Estimating multiple time-fixed treatment effects using a semi-Bayes semiparametric marginal structural Cox proportional hazards regression model

Marginal structural models for time-fixed treatments fit using inverse-probability weighted estimating equations are increasingly popular. Nonetheless, the resulting effect estimates are subject to finite-sample bias when data are sparse, as is typical for large-sample procedures. Here we propose a semi-Bayes estimation approach which penalizes or shrinks the estimated model parameters to improve finite-sample performance. This approach uses simple symmetric data-augmentation priors. Limited simulation experiments indicate that the proposed approach reduces finite-sample bias and improves confidence-interval coverage when the true values lie within the central "hill" of the prior distribution. We illustrate the approach with data from a nonexperimental study of HIV treatments.