Lifetable Analysis Appendix D


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1	APPENDIX H
2
3	H.l. Lifetable Analysis:
4
5	A spreadsheet illustrating the extra risk calculation for the derivation of the LECoi for
6	RCC incidence is presented in Table H-l.
7
8
9
10
11
This document is a draft for review purposes only and does not constitute Agency policy.
06/02/09	H-l

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Table H-l. Extra risk calculation3 for environmental exposure to 1.82 ppm TCE (the LEC0i for RCC
incidence)b using a linear exposure-response model based on the categorical cumulative exposure results of
Charbotel et al. (2006), as described in Section 5.2.2.1.2.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P














Exposed





All

Prob of
RCC
Cond prob Exp

Exposed
Exposed Exposed
prob of
Exposed




cause
Prob of
surviving
cancer
of RCC
duration Cum
RCC
all cause prob of
surviving
cond prob
Interval

All cause
RCC
hazard
surviving
up to
hazard
incidence
mid
exp mid
hazard
hazard
surviving
up to
of RCC in
number Age
mortality
incidence
rate
interval
interval
rate
in interval
interval
interval
rate
rate
interval
interval
interval
(i)
interval (xlO/yr)
(xl05/yr)
(h«)
(q)
(S)
(h)
(R0)
(xtime)
(xdose)
(hx)
(h*x)
(qx)
(Sx)
(Rx)
1
<1
685.2
0
0.0069
0.9932
1.0000
0.000000
0.000000
0.5
2.77
0.000000
0.0069
0.9932
1.0000
0.000000
2
1-4
29.9
0
0.0012
0.9988
0.9932
0.000000
0.000000
3
16.61
0.000000
0.0012
0.9988
0.9932
0.000000
3
5-9
14.7
0
0.0007
0.9993
0.9920
0.000000
0.000000
7.5
41.52
0.000000
0.0007
0.9993
0.9920
0.000000
4
10-14
18.7
0.1
0.0009
0.9991
0.9913
0.000005
0.000005
12.5
69.20
0.000006
0.0009
0.9991
0.9913
0.000006
5
15-19
66.1
0.1
0.0033
0.9967
0.9903
0.000005
0.000005
17.5
96.88
0.000006
0.0033
0.9967
0.9903
0.000006
6
20-24
94
0.2
0.0047
0.9953
0.9871
0.000010
0.000010
22.5
124.56
0.000013
0.0047
0.9953
0.9871
0.000013
7
25-29
96
0.7
0.0048
0.9952
0.9824
0.000035
0.000034
27.5
152.24
0.000049
0.0048
0.9952
0.9824
0.000048
8
30-34
107.9
1.6
0.0054
0.9946
0.9777
0.000080
0.000078
32.5
179.91
0.000117
0.0054
0.9946
0.9777
0.000114
9
35-39
151.7
3.2
0.0076
0.9924
0.9725
0.000160
0.000155
37.5
207.59
0.000245
0.0077
0.9924
0.9724
0.000237
10
40-44
231.7
6.3
0.0116
0.9885
0.9651
0.000315
0.000302
42.5
235.27
0.000504
0.0118
0.9883
0.9650
0.000484
11
45-49
352.3
11
0.0176
0.9825
0.9540
0.000550
0.000520
47.5
262.95
0.000919
0.0180
0.9822
0.9537
0.000869
12
50-54
511.7
17.3
0.0256
0.9747
0.9373
0.000865
0.000801
52.5
290.63
0.001507
0.0262
0.9741
0.9367
0.001393
13
55-59
734.8
26.2
0.0367
0.9639
0.9137
0.001310
0.001175
57.5
318.31
0.002375
0.0378
0.9629
0.9124
0.002127
14
60-64
1140.1
36.2
0.0570
0.9446
0.8807
0.001810
0.001549
62.5
345.99
0.003409
0.0586
0.9431
0.8786
0.002909
15
65-69
1727.4
44.6
0.0864
0.9173
0.8319
0.002230
0.001777
67.5
373.67
0.004358
0.0885
0.9153
0.8286
0.003456
16
70-74
2676.4
49
0.1338
0.8747
0.7631
0.002450
0.001750
72.5
401.35
0.004961
0.1363
0.8726
0.7584
0.003518
17
75-59
4193.2
51.6
0.2097
0.8109
0.6675
0.002580
0.001554
77.5
429.03
0.005407
0.2125
0.8086
0.6617
0.003223
18
80-84
6717.2
44.4
0.3359
0.7147
0.5412
0.002220
0.001021
82.5
456.71
0.004809
0.3384
0.7129
0.5351
0.002183







