Abstract: The average treatment effect (ATE) is commonly used to assess the effect of treatment. However, the ATE implicitly assumes a homogenous treatment effect even amongst individuals with different characteristics. In order to describe the magnitude of heterogeneity, we define the treatment benefit rate (TBR) as the proportion of individuals in different subgroups who benefit from the treatment and define the treatment harm rate (THR) as the proportion harmed. These rates involve the joint distribution of the potential outcomes and cannot be identified without further assumptions, even in randomized clinical trials. Under the assumption that the potential outcomes are independent conditional on the observed covariates and an unmeasured latent variable, we show the identification of the TBR and THR in non-separable (generalized) linear mixed models for both continuous and binary outcomes. We then propose estimators and derive their asymptotic distributions. The proposed methods are implemented in an extensive simulation study and two randomized controlled trials.

Key words and phrases: Average treatment effect, causal inference, heterogeneity, latent variable.