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

Sean Yiu,Li Su

doi:10.1111/biom.13411

Abstract

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.

Highlights

Marginal structural models (MSMs) (Robins, 1999b; Robins et al, 2000) with inverse probability of treatment weighting (IPTW) are widely used to estimate causal effects of treatment sequences on a longitudinal outcome in the presence of time-varying confounders that are affected by treatment history
With dependent censoring, MSMs are estimated by IPTW and inverse probability of censoring weighting (IPCW) that addresses the additional selection bias from censoring (Hernan et al, 2001)
To implement IPTW and IPCW for MSMs, time-varying weights are commonly estimated by fitting parametric models for treatment assignment and censoring processes and plugging in parameter estimates from maximum likelihood estimation (MLE)

Summary

Introduction

Marginal structural models (MSMs) (Robins, 1999b; Robins et al, 2000) with inverse probability of treatment weighting (IPTW) are widely used to estimate causal effects of treatment sequences on a longitudinal outcome in the presence of time-varying confounders that are affected by treatment history (i.e., time-varying confounding, Hernan et al, 2001; Daniel et al, 2013). The MLE approach to weight estimation can result in inefficient and unstable inverse probability weighted estimators (IPWEs), especially when the treatment assignment and/or censoring model is misspecified (Kang and Schafer, 2007; Cole and Hernan, 2008; Lefebvre et al, 2008; Howe et al, 2011). Recent theoretical investigations by Tan (2020) reveal that, unlike the MLE approach, CBW methods can bound the MSEs of IPWEs even under model misspecification

Objectives

Results

Discussion

Conclusion