Estimating survival parameters under conditionally independent left truncation

Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias induced due to patients needing to survive long enough to satisfy certain entry criteria. Standard methods to adjust for left truncation bias rely on an assumption of marginal independence between entry and survival times, which may not always be satisfied in practice. In this work, we examine how a weaker assumption of conditional independence can result in unbiased estimation of common statistical parameters. In particular, we show the estimability of conditional parameters in a truncated dataset, and of marginal parameters that leverage reference data containing non-truncated data on confounders. The latter is complementary to observational causal inference methodology applied to real world external comparators, which is a common use case for real world databases. We implement our proposed methods in simulation studies, demonstrating unbiased estimation and valid statistical inference. We also illustrate estimation of a survival distribution under conditionally independent left truncation in a real world clinico-genomic database.