Estimation of individual causal effects in observational longitudinal studies

Causal effect sizes may vary among individuals and they can even be of opposite directions. When there exists serious effect heterogeneity, the population average causal effect (ACE) is not very informative. It is well-known that individual causal effects (ICEs) cannot be determined in cross-sectional studies, but we will show that ICEs can be retrieved from longitudinal data under certain conditions. We will present a general framework for individual causality where we will view effect heterogeneity as an individual-specific effect modification that can be parameterized with a latent variable, the receptiveness factor. The distribution of the receptiveness factor can be retrieved, and it will enable us to study the contrast of the potential outcomes of an individual under stationarity assumptions. Within the framework, we will study the joint distribution of the individual's potential outcomes conditioned on all individual's factual data and subsequently the distribution of the cross-world causal effect (CWCE). We discuss conditions such that the latter converges to a degenerated distribution, in which case the ICE can be estimated consistently. To demonstrate the use of this general framework, we present examples in which the outcome process can be parameterized as a (generalized) linear mixed model.