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Parametric Sequential Causal Inference in Point Parametrization

Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments there exist time-dependent covariates that may be posttreatment variables of the earlier treatments and confounders of the subsequent treatments. In this article, we develop a parametric approach to inference of the causal effect of the treatment sequence on the outcome called the sequential causal effect. We construct a point parametrization for the conditional distribution of an outcome given all treatments and time-dependent covariates, in which the point parameters of interest are the point effects of treatments considered as single-point treatments. We (1) identify net effects of treatments by point effects of treatments, (2) express patterns of net effects of treatments by constraints on point effects of treatments, and (3) show that all sequential causal effects are determined by net effects of treatments. Accordingly we (1) estimate net effects of treatments through point effects of treatments by maximum likelihood, (2) improve the estimation by constraints on point effects of treatments and assignment conditions of treatments, and (3) use the estimates of net effects of treatments to obtain those of sequential causal effects. As a result, we obtain unbiased consistent maximum-likelihood estimates of sequential causal effects even for long treatment sequences. For illustration of our method, we study the causal effects of various sequences of recreational drugs on the CD4 count among HIV patients.