| Results
A Poisson regression of observed over
expected cancer deaths in 96 Bavarian districts, 1979-1997, is conducted
with the average background gamma radiation (ODL in mSv/y) as an
independent variable and unemployment rate (ALO1-ALO3) and population
density (URB1-URB3) as possible confonders. Both confounder variables are
categorized into 4 quartiles with the lowest quartile (ALO0 and URB0,
resp.) being the reference category. The estimates for the parameters are
corrected for overdispersion (family=quasipoisson).
1) Regression without
confounders ALO and URB
Model:
(1) glm(OBS~offset(log(EXP))+ODL,quasipoisson)
(notation: statistical package R)
Parameter estimates:
|
estimate |
SE |
t-value |
p-value |
| (Intercept) |
-0.1049 |
0.0183 |
-5.7453 |
0.0000 |
| ODL |
0.1553 |
0.0261 |
5.9460 |
0.0000 |
The residual deviance is 1009.9 on 94
degrees of freedom (dispersion parameter 10.7)
2)
Regression with confounders ALO1-3
and URB1-3
Model:
(2) glm(OBS~offset(log(EXP))+ALO1+ALO2+ALO3+URB1+URB2+URB3+ODL,quasipoisson)
Parameter estimates:
|
estimate |
SE |
t-value |
p-value |
| (Intercept) |
-0.0823 |
0.0207 |
-3.9677 |
0.0001 |
| ALO1 |
0.0108 |
0.0117 |
0.9270 |
0.3565 |
| ALO2 |
0.0405 |
0.0139 |
2.9156 |
0.0045 |
| ALO3 |
0.0492 |
0.0164 |
3.0042 |
0.0035 |
| URB1 |
-0.0064 |
0.0121 |
-0.5317 |
0.5963 |
| URB2 |
-0.0195 |
0.0131 |
-1.4913 |
0.1394 |
| URB3 |
0.0041 |
0.0117 |
0.3473 |
0.7292 |
| ODL |
0.0950 |
0.0294 |
3.2314 |
0.0017 |
The residual deviance is 719.3 on 88
degrees of freedom (dispersion parameter 8.1)
Both regressions - model (1) and model
(2) - yield highly significant effects of background radiation
(p<0.0001 and p=0.0017, respectively).
Excess relative risks:
Regression 1)
The regression without confounders yields an excess relative risk (RR) of
RR=exp(0.1553)=1.168 per mSv/y
ie the excess relative risk is ERR = RR-1 = 16.8% per mSv/y
Regression 2)
The regression with confounders ALO1-3 and URB1- yields
RR=exp(0.0950)=1.100 per mSv/y
ie the excess relative risk is ERR = RR-1 = 10.0% per mSv/y
The following table shows the estimates of RR obtained by regressions with
model (2) for
1. all malignancies (both genders, males, females)
2. lung cancers (both genders, males, females)
3. all but lung cancers (both genders, males, females)
|
ODL |
SE |
RR |
95%
CI |
| all
malignancies |
0,0950 |
0,0294 |
1,0997 |
1,0284 |
1,1759 |
| all
malignancies, males |
0,1834 |
0,0351 |
1,2013 |
1,1091 |
1,3013 |
| all
malignancies, females |
0,0141 |
0,0303 |
1,0142 |
0,9465 |
1,0867 |
| lung
cancers |
0,1394 |
0,0619 |
1,1496 |
0,9982 |
1,3240 |
| lung
cancers, males |
0,2667 |
0,0660 |
1,3056 |
1,1231 |
1,5177 |
| lung
cancers, females |
-0,1621 |
0,1086 |
0,8504 |
0,6639 |
1,0892 |
| all
but lung cancers |
0,0904 |
0,0292 |
1,0946 |
1,0241 |
1,1699 |
| all
but lung cancers, males |
0,1278 |
0,0348 |
1,1363 |
1,0495 |
1,2303 |
| all
but lung cancers, females |
0,0379 |
0,0310 |
1,0386 |
0,9677 |
1,1146 |
|