Ro =
0.010736





Rx =
0.020586
extra risk = (Rx-Ro)/(l-Ro) = 0.00996
06/02/09
This document is a draft for review purposes only and does not constitute Agency policy.
H-2

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Column A: interval index number (i).
Column B: 5-year age interval (except <1 and 1-4) up to age 85.
Column C: all-cause mortality rate for interval i (x 105/year) (2004 data from NCHS).
Column D: RCC incidence rate for interval i (x 105/year) (2001-2005 SEER data).
Column E: all-cause hazard rate for interval i (h*,) (= all-cause mortality rate x number of years in age interval).0
Column F: probability of surviving interval i without being diagnosed with RCC (q,) (= cxp(-h*,)).
Column G: probability of surviving up to interval i without having been diagnosed with RCC (SO (S| = 1: S, = S, i x q, for i>l).
Column H: RCC incidence hazard rate for interval i (h,) (= RCC incidence rate x number of years in interval).
Column I: conditional probability of being diagnosed with RCC in interval i (= (h/h*,) x S, x (1-q,)). i.e., conditional upon surviving up to interval i without
having been diagnosed with RCC [Ro, the background lifetime probability of being diagnosed with RCC = the sum of the conditional probabilities
across the intervals].
Column J: exposure duration (in years) at mid-interval (xtime).
Column K: cumulative exposure mid-interval (xdose) (= exposure level (i.e., 1.82 ppm) x 365/240 x 20/10 x xtime) [365/240 x 20/10 converts continuous
environmental exposures to corresponding occupational exposures].
Column L: RCC incidence hazard rate in exposed people for interval i (hxj) (= h, x (1 + (} x xdose), where (3 = 0.001205 + (1.645 x 0.0008195) = 0.002554)
[0.001205 per ppm x year is the regression coefficient obtained from the weighted linear regression of the categorical results (see Section 5.2.2.1.2).
To estimate the LEC0i, i.e., the 95% lower bound on the continuous exposure giving an extra risk of 1%, the 95% upper bound on the regression
coefficient is used, i.e., MLE + 1.645 x SE],
Column M: all-cause hazard rate in exposed people for interval i (h*x,) (= h* + (hx - h,)).
Column N: probability of surviving interval i without being diagnosed with RCC for exposed people (qx,) (= cxp(-h*x,)).
Column O: probability of surviving up to interval i without having been diagnosed with RCC for exposed people (Sx,) (Sx, = 1: Sx = Sx , x qx,_i. for i>l).
Column P: conditional probability of being diagnosed with RCC in interval i for exposed people (= (hx,/h*x,) x Sx x C1 qx,)) [Rx, the lifetime probability of
being diagnosed with RCC for exposed people = the sum of the conditional probabilities across the intervals].
a Using the methodology of BEIRIV (1988).
b The estimated 95% lower bound on the continuous exposure level of TCE that gives a 1% extra lifetime risk of RCC.
0 For the cancer incidence calculation, the all-cause hazard rate for interval i should technically be the rate of either dying of any cause or being diagnosed with
the specific cancer during the interval, i.e., (the all-cause mortality rate for the interval + the cancer-specific incidence rate for the interval—the cancer-specific
mortality rate for the interval [so that a cancer case isn't counted twice, i.e., upon diagnosis and upon death]) x number of years in interval. This adjustment
was ignored here because the RCC incidence rates are small compared with the all-cause mortality rates.
MLE = maximum likelihood estimate, SE = standard error.
06/02/09
This document is a draft for review purposes only and does not constitute Agency policy.
H-3

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H.2. Equations Used for Weighted Linear Regression of Results from Charbotel et al.
(2006):
[source: Rothman (1986), p. 343-344]
linear model: RR=l+bX
where RR = risk ratio, X = exposure, and b = slope
b can be estimated from the following equation:
HwjxjRR, -
b = ^
wix,
s
7 = 2
WJXJ
where j specifies the exposure category level and the reference category (j = 1) is ignored.
the standard error of the slope can be estimated as follows:
SE(b)
Z »,*/
}=2
the weights, Wj, are estimated from the confidence intervals (as the inverse of the variance):
Var(RR]) « RR]2Var[ln(RRi)] ~ RR2 x
ln(RR})-ln(RRj)
2x1.96
where RRj is the 95% upper bound on the RRj estimate (for the jth exposure category) and RR,
is the 95% lower bound on the RRj estimate.
This document is a draft for review purposes only and does not constitute Agency policy.
06/02/09	H-4

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