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

Marginal structural models (MSMs) with inverse probability weighted estimators (IPWEs) are widely used to estimate causal effects of treatment sequences on longitudinal outcomes in the presence of time-varying confounding and dependent censoring. However, IPWEs for MSMs can be inefficient and unstable if weights are estimated by maximum likelihood. To improve the performance of IPWEs, covariate balancing weight (CBW) methods have been proposed and recently extended to MSMs. However, existing CBW methods for MSMs are inflexible for practical use because they often do not handle dependent censoring, nonbinary treatments, and longitudinal outcomes (instead of eventual outcomes at a study end). In this paper, we propose a joint calibration approach to CBW estimation for MSMs that can accommodate (1) both time-varying confounding and dependent censoring, (2) binary and nonbinary treatments, (3) eventual outcomes and longitudinal outcomes. We develop novel calibration restrictions by jointly eliminating covariate associations with both treatment assignment and censoring processes after weighting the observed data sample (i.e., to optimize covariate balance in finite samples). Two different methods are proposed to implement the calibration. Simulations show that IPWEs with calibrated weights perform better than IPWEs with weights from maximum likelihood and the "Covariate Balancing Propensity Score" method. We apply our method to a natural history study of HIV for estimating the effects of highly active antiretroviral therapy on CD4 cell counts over time.