United States
Environmental Protection
Agency
Health Effects Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S1 -84-017 Dec. 1984
v°/EPA Project Summary
Adjustment of Incidence
Rates for Migration in
Indirect Ecologic Studies
Chin Long Chiang and Paul M. Conforti
The overall objective of this research
program was to develop a method for
adjusting incidence rates for migration
in studies relating environmental agents
to diseases with long latent periods.
Various methods of estimating migra-
tion and population change are con-
sidered.
An example of a situation requiring
this adjustment is described. Cancer
incidence rates were compared for
census tracts with varying levels of
asbestos in drinking water. Because
cancer has a long latent period, recent
in-migrants would not have been ex-
posed for sufficient periods of time to
be at risk for cancer. Unless the in-
migrants were equally distributed across
census tracts, an analysis of the rela-
tionship between asbestos and cancer
based on incidence rates would be
biased.
This report reviews a number of
measures of migration and population
change as well as stochastic models of
migration and of population growth.
The stochastic models of migration
include models that are time-indepen-
dent and time-dependent. They vary in
complexity from a simple in-migrant
model to one in which in-, out-, and
within-migration are included. The sto-
chastic models of population growth
extend this work to include birth and
death considerations.
Migration data available through the
Census of Population and Housing of
the Bureau of the Census are described.
A method is developed that uses these
data to estimate migration by census
tract. This method is applied to data
from a project supported by the U.S.
Environmental Protection Agency (EPA)
on the relationship between ingested
abestos and cancer. A reanalysis of the
data with the addition of migration
information is compared to the original
results.
This Project Summary was developed
by EPA's Health Effects Research Labo-
ratory, Research Triangle Park, NC, to
announce key findings of the research
project that is fully documented in a
separate report of the same title (see
Project Report ordering information at
back).
Introduction
The problem of migration arises in
studying the relationship between a risk
factor and disease of a long latent period
by the indirect method. The indirect
method uses groups of individuals as the
observational units to compare risk factor
presence or magnitude with disease
outcome(morbidity or mortality). In study-
ing a disease with a long latent period,
unless groups are closed to migration,
risk factor presence or risk factor exposure
times of individuals within these groups
will vary and effect the observed relation-
ship.
An example in which the migration
problem arises is an investigation sup-
ported by the U.S. Environmental Protec-
tion Agency (EPA) and carried out at the
University of California, Berkeley, on the
relationship between ingested asbestos
and cancer. In this example, the study
area was the five-county San Francisco/
Oakland Standard Metropolitan Statisti-
cal Area (SMSA), which included 722
census tracts, of the 1970 Census Bureau
Census tracts were compared for their
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cancer incidence rates over 3- and 6-year
periods (1969-71 and 1969-74, respec-
tively), and asbestos levels in drinking
water supplies. Because cancer has a
long latent period, it is important to know
if the population of the study area had
changed in the years preceding the
collection of cancer incidence data. If
there was an increase in the study area
population such that census tracts grew
in a uniform manner, then, although the
relationship observed may be diluted, it
would not be biased. Population of the
San Francisco/Oakland SMSA by county
and decade (for 1950,1960, and 1970) is
shown in Table 1.
median school years completed), marital
status, and asbestos workers were also
taken from the 1970 Census of Popula-
tion.
A description of the observed cancer
cases and study population shows the
assumptions made about migration in the
original asbestos-cancer study and the
assumptions necessary to accurately
portray the population at risk. The changes
these assumptions make on the indirect
age-adjusted rates are given.
A review is made of non-stochastic
migration measures. The measures in-
clude direct methods, which involve data
on mobility and prior residence from the
Table 1.
County
Population of San Francisco/Oakland SMSA by County and Decade for 1950, 1960,
and 1970
1950
1960
1970
Alameda
Contra Costa
Marin
San Francisco
San Mateo
Total
740.315
298,984
85,619
775,357
235,659
2,135,934
908,209
409,030
146.820
740.316
444.387
2,648,762
1,073,184
558,389
206.038
715,674
556.234
3.109,519
During 1950-1970, the SMSA popula-
tion grew from 2.1 million to 3.1 million.
Furthermore, this growth is clearly not
uniform across the counties and, there-
fore, not uniform across the census tracts
of the study area.
Exposure time to asbestos levels in
census tracts varies and may yield a
biased view of the actual relationship
between asbestos and cancer.
The present study reviews the method-
ology of measuring migration, presents
stochastic modelling of population
growth, and suggests a method for esti-
mating census tract migration from
available data.
The review of the asbestos-cancer
study includes descriptions and sources
of the variables analyzed. Asbestos levels
in drinking water were determined from a
water sampling plan throughout the
SMSA. Samples were analyzed for asbes-
tos by a well-developed method of elec-
tron microscopy. Cancer incidence rates
were obtained by merging data on cancer
incidence for the years 1969-1971 col-
lected under the Third National Cancer
Survey and data in the 1970 Census of
Population. Race, sex, and site specific
rates were age-adjusted by the indirect
method using the entire SMSA population
as the standard. Thirty-five cancer site
and cancer site groupings were analyzed.
