On the distribution of individual causal effects of binary exposures using latent variable models

In recent years the field of causal inference from observational data has emerged rapidly. This literature has focused on (conditional) average causal effect estimation. When (remaining) variability of individual causal effects (ICEs) is considerable, average effects may be less informative, and possibly misleading for an individual. The fundamental problem of causal inference precludes the estimation of the joint distribution of potential outcomes without making assumptions, while this distribution is necessary to describe the heterogeneity of causal effects. In this paper, we describe these assumptions and present a family of flexible latent variable models that can be used to study individual effect modification and estimate the ICE distribution from cross-sectional data. We will also discuss how the distribution is affected by misspecification of the error distribution or ignoring possible confounding-effect heterogeneity. How latent variable models can be applied and validated in practice is illustrated in a case study on the effect of Hepatic Steatosis on a clinical precursor to heart failure. Assuming that there is (i) no unmeasured confounding and (ii) independence of the individual effect modifier and the potential outcome under no exposure, we conclude that the individual causal effect distribution deviates from Gaussian. We estimate that the `treatment' benefit rate in the population is 23.7% (95% Bayesian credible interval: 2.6%, 53.7%) despite a harming average effect.