Stratified Analysis

Confounding is a kind of bias that can create the appearance of a causal relationship between exposure and disease where there is none. It can occur when a confounder is a cause of the disease and exposure is associated with the confounder. Confounding can be controlled in the design of a study. Two mechanisms for doing that are matching and randomization. They control for confounding by removing the association between the confounder and exposure. Confounding can also be controlled in the analysis of study data. One way to do that is to stratify the data by the value of the confounder. If everyone has the same value of the confounder in a stratum, there can be no association between the confounder and exposure. For continuous confounders, each stratum must represent an interval of values of the confounder. Since there is still some variation in the value of the confounder in a stratum, there still can be some association with exposure. This leads to some uncontrolled confounding. This is called residual confounding. There are three steps in stratified analysis. First is creation of the strata by dividing the data into groups according to the value of the confounder. Second is estimation of the association within each stratum. Third is combining the strata-specific estimates to obtain a summary estimate to apply to all strata. There are two kinds of summary estimates: precision-based and Mantel–Haenszel. Mantel–Haenszel is easier to calculate, and it is the one provided by RR. Combining strata-specific estimates to obtain a summary estimate only makes sense if the strata-specific values in the population are all equal. If they are not, we have effect modification. If there is effect modification, we should report the strata-specific estimates rather than calculate a summary estimate. To evaluate for effect modification, we can visually compare strata-specific estimates or we can do a formal test of homogeneityHomogeneity. If we fail to reject the null hypothesis in a test of homogeneity, we conclude that there is no effect modification, and we can report the summary estimate rather than strata-specific results. To test the null hypotheses that the risk ratio and the odds ratioOdds ratio are equal to one in the population, we use the Mantel–Haenszel test. If there is no effect modification this Mantel–Haenszel test can be performed over all the strata.