Data on covariables such as socioeco-
nomic status (median family income and
census or surveys, and indirect methods,
which require estimating net migration
(the difference between in- and out-
migrants) from population figures at two
censuses or from natural increase (births
minus deaths) or intercensal survival
rates derived from life tables or compari-
son of age distributions of successive
censuses. These indirect methods are
called estimation by the "residual me-
thod." The difference between total
change in population and change due to
natural increase is imputed to net migra-
tion.
Because direct methods are fairly
straightforward when the proper ques-
tions are asked in the census or surveys,
the concentration here is on the indirect
methods. The indirect methods of measur-
ing migration presented are (1) the
national growth rate method, which uses
data from two censuses, and (2) the
residual method, comprising (a) the vital
statistics method, which requires com-
plete registration of births and deaths in
intercensal periods, and (b) the survival
rate method, which requires census data
with survival rates obtained from either
life tables or censuses.
Procedures
The stochastic models of migration that
are presented begin with a simple time
independent process for the probability of
observing k in-migrants in an area during
a time interval (O,t). This results in a
Poisson process. This process is extended
to a system of Poisson processes that
might represent the probabilities of ob-
serving varying numbers of in-migrants
in the 722 census tracts of the San
Francisco/Oakland SMSA. Since it is
more realistic to assume that the prob-
ability of migrating depends on time, the
system of Poisson processes is modified
to include this assumption.
A model which yields the probability of
observing k individuals in an area while
allowing for both in- and out-migration is
developed. It is assumed that the prob-
abilities of in- and out-migration are
dependent on time and the probability of
out-migration is also dependent on the
number of persons in an area at a
particular time. The result is a process in
which the population in the area of
interest at time t is the sum of two random
variables. One of these random variables
is binomial and represents the number of
survivors of an initial number of people
from time O and the other random variable
is Poisson and represents the total num-
ber of surviving immigrants in (O,t).
A process is presented that includes
parameters for births, deaths, and migra-
tion. These parameters are time inde-
pendent. The probability of having k
individuals in the area of interest at time t
is the sum of two random variables, one
of which is negative binomial and one of
which is unnamed.
The most realistic stochastic model is
one in which birth, death, and migration
are considered in a linear growth, time-
dependent process. In this model the 722
census tracts and the area outside of the
San Francisco/Oakland SMSA are the
areas of interest. The parameters include
possibilities for increases and decreases
within the areas of interest and allows for
individuals to move from one area to
another. Each time-dependent parameter
is multiplied by the current population of
respective areas to yield a linear growth
model. The differential equation for the
probability generating function of the
number of people in an area cannot be
solved explicitly.
When the aforementioned system of
Poisson processes is modified to allow
parameters to depend on the number of
individuals in an area such that growth is
considered linear, the resulting process is
the time-dependent Yule process. An
unnamed process results when the prob-
ability of in-migration is dependent on
time and dependent on the number of
individuals in an area in a non-linear way.
Models are also presented which include
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parameters for in- and out-migration and
parameters for in-, out-, and within-
migration. A model is discussed that
extends the in-, out-, and within-migra-
tion process to include births and deaths.
Conclusions
Unless special surveys are made to
obtain information about migration per-
taining to census tracts, data from the
Census of Population and Housing from
the Bureau of the Census of the U.S.
Department of Commerce must be used
to estimate migration at the census tract
level.
Under the reports of the Bureau of the
Census there are two variables that relate
to the subject of migration or population
mobility. Under the Population portion of
the 1970 census report is an item entitled
"Residence in 1965." Residence on April
1, 1965, is the usual place of residence
five years before enumeration. The cate-
gory "same house" includes all persons
five-years-old and over who did not move
during the five years as well as those who
had moved, but by 1970 had returned to
their 1965 residence. The category "dif-
ferent house" includes persons who, on
April 1,1 965, lived in the United States in
a different house from the one they
occupied on April 1, 1970, and for whom
sufficient information concerning the
1965 residence was collected. These
persons were subdivided into three
groups according to their 1965 residence
in or outside a standard metropolitan
statistical area: "in central city of this
SMSA," "in other parts of this SMSA,"
and "outside this SMSA." The category
"abroad" includes those with residence
in a foreign country or outlying area of the
United States in 1965.
The Housing Characteristics portion of
the 1970 Bureau of the Census reports
lists a variable entitled "year moved into
unit." Data on year moved into unit are
tased on the information reported for the
head of the household. The question
refers to the year of the latest move. Thus,
if the head of the household moved back
into a unit he had previously occupied or if
he moved from one apartment to another
in the same building, the year he moved
into his present unit was to be reported.
"Year moved into unit" was reported in
five categories: 1968 to March 1970,
1965 to 1967, 1960 to 1964, 1950 to
1959, and 1949 or earlier.
A procedure is presented for estimating
migrants by census tract using the 1970
census item "year moved into unit." The
assumptions necessary for making this
stimation are discussed.
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Chin Long Chiang and Paul M. Conforti are with the University of California,
Berkeley, CA 94720.
Judy A. Stober is the EPA Project Officer (see below).
The complete report, entitled "Adjustment of Incidence Rates for Migration in
Indirect Ecologic Studies," (Order No. PB 85-124139; Cost: $11.50, subject to
change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield. VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Health Effects Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
•if US GOVERNMENT PRINTING OFFICE. 559-016/7862
United States
Environmental Protection
Agency
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