Correcting for a Baseline Difference in Group Comparisons on a Binary Outcome: Covariate Adjustment or Analysis of Change?

Effects of treatments or exposures are evaluated by comparing a treated or exposed group with a control group after treatment or exposure. A baseline group difference can be accounted for by covariate adjustment or by analyzing change from baseline. For quantitative outcomes these two methods can give contradictory results (Lord's paradox) and especially covariate adjustment is questionable for nonrandomized group comparisons. This paper explores analogous methods for the case of a binary outcome, specifically logistic regression of the outcome on group and baseline, ordinal regression of change from baseline on group, and mixed logistic regression and generalized estimating equations (GEE) for repeated measures. The methods were compared mathematically, conceptually in terms of causal diagrams and estimands, and numerically on fictitious scenarios that varied in whether groups differed at baseline and/or in change over time on the logodds scale. The methods were also compared on a smoking prevention study among school children. The scenario results were similar to those published for quantitative outcomes: Logistic regression of outcome on group and baseline gave almost the same results as mixed logistic regression and GEE without parameter for a baseline group difference. Ordinal regression of change from baseline gave almost the same results as mixed logistic regression and GEE allowing for a baseline group difference. These (near-)equivalences are in line with two mathematical proofs in this paper. Further, in data sets with a baseline group difference, covariate adjustment and change analysis led to contradictory conclusions. The results from the smoking prevention study confirmed the above results and showed Lord's paradox.