摘要：Observational studies of relatively large data can have potentiallyhidden heterogeneity with respect to causal e ects and propensityscores{patterns of a putative cause being exposed to study subjects. Thisunderlying heterogeneity can be crucial in causal inference for any observationalstudies because it is systematically generated and structured bycovariates which inuence the cause and/or its related outcomes. Addressingthe causal inference problem in view of data structure, machine learningtechniques such as tree analysis can be naturally necessitated. Kang, Su,Hitsman, Liu and Lloyd-Jones (2012) proposed Marginal Tree (MT) procedureto explore both the confounding and interacting e ects of the covariateson causal inference. In this paper, we extend the MT method to the case ofbinary responses along with a clear exposition of its relationship with establishedcausal odds ratio. We assess the causal e ect of dieting on emotionaldistress using both a real data set from the Lalonde's National SupportedWork Demonstration Analysis (NSW) and a simulated data set from theNational Longitudinal Study of Adolescent Health (Add Health).
关键词：Binary potential outcomes; causal inference; maximum likelihood;tree; propensity scores.
