Treatment Heterogeneity and Individual Qualitative Interaction

Abstract

Plausibility of 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 a"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." We elucidate underlying connections among them, their limitations and some assumptions that may be required. We do so under a potential outcomes framework that can add insights to results from usual data analyses and to study design features that improve the capability to more directly assess treatment heterogeneity.

Figure 1

Plot of weight loss in kilograms (kg) at 12 weeks (positive values are a weight loss) versus baseline weight in kg. The fitted lines are from regressing X on Z and Y on Z. The vertical dashed line is at the sample mean baseline weight.

Figure 2

Illustration of the PSR using only the marginal distributions of X and Y (panel (a)) and at three values of baseline weight given in Table 1 (panels b – d).