  In sequential causal inference, one estimates the causal net effect of
treatment in treatment sequence on an outcome after last treatment in the
presence of time-dependent covariates between treatments, improves the
estimation by the untestable assumption of strongly ignorable treatment
assignment, and obtains consistent but non-genuine likelihood-based estimate.
In this article, we introduce the net effect of treatment as parameter for the
conditional distribution of outcome given all treatments and time-dependent
covariates and show that it is equal to the causal net effect of treatment
under the assumption of strongly ignorable treatment assignment. As a result,
we can estimate the net effect of treatment and evaluate its causal
interpretation in two separate steps. The first step is fucus of this article
while the second step can be accomplished by usual sensitivity analyses. We
construct point parametrization for the conditional outcome distribution in
which the parameters of interest are the point effects of single-point
treatments. With point parametrization and without the untestable assumption,
we estimate the net effect of treatment by maximum likelihood, improve the
estimation by testable pattern of the net effect of treatment, and obtain
unbiased consistent maximum-likelihood estimate for the net effect of treatment
with finite-dimensional pattern.
