Marginal Structural Models for Multi-level Clustered Data

Yujie Wu, Benjamin Langworthy, Molