' values:  Women's decisions during
     childbirth.  Med. Dec. Mak., 1984, 4, 1, 47-58.

45.   Pauker,  S.P., and Pauker, S.G.  Prenatal diagnosis:  A
     directive approach to genetic counseling using decision
     analysis.  Yale J. Biol. Med., 1977, 50, 275-289.

46.   Pauker,  S.P., and Pauker, S.G.  The amniocentesis decision:
     An explicit guide for parents.  in Risk, Communication,  and
     Decision Making in Genetic Counseling.  Epstein, C.J.,
     Curry, C.J.R., Packman, S., Sherman, S., and Hall, B.D.,
     eds.  New York,Alan R. Liss, 1982, 289-324.

47.   Pauker,  S.G., Pauker, S.P., and McNeil, B.J.  The effect of
     private attitudes on public policy:  Prenatal screening
     for  neural tube defects as a prototype.  Med. Dec. Mak.,
     1981,  1,  103-114.
                                69

-------
48.  Lane, D.L., and Hutchinson, T.A.  The notion of "acceptable
     risk:"  The role of utility in drug management.  J.
     Chron. Dis., 1987, 40, 6, 621-625.

49.  Eraker, S.A., and Sox, H.C.  Assessment of patients'
     preferences for therapeutic outcomes.  Med. Dec. Mak., 1981,
     1, 1, 29-39.

50.  Torrance,  G.W.  "Multiattribute Utility Theory as a Method
     of Measuring Social Preferences for Health Status in Long-
     term Care" in Values and Long-term Care. Robert L. Kane
     and Rosalie A. Kane, eds., Lexington Books B.C. Heath and
     Co., Lexington Mass, 1982.

51.  Torrance,  G.W., Boyle, M.H., and Horwood, S.P.  Application
     of multi-attribute utility theory to measure social
     preferences for health states.  Oper. Res., 1982, 30, 6,
     1043-1069.

52.  Boyle, M.H., and torrance, G.W.  Developing  multiattribute
     health indexes.  Med. Care, 1984, 22, 11, 1045-1057.

53.  Gustafson, D.H., Fryback, D.G., Rose, J.H., et. al.  A
     decision theoretic methodology for severity index
     development.  Med. Dec. Mak., 1986, 6, 27-35.

54.  Choi, T.,  Brekka, M.L., Campion, B.C., et. al. Feasibility
     of simulating physicians' judgments of  patient severity.
     Med. Care, 1984, 22, 1, 30-41.

55.  Kaplan, R.M., Bush, J.W., and Berry, C.C.  Health status:
     Types of validity and the index of well-being.  Health Serv.
     Res., 1976, 11, 478-507.

56.  Dowie, J.A.  Valuing the benefits of health improvement.
     Austral. Econ. Papers, 9:21 June, 1970.

57.  Torrance,  G.W., Thomas, W.H., and Sackett, D.L.  A utility
     maximization model for evaluation of health care  programs.
     Health Serv. Res., 1972, 7, 118-133.

58.  Torrance,  G.W.  Utility approach to measuring health-
     related quality of life.  J. Chron. Dis., 1987, 40, 6, 593-
     600.

59.  Torrance,  G.W.  Measurement of health state utilities for
     economic appraisal.  J. Health Econ., 1986, 5, 1-30.

60.  Torrance,  G.W. and Feeny, D.  Utilities and quality-
     adjusted  life years.  Intl. J. of Tech. Assess, in Health
     Care, 1989, 5, 559-575.


                                70

-------
61.  Weinstein, M.C., and Fineberg, H.V.  Clinical Decision
     Analysis, W.B. Saunders Company, Philadelphia, 1980,  184-
     227.

62.  McNeil, B.J., Weichselbaum, R., and Pauker, S.G.  Speech and
     survival: Tradeoff between quantity and quality of  life in
     laryngeal cancer.  New Eng. J. Med., Oct. 22, 1981,  982-987.

63.  Mehrez, A., and Gafni, A.  Quality-adjusted life years,
     utility theory, and healthy-years equivalents.  Med.  Dec.
     Mak., 1989, 9, 2, 142-149.

64.  Pliskin, J.S., Shepard, D.S., and Weinstein, M.C.   Utility
     functions for life years and health status.  Oper.  Res.,
     1980, 28, 1, 206-224.

65.  Pliskin, J.S., Stason, W.B., Weinstein, M.C., et. al.
     Coronary artery bypass graft surgery:  Clinical decision
     making and cost-effectiveness analysis.  Med. Dec.  Mak.,
     1981, 1, 1, 10-28.

66.  Miyamoto, J.M., and Eraker, S.A.  Parameter estimates for  a
     QALY utility model.  Med. Dec. Mak., 1985, 5, 2, 191-213.

67.  Loomes, G., and McKenzie, L.  The use of QALYs in health
     care decision making.  Soc. Sci. Med., 1989, 28, 4,  299-
     308.

68.  Gafni, A., and Torrance, G.W.  Risk attitudes and time
     preference in health.  Management Sci., 1984, 30, 4,  440-
     451.

69.  Harris, J. Life: quality, value and justice. Health Policy,
     1988, 10, 259-266.

70.  Smith, A.  Qualms about QALYs.  The Lancet, May 16,  1987,
     1134-1136.

71.  Rawles, J.  Castigating QALYs.  J. of Med. Ethics.,  1989,
     15, 143-147.

72.  Beck, R., Kassiner, J.P., and Pauker, S.G.  A convenient
     approximation of life expectancy  (the DEALE).  I.
     Validation of the method.  Am. J. Med., 1982, 73, 883- 888.

73.  Beck, R., Pauker, S.G., Gottlieb, J.E., et. al.  A
     convenient approximation of life expectancy  (the DEALE).
     II.  Use in medical decision-making.  Am. J. Med.,  1982,
     73, 889-897.
                                71

-------
74.  Molitch, M.E., Beck, R.,  Dreisman, M., et. al.  The cold
     thyroid nodule:  An analysis of diagnostic and therapeutic
     options. Endocrine Rev.,  1984,'5, 2, 185-199.

75.  Cummings, E.R., Lillington, G.A., Richard, R.J. Managing
     solitary pulmonary nodules. Am.  Rev. Resp. Dis. 1986, 134,
     453-460.

76.  Eckman, M.H., Robert, N.J., Parkinson, D.R. Eaton-Lambert
     syndrome and small cell lung cancer. Side effects and
     certainty. Med. Dec. Mak. 1986,  6, 174-186.

77.  Mandelblatt, J.S., Fahs,  M.C. The cost-effectiveness of
     cervical cancer screening for low-income elderly women. J.
     Am. Med. Assoc. 1988, 259,  2409-2413.

78.  Plante, D.A., Piccirillo, J.F.,  Sofferman, R.A. Decision
     analysis of treatment options in pyriform sinus carcinoma.
     Med. Dec. Mak. 1987, 7, 74-83.

79.  Tversky, A., and Kahneman,  D.  Judgment under
     uncertainty: Heuristics and biases.  Science, 1974, 185,
     1124-1131.

80.  Slovic, P.  Perception of Risk.   Science, 1981, 236, 280-
     285.

81.  Ravitch, M.M.  Subjectivity in decision making:  Common
     problems and limitations.  World J. Surg., 1989, 13, 281-
     286.

82.  Kassiver, J.P.  The principles of clinical decision making:
     An introduction to decision analysis.  Yale J. Bio. and
     Med., 1976, 2, 149-164.

83.  Mulley, A.G.  Assessing patients' utilities:  Can the  ends
     justify the means?  Med.  Care, 1989, 27, 3,  Supplement,
     5269-5281.

84.  Drummond, M.F.  Discussion:  Torrance's "Utility  approach
     to measuring health-related quality of life."     J. Chron.
     Dis., 1987, 40, 6, 601-603.

85.  Rifkin, R.D.  Classical statistical considerations in
     medical decision models.   Med. Dec. Mak., 1983, 3, 2,  197-
     214.

86.  Mehrez, A., and Gafni, A.  An empirical evaluation of two
     assessment methods for utility measurement for life years.
     Socio-Econ. Plann. Sci.,  1987, 21, 6, 371-375.
                                72

-------
87.  Krzysztofowicz, R., and Duckstein, L.  Assessment errors  in
     multiattribute utility functions.  Org. Behav. Hum. Perf.,
     1980, 26, 326-348.

88.  Bursztajn, H., and Hamm, R.M.  The clinical utility of
     utility assessment.  Med. Dec. Mak., 1982, 2, 2, 161-   165.

89.  Torrance, G.W.  Social preference for health states, an
     empirical evaluation of three measurement techniques.
     Socio-Econ. Plann. Sci., 1976, 10, 129-136.

90.  Quinn, R.J.  The effect of measurement method on  preference
     scales in a medical decision making context.  Med.-Dec.
     Mak., 1981, 1, 431.

91.  Fischer, G.W.  Multidimensional utility models for risky  and
     riskless choice.  Organ. Behav. Hum. Perf., 1976, 17, 127-
     146.

92.  Hershey, J.C., Konreuther, H.C., and Schoemaker, P.J..
     Sources of bias in assessment procedures for utility
     functions.  Management Sci., 1982, 28, 8, 936-954.

93.  Zarin, D.A., and Pauker, S.G.  Decision analysis as a   basis
     for medical decision-making:  The true hippocrates.  J. Med.
     Philos., 1984, 9, 181-213.

