Joint calibrated estimation of inverse probability of treatment and censoring weights for marginal structural models

Marginal structural models (MSMs) with inverse probability weighting offer an approach to estimating causal effects of treatment sequences on repeated outcome measures in the presence of time-varying confounding and dependent censoring. However, when weights are estimated by maximum likelihood, inverse probability weighted estimators (IPWEs) can be inefficient and unstable in practice. We propose a joint calibration approach for inverse probability of treatment and censoring weights to improve the efficiency and robustness of the IPWEs for MSMs with time-varying treatments of arbitrary (i.e., binary and non-binary) distributions. Specifically, novel calibration restrictions are derived by explicitly eliminating covariate associations with both the treatment assignment process and the censoring process after weighting the current sample (i.e., to optimise covariate balance in finite samples). A convex minimization procedure is developed to implement the calibration. Simulations show that IPWEs with calibrated weights perform better than IPWEs with weights from maximum likelihood. We apply our method to a natural history study of HIV for estimating the cumulative effect of highly active antiretroviral therapy on CD4 cell counts over time.