  The positivity assumption, or the experimental treatment assignment (ETA)
assumption, is important for identifiability in causal inference. Even if the
positivity assumption holds, practical violations of this assumption may
jeopardize the finite sample performance of the causal estimator. One of the
consequences of practical violations of the positivity assumption is extreme
values in the estimated propensity score (PS). A common practice to address
this issue is truncating the PS estimate when constructing PS-based estimators.
In this study, we propose a novel adaptive truncation method,
Positivity-C-TMLE, based on the collaborative targeted maximum likelihood
estimation (C-TMLE) methodology. We demonstrate the outstanding performance of
our novel approach in a variety of simulations by comparing it with other
commonly studied estimators. Results show that by adaptively truncating the
estimated PS with a more targeted objective function, the Positivity-C-TMLE
estimator achieves the best performance for both point estimation and
confidence interval coverage among all estimators considered.
