Post-Hoc Analyses in Clinical Trials, a Case for Logistic Regression Analysis

Multivariate methods are used to adjust asymmetries in the patient characteristics in a trial. It can also be used for a subsequent purpose. In many trials simple primary hypotheses in terms of efficacy and safety expectations, are tested through their respective outcome variables as described in the protocol. However, sometimes it is decided already at the design stage that post hoc analyses will be performed for the purpose of testing secondary hypotheses. E.g., suppose we first want to know whether a novel beta-blocker is better than a standard beta-blocker, and second, if so, whether this better effect is due to a vasodilatory property of the novel compound. The first hypothesis is assessed in the primary (univariate) analysis. For the second hypothesis, we can simply adjust the two treatment groups for difference in vasodilation by multiple regression analysis and see whether differences in treatment effects otherwise are affected by this procedure. However, with small data power is lost by such procedure. More power is provided by the following approach. We could assign all of the patients to two new groups: patients who actually have improvement in the primary outcome variable and those who have not, irrespective of the type of beta-blocker. We, then, can perform a regression analysis of the two new groups trying to find independent determinants of this improvement. If the dependent determinant is binary, which is generally so, our choice of test is logistic regression analysis. Testing the second hypothesis is, of course, of lower validity than testing the first one, because it is post-hoc and makes use of a regression analysis which does not differentiate between causal relationships and relationships due to an unknown common factor.