94.  Llewellyn-Thomas H., Sutherland, H.J., Tibishirani, R.,
     et. al.  The measurement of patients' values in medicine.
     Med. Dec. Mak., 1982, 2, 4, 449-462.

95.  Ciampi, A., Silberfeld, M., and Till, J.E.  Measurement
     of individual preferences:  The importance of "situation-
     specific" variables.  Med. Dec. Mak., 1982, 2, 4, 483-  495.

96.  Eraker, S.A., and Pollster, P.  How decisions are reached:
     Physician and patient.  Ann. Int. Med., 1982, 97, 262-268.

97.  Llewellyn-Thomas, H., Sutherland, H.J., Tibishirani, R.,
     et. al.  Describing health states:  Methodologic issues in
     obtaining values for health states.  Med. Care, 1984, 22, 6,
     543-552.

98.  O'Connor, A.  Effects of framing and level of probability on
     patients' preferences for cancer chemotherapy.  J. Clin.
     Epid., 1989, 42, 2, 119-126.

99.  Bellinger, F.J.  Expected utility theory and risky choices
     with health outcomes.  Med. Care, 1989, 27, 3, 273-279.

100.  Kawachi, I.  QALYs and justice.  Health Policy, 1989,   13,
     115-120.

                                73

-------
101.  Mendeloff, J.  Measuring elusive benefits:  On the value
     of health.  J. of Health Politics, Policy and Law, 1983,
     8, 3,  554-580.

102.  Mooney,  G.  QALYs:   Are they enough?  J. of Med. Ethics,
     1989,  15, 148-152.

103.  Williams, A.; Evans, R.W.; Drummond, M.F. Letters: Quality-
     adjusted life years. The Lancet, June 13, 1987.

104.  Merchant, J., Memorandum: Opening remarks, workshop
     findings, and summary for proceedings of the workshop on
     environmental and occupational asthma.

105.  Josephs, L.,  Gregg,  I., Holgate, S. Does non-specific
     bronchial responsiveness indicate the severity of asthma?
     Eur. Respir.  J. 1990, 3, 2, 220 - 227.

106.  O'Connor, G., Weiss, S., Speizer, F. The epidemiology of
     asthma.  In Bronchial Asthma: Principals of Diagnosis and
     Treatment. 2nd edition, M. Eric Gershwin editor, Grune and
     Stratton, Inc. Orlando, 1986.

107.  Gross, N. What is this thing called love? - or, defining
     asthma.  Am. Rev. Respir. Dis. 1980, 121, 203.

108.  Scadding, J.  Definition and clinical categorization. In
     Bronchial Asthma: Mechanisms and Therapeutics, 2nd edition,
     E.B. Weiss, M. S. Segal, M. Stein editors. Little, Brown,
     and Company,  Boston, 1985

109.  Dawson,  A., Simon,  R. Bronchospastic disorders: An overview.
     In The Practical Management of Asthma. A. Dawson and R.
     Simon editors, Grune and Stratton, Inc. Orlando, 1984.

110.  Cohen, J. Memorandum: Assessing asthmatic response to S02:
     Summary of expert opinions. 1984. United States
     Environmental Protection Agency, Office of Air Quality
     Planning and Standards, Ambient Standards Branch, Research
     Triangle Park, NC.

111.  Bateman, J.,  Pavia,  D., Sheehan, N., et al. Impaired
     tracheobronchial clearance in patients with mild stable
     asthma.  Thorax, 1983, 38, 463 - 467.

112.  Aas, K.  Heterogeneity of bronchial asthma. Subpopulations or
     different stages of disease. Allergy, 1981, 36, 3-14.

113.  Godard,  P., Chaney,  P., Hors, V., et al. Evaluation of a
     symptom-indication score or chronic asthma. J. Allerg. Clin.
     Immun. 1989,  83, 175.


                                74

-------
114.  Juji,  F,  Takashima, H., Takaishi, T. Clinical study of
     asthma in adolescents and in young adults. 'Correlation
     between lab findings and severity of asthma. Annals of
     Allergy,  1989, 63,427 -433.

115.  Pereira,  J., Carswell, F. Measurement and prediction of
     asthma severity. J. Allerg. Clin. Immun. 1989, 83, 249

116.  Jones, E. The intensive therapy of asthma. Proc. Roy.. Soc.
     Med. 1971,  64, 1151 - 1152.


117.  Brooks, S., Bernstein, I., Raghuprasad, P., et al.
     Assessment o airway hyperresponsiveness in chronic stable
     asthma.  J. Allerg. Clin. Immun. 1990, 85  (1 pt 1), 17 - 26.

