  In empirical studies with time-to-event outcomes, investigators often
leverage observational data to conduct causal inference on the effect of
exposure when randomized controlled trial data is unavailable. Model
misspecification and lack of overlap are common issues in observational
studies, and they often lead to inconsistent and inefficient estimators of the
average treatment effect. Estimators targeting overlap weighted effects have
been proposed to address the challenge of poor overlap, and methods enabling
flexible machine learning for nuisance models address model misspecification.
However, the approaches that allow machine learning for nuisance models have
not been extended to the setting of weighted average treatment effects for
time-to-event outcomes when there is poor overlap. In this work, we propose a
class of one-step cross-fitted double/debiased machine learning estimators for
the weighted cumulative causal effect as a function of restriction time. We
prove that the proposed estimators are consistent, asymptotically linear, and
reach semiparametric efficiency bounds under regularity conditions. Our
simulations show that the proposed estimators using nonparametric machine
learning nuisance models perform as well as established methods that require
correctly-specified parametric nuisance models, illustrating that our
estimators mitigate the need for oracle parametric nuisance models. We apply
the proposed methods to real-world observational data from a UK primary care
database to compare the effects of anti-diabetic drugs on cancer clinical
outcomes.
