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Primary Submission Category: Machine Learning and Causal Inference

Doubly Robust Inference for Hazard Ratio under Covariate-Induced Dependent Left Truncation with Machine Learning

Authors: Yuyao Wang, Andrew Ying, Ronghui Xu,

Presenting Author: Yuyao Wang*

In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. For comparing the time-to-event outcome between treatment groups, Cox proportional hazards models accounting for confounders are typically considered. While such Cox models have addressed confounding, the selection bias caused by left truncation still needs to be handled. The partial likelihood approach with risk set adjustment can properly handle left truncation under the conditional quasi-independent left truncation assumption that the truncation time and the event time are independent on the observed region given the covariates involved in the Cox model. However, this assumption can be violated when the dependence between the left truncation time and the event time is induced by other covariates. Inverse probability of truncation weighting (IPW) leveraging additional covariate information can be used in this case, but it is sensitive to misspecification of the truncation model. In this work, we propose an augmented IPW estimator that has doubly robust properties: 1) model double-robustness, that is, it is consistent and asymptotically normal (CAN) when one of the two nuisance models is correctly specified; 2) rate double-robustness, that is, it is CAN when both of the nuisance parameters are consistent and the error product rate under the two nuisance models is faster than root-n.