118.  Donnelly, W., Donnelly, J., Thong, Y. Guidelines for
     maintenance treatment o childhood asthma: Developments of a
     score card system by multivariate cluster analysis. Soc.
     Sci. Med. 1987, 25, 9, 1033 - 1038.

119.  Iwamoto,  I., Nawata, Y., Koike, T., et al. Relationship
     between anti-IgE autoantibody and severity of bronchial
     asthma. Int. Arch. Allergy Appl. Immun. 1989, 90, 4, 414 -
     416.

120.  Baker, M. Pitfalls in the use of clinical asthma scoring.
     Am. J. Dis. Child. 1988, 142, 183 - 185.

121.  Hackney,  J., et al. Replicated dose-response study of'sulfur
     dioxide efffets in normal, atopi, and asthmati volunteers,
     Interim Special Report for Researh Project 1225 prepared by
     the professional Staff Association of Ranho Los Amigos
     Medical enter Inc., for EPRI, Palo Alto, CA, July 1987.

122.  Dhand, R.,  Kalva, S., Malik, S. Use of visual analogue
     scales for assessment of the severity o asthma. Respiration,
     1988,  54, 255 - 262.

123.  Gift,  A.  Validation of a vertical visual analogue scale as a
     measure of clinical dyspnea. Am. R. Resp. Dis. 1986, 133, 4,
     A163

124.  Stark, R.,  Gambles, S., Lewis, J. Method to assess
     breathlessness in healthy subjects: A clinical evaluation
     and application to analyze the acute effects of diazepam and
     promethazine on breathlessness induced by exercise or by
     exposure to raised levels of C02- Clin. Sci. 1981, 61,  429 -
     439.
                                75

-------
125. McManus, M.,  Koenig, J., Altman, L., et al.  Pulmonary
     effects of sulfur dioxide exposure and ipratropium bromide
     pretreatment in adults with noh-allergenic asthma. J.
     Allerg. Clin. Immun. 1989, 83, 3, 619 - 626.

126. Selcow, J., Mendelson, L., Rosen, J. A comparison of
     cromyolyn and bronchodilators in patients with mild to
     moderately severe asthma in an office practice. Annals of
     Allergy, 1983,  50, 13 - 18.

127. Kotses, H., Harver, A., Creer, T., et al. Measures of asthma
     severity recorded by patients. J. Asthma, 1988, 25, 6, 373 -
     376.

128. Sheppard, D.  Sulphur-dioxide and asthma - A double edged
     sword? J. Allerg. Clin. Immun. 1988, 82,  961-964.

129. U.S.EPA. 2nd Addendum to air quality criteria for
     particulate matter and sulfur oxides. Assessment of newly
     available health effects information. 1986.  Environmental
     Criteria and Assessment Office,  Research Triangle Park, NC.
  '   600/8-86-020F

130. Linn, W.S., T.G. Venet, D.A. Shamoo, et al.  Respiartory
     effects of sulfur-dioxide in heavily exercising asthmatics -
     a dose-response study.  Am R Resp Dis,  1983, 127, 278-283.

131. Schachter,  E.N., T.J. Witek, G.J. Beck, et al. Airways
     effects of low concentrations of sulfur-dioxide: Dose-
     response characteristics.  Arch. Env. Health, 1985, 39, 34-
     42.

132. Koenig, J.Q., W.E.Pierson, M. Horike, R.  Frank. A comparison
     of the pulmonary effects of 0.5 ppm versus 1.0 ppm sulfur-
     dioxide plus sodium chloride droplets in asthmatic
     adolescents.  J. Tox. Env. Health, 1983, 11,  129-139.

133. Roger, L.J.,  H.R. Kehrl, M. Hazucha, D.H. Horstman.
     Bronchoconstriction in asthmatics exposed to sulfur-dioxide
     during repeated exercise. J. Appl Phys, 1985, 59, 784-791:

134. U.S.EPA. Review of the national ambient air quality
     standards for ozone. Assessment of scientific and technical
     information.  OAQPS staff paper.  Air Quality Management
     Division, Office of Air Quality Planning and Standards.
     U.S. Environmental Protection Agency, Research Triangle
     Park, N.C.   1989
                                76

-------
135.  McDonnell,  W.F.,  D.H. Horstman, S. Abdul-Salaam, L. Raggio,
     J.A.  Green.  The respiratory responses of subjects with
     allergic rhinitis to ozone exposure and their relationship
     to nonspecific airway reactivity. Toxicol. Ind. Health 1987,
     3, 507-517.

136.  Kreit,  J.W.,  K.B. Gross,  T.B. Moore,  et al. Ozone-induced
     changes in pulmonary function and bronchial responsiveness
     of asthmatics. J. Appl. Phys., 1988,  66,  217-222.
                               77

-------