Estimating scaled treatment effects with multiple outcomes

In classical study designs, the aim is often to learn about the effects of a treatment or intervention on a single outcome; in many modern studies, however, data on multiple outcomes are collected without a priori preference given to any one. Such designs can be particularly useful in patient-centered research, where different outcomes might be more or less important to different patients. In this paper we propose scaled effect measures (via potential outcome notation) that translate effects on multiple outcomes to a common scale, using mean-variance and median-interquartile-range -based standardizations. We present efficient semiparametric (e.g., doubly robust) methods for estimating these scaled effects (and weighted average summary measures), and for testing the null hypothesis that treatment affects all outcomes equally. We also discuss methods for exploring how treatment effects depend on covariates (i.e., effect modification). In addition to describing semiparametric theory for our estimands and the asymptotic behavior of our estimators, we illustrate the methods in a simulation study. Importantly, and in contrast to much of the literature concerning effects on multiple outcomes, our methods are nonparametric and can be used not only in randomized trials but also in observational studies with high-dimensional covariates.