305 In the previous chapter we discussed briefly how confounding could be dealt with at both the design stage of a study and during the analysis of the results. We then mentioned that there are two main statistical proce- dures that we can use in the analysis: stratification and regression modelling . In this chapter we will discuss these two approaches in more detail. Obviously, these techniques can be applied only if data on potential con- founding factors are available. Thus, potential confounding variables have to be identified at the design stage of the study to ensure that valid infor- mation on them is collected. A confounding factor is one that is related to both the exposure and the outcome variables and that does not lie on the causal pathway between them (see Section 13.2). Ignoring confounding when assessing the associ- ation between an exposure and an outcome variable can lead to an over- estimate or underestimate of the true association between exposure and outcome and can even change the direction of the observed effect. In , women with ovarian cancer had a much lower preva- lence of smoking (24/60 = 40%) compared with the controls (58/98 = 59%). This suggests that smoking protects against ovarian cancer (odds ratio (OR) = 0.46). As discussed in the previous chapter, there are several possible explanations for this finding: Chapter 14 Results of a case–control study on smoking and ovarian cancer: hypothet- ical data. 14.1 Introduction to stratification Example 14.1 Dealing with confounding in the analysis Example 14.1. In a hypothetical case–control study to examine the rela- tionship between smoking and ovarian cancer among nulliparous women, the results shown in Table 14.1 were obtained. Smoking Total Yes No Ovarian cancer cases 24 ( a ) 36 ( b ) 60 ( n 1 ) Controls 58 ( c ) 40 ( d ) 98 ( n 0 ) Total 82 ( m 1 ) 76 ( m 0 ) 158 ( N ) Crude odds ratio = (24/36) / (58/40)=0.46 95% confidence interval = 0.23–0.93 χ 2 = 5.45 on 1d.f.; P = 0.02 Table 14.1.
(i) Bias : the observed odds ratio of 0.46 does not accurately repre- sent the true odds ratio because of either selection or measurement bias. (ii) Chance : the observed association between smoking and ovarian cancer arose by chance. The 95% confidence interval around the observed odds ratio is equal to 0.23–0.93 and the χ 2 test yields P =0.02. Thus, chance is an unlikely explanation for the finding. (iii) Confounding : the observed odds ratio of 0.46 is due to the effect of another variable. For example, it may be that women who smoked were different in other respects from non-smokers and less likely to develop ovarian cancer because of this, rather than because of smoking. (iv) Causation : smoking reduces the risk of ovarian cancer and the 95% confidence interval indicates how precisely the sample estimate corresponds to the true effect in the population. In , it is possible that the association between smoking and ovarian cancer arose because of the confounding effect of other fac- tors such as oral contraceptive use. The results shown in are for all women combined regardless of their history of oral contraceptive use. To assess whether oral contraceptive use is a confounder, we need
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