Statistical Methods in Medical Research 4ed

Table 19.6 Subject-years at risk ( y) of asbestos workers and death rates (d ) per 100 000 for lung
cancer in men in England and Wales.
Period
1941±50 1951±60 1961±70 1971±80
Age group y d y d y d y d
25±29 82 2 62 1 13 1 3 1
30±34 148 3 273 4 156 3 43 2
35±39 74 9 446 10 435 8 141 6
40±44 41 21 395 25 677 22 290 16
45±49 33 46 229 58 749 54 485 46
50±54 23 78 172 124 590 119 642 106
55±59 14 112 158 216 399 226 621 201
60±64 11 137 109 294 288 370 479 346
65±69 4 137 78 343 185 508 273 530
70±74 0 107 47 325 124 562 151 651
75‡ 0 86 16 270 58 518 72 756
The expected number of deaths due to lung cancer is
…82 2 ‡ 62 1 ‡ 13 1 ‡ ...‡ 72 756† 10 5 ˆ 13 8:
The observed number was 67, so the SMR is 67=13 8 ˆ 4 9. Using the methods given in
§5.2, a test of the null hypothesis that the asbestos workers experienced national death
rates is
z ˆ…67 13 8†= 1
p 3 8 ˆ 14 3 …P < 0 001†,
and approximate 95% confidence limits for the SMR are 3 8 and 6 2.
The method has usually been applied to compare observed and expected
mortality within single groups but may be extended to compare the SMR
between different subgroups or, more generally, to take account of covariates
recorded for each individual, by expressing the SMR as a proportional-hazards
regression model (Berry, 1983)Ðthat is, by the use of a generalized linear model
(§14.4). For subgroup i, if mi is the cumulative hazard from the reference
population and g i the proportional-hazards multiplier, then m i, the expected
number of deaths, is given by
ln m i ˆ ln mi ‡ ln g i:
If g i is modelled in terms of a set of covariates by
then
ln g i ˆ b 0 ‡ b 1x i1 ‡ b 2x i2 ‡ ...‡ bpxip
19.7 Subject-years method 687