Stratification for confounding--part 1: the Mantel-Haenszel formula

Abstract

Stratification allows to control for confounding by creating two or more categories or subgroups in which the confounding variable either does not vary or does not vary very much. The Mantel-Haenszel formula is applied in cohort and in case-control studies to calculate an overall, unconfounded, effect estimate of a given exposure for a specific outcome by combining stratum-specific relative risks (RR) or odds ratios (OR). Stratum-specific RRs or ORs are calculated within each stratum of the confounding variable and compared with the corresponding effect estimates in the whole group (that is, with the unstratified RR or OR). The use of the Mantel-Haenszel formula presents some limitations: (1) if there is more than a single confounder, the application of this formula is laborious and demands a relatively large sample size, and (2) this method requires continuous confounders to be constrained into a limited number of categories thus potentially generating residual confounding (a phenomenon particularly relevant when the variable is categorized into few strata). In the stratified analysis, residual confounding can be minimized by increasing the number of strata, a possibility strictly dependent on sample size.