Inference About Separable Causal Effects With Longitudinal Bivariate Ordinal Responses With Missingness and Censoring

Causal inference has gained extensive attention in various fields, including healthcare, epidemiology, and social sciences. While many methods have been developed, most research has been directed to handle data with a univariate response variable. This paper highlights the complication of handling causal inference with bivariate responses in the context of longitudinal studies, which can be further challenged by the presence of missingness and censoring. We begin by defining the overall treatment effect on bivariate responses and conceptualizing the treatment as having two components, each operating through different causal pathways. By using the decomposed treatment framework, we break down the overall treatment effect into the separable treatment effects on each response, which offers us a transparent interpretation with the sum of separable treatment effects equals twice the overall treatment effects. We establish that the separable treatment effect on each response can be identified using the observed data, provided our identification conditions. Subsequently, we employ the likelihood method to estimate the separable treatment effects and derive a hypothesis testing procedure to compare them. Finally, we conduct real data analysis and simulation studies to demonstrate the effectiveness of the proposed methods.