Appendix B:
Method of Combining Data from Studies of Environmental Tobacco Smoke Exposure and Lung Cancer
Consider the following kinds of data that might be reported in an epidemiological study of chronic exposure to environmental tobacco smoke (ETS) and lung cancer:

Lung Cancer 
Total 

Yes 
No 

Exposure to ETS 
Yes 
a 
b 
m_{1} 
No 
c 
d 
m_{2} 

Total: 

m_{3} 
m_{4} 
T 
Therefore, T is the total number of people in the study, a is the number of people chronically exposed to ETS who also have lung cancer, b is the number of people chronically exposed to ETS who do not have lung cancer, c is the number of people not chronically exposed to ETS who have lung cancer, and d is the number of people not chronically exposed to ETS who do not have lung cancer. The marginal totals are m_{1}=a+b, m_{2}=c+d, m_{3}=a +c, and m_{4}=b+d. The data that correspond to these variables from all of the studies examined in Chapter 12 are shown in Table B1.
CASECONTROL STUDIES
In a casecontrol design, the subjects are chosen on the basis of the health outcome, and their exposure history is assessed.
TABLE B1 Passive Smoking and Lung Cancer: Observed Numbers Used to Calculate Values in Table 12–4^{a}
The expected number of people who are exposed to environmental tobacco smoke and develop lung cancer is given by:
Expected numbers for each of the studies are shown in Table 12–4. The difference between observed and expected numbers of people with lung cancer who are exposed to ETS can be calculated, and the variance of this difference is given by:
Therefore, the natural logarithm of the odds ratio (ψ) can be estimated by:
and the variance of this estimate is given by:
Variance of ψ=[(Variance(Observed−Expected)]^{−1} (Yusuf et al., 1985).
The odds ratio is estimated by exp[ψ] and is shown in Tables 12–4 (and B1) with its 95% confidence intervals for each of the studies.
PROSPECTIVE (OR COHORT) STUDIES
In prospective studies, also known as cohort studies, the subjects are classified (or chosen) on the basis of exposure and the health endpoint is then assessed.
In all of the articles the authors have estimated the relative risk, adjusting for such variables as age. Therefore, the published relative risk values were used in the following calculations rather than the estimates of the crude relative risk that could be calculated from the data given in the text. For those studies where a relative risk estimate was given for different levels of smoking by the spouse (Garfinkel et al, 1981; Hirayama, 1984), a combined estimate of the relative risk was calculated using the method given below for combining the prospective studies.
The number of people who are exposed to ETS who are expected, under the null hypothesis of no effect, to develop lung cancer is:
where E is the expected number for m_{3}, based on the published relative risk (RR), that is:
The approximate variance of the observed minus expected numbers of people with lung cancer who are exposed to environmental tobacco smoke is:
The variance of the natural logarithm of the relative risk was calculated using the published confidence limits for the estimate of the relative risk, except for one study (Gillis et al., 1984), where the method given above for the casecontrol studies use used since no confidence limits were available.
SUMMING OVER STUDIES
The overall values for the casecontrol studies were calculated by adding the values of Observed−Expected (i.e., O−E) and their variance for the individual studies as follows:
and for the variance:
(Yusuf et al., 1985).
For the prospective studies, the overall value for the ln RR was calculated as:
and for the variance:
(Kleinbaum et al., 1982).
The overall value, for all of the studies combined, was obtained
using the same method as was used to pool results from the prospective studies using the overall values for the casecontrol and prospective studies in the above equations.
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