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In sequential causal inference, one estimates the causal net effect oftreatment in treatment sequence on an outcome after last treatment in thepresence of time-dependent covariates between treatments, improves theestimation by the untestable assumption of strongly ignorable treatmentassignment, and obtains consistent but non-genuine likelihood-based estimate.In this article, we introduce the net effect of treatment as parameter for theconditional distribution of outcome given all treatments and time-dependentcovariates and show that it is equal to the causal net effect of treatmentunder the assumption of strongly ignorable treatment assignment. As a result,we can estimate the net effect of treatment and evaluate its causalinterpretation in two separate steps. The first step is fucus of this articlewhile the second step can be accomplished by usual sensitivity analyses. Weconstruct point parametrization for the conditional outcome distribution inwhich the parameters of interest are the point effects of single-pointtreatments. With point parametrization and without the untestable assumption,we estimate the net effect of treatment by maximum likelihood, improve theestimation by testable pattern of the net effect of treatment, and obtainunbiased consistent maximum-likelihood estimate for the net effect of treatmentwith finite-dimensional pattern.

Estimating Net Effects of Treatments in Treatment Sequence without the Assumption of Strongly Ignorable Treatment Assignment