Treatment heterogeneity and individual qualitative interaction

Abstract

The potential for high variability in treatment effects across individuals has been recognized as an important consideration in clinical studies. Surprisingly, little attention has been given to evaluating this variability in design of clinical trials or analyses of resulting data. High variation in a treatment’s efficacy or safety across individuals (referred to herein as treatment heterogeneity) may have important consequences because the optimal treatment choice for an individual may be different from that suggested by a study of average effects. We call this an individual qualitative interaction (IQI), borrowing terminology from earlier work - referring to a qualitative interaction (QI) being present when the optimal treatment varies across ‘groups’ of individuals. At least three techniques have been proposed to investigate treatment heterogeneity: techniques to detect a QI, use of measures such as the density overlap of two outcome variables under different treatments, and use of cross-over designs to observe ‘individual effects.’ Connections, limitations, and the required assumptions are compared among these techniques through a quantity frequently referred to as subject-treatment (S-T) interaction, but shown here to be the probability of an IQI (PIQI). Their association is studied utilizing a potential outcomes framework that can add insights to results from usual data analyses and to study design features to more directly assess treatment heterogeneity. Particular attention is given to the density overlap of two outcome variables, each representing an individual’s ‘potential’ response under a different treatment. Connections are made between the overlap quantified as the proportion of similar responses (PSR) and the PIQI. Given a bivariate normal model, the maximum PIQI is shown to be an upper bound for ½ the PSR. Additionally, the characterization of a conditional PSR allows for the PIQI boundaries to be developed within subgroups defined over observable covariates so that the subset contribution to treatment heterogeneity may be identified. The possibility of similar boundaries is explored outside the normal model using the skew normal distribution. Furthermore, a bivariate PIQI is developed along with its PSR counterpart to help characterize treatment heterogeneity resulting from a bivariate response such as the efficacy and safety of a treatment.