Estimating survival parameters under conditionally independent left truncation

Abstract

Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias that occurs when patients need 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.

Keywords: left truncation; real world data; survival analysis.

FIGURE 1

Graphical illustrations of independent (left), dependent (center), and conditionally independent (right) left truncation

FIGURE 2

Relative bias for estimated conditional hazard ratio comparing non‐truncated arm (ground truth fit) to real‐world treatment arm across simulation settings

FIGURE 3

95% confidence interval coverage for estimated conditional hazard ratio comparing non‐ truncated arm (ground truth fit) to real‐world treatment arm across simulation settings

FIGURE 4

Relative bias for estimated marginal hazard ratio comparing non‐truncated arm to real‐world treatment arm across simulation settings

FIGURE 5

95% confidence interval coverage for estimated marginal hazard ratio comparing non‐truncated arm to real‐world treatment arm across simulation settings

FIGURE 6

Relative bias for estimated median survival time in real‐world treatment arm across simulation settings

FIGURE 7

Covariate balance plot comparing FH and CGDB cohorts, displaying both weighted and unweighted absolute standardized mean differences. A threshold of 0.1 is used to indicate balance