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 B-1) with its 95% confidence intervals for each of the 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:

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