Comparison of Approaches to Weight Truncation for Marginal Structural Cox Models

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Abstract
Marginal structural Cox Models (Cox MSMs) have been used to estimate the causal effect of a time-varying treatment on the hazard when there exist time-dependent confounders, which are themselves also affected by previous treatment. A Cox MSM can be estimated via the inverse-probability-of-treatment weighting (IPTW) estimator. However, IPTW estimators suffer from large variability if some observations are assigned extremely high weights. Weight truncation has been proposed as one simple solution to this problem, but truncation levels are typically chosen based on ad hoc criteria that have not been systematically evaluated. Bembom et al. proposed data-adaptive selection of the optimal truncation level using the estimated mean-squared error (MSE) of a truncated IPTW estimator for cross-sectional data. Based on a similar principle, we proposed data-adaptive approaches to select the truncation level that minimizes the expected MSE for time-to-event data with time-varying treatments. The expected MSE is approximated by using either observed statistics as a proxy for the true unknown parameter or using cross-validation. Simulations confirm that simple weight truncation at high percentiles such as the 99th or 99.5th of the distribution of weights improves the IPTW estimators in most scenarios we considered. Our newly proposed approaches exhibit similarly good performance and may be applied in a wide range of settings.

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