Accuracy of Conventional and Marginal Structural Cox Model Estimators: A Simulation Study

Abstract

Marginal structural models (MSM) provide a powerful tool to control for confounding by a time-dependent covariate without inappropriately adjusting for its role as a variable affected by treatment (Hernán et al., 2000). In this paper, we demonstrate that it is possible to fit a marginal structural Cox model directly, rather than the typical approach of using pooled logistic regression, using the weighted Cox proportional hazards function that has been implemented in standard software. To evaluate the performance of the marginal structural Cox model directly via inverse probability of treatment weighting, we conducted several simulation studies based on two data-generating models: one which replicates the simulations of Young et al. (2009) and an additional, more clinically plausible approach which mimics survival data with time-dependent confounders and time-varying treatment. Using the simulations, we illustrate the limitations of the conventional time-dependent Cox model and the MSM fitted via pooled logistic regression. Furthermore, we propose two novel normalized weights with the goal of reducing the MSM estimators' variability. The performance of the normalized weights is evaluated alongside the usual unstabilized and stabilized weights.