Interaction effects and subgroup analyses in clinical trials: more than meets the eye?

In clinical trials, it is common practice to follow up significant interactions between the factors under investigation with subgroup analyses. Such analyses pose at least two analytical and interpretational challenges. The first challenge is that performing multiple subgroup analyses increases the likelihood of obtaining spuriously significant results. This has been acknowledged and relevant guidance exists in the medical literature. The second challenge is that the effects that are obtained at the level of subgroup are composite. This has yet to be fully acknowledged and discussed in the context of medical research. This paper aims to fill this lacuna. Using a simple additive model, we use recent findings from the CHARISMA trial on the efficacy of clopidogrel in addition to aspirin in the treatment of patients at risk for atherothrombotic events to demonstrate quantitatively the composition of effects at the level of subgroups. In the simplest case of a design involving an interaction (two crossed factors, with two levels each, i.e. a 2 x 2 design), effects at the level of subgroup consist of influences that stem (i) from the incidence of the measured outcome in the study population as a whole; (ii) from the factor of interest (e.g. treatment vs. placebo); (iii) from the second factor (e.g. patient group membership); (iv) from the interaction between the two factors; and (v) from random error in the measured outcome. The value of the approach illustrated here is that it is generalizable to any research design irrespective of its complexity and that it prompts clinicians to consider the multiple causality underlying medical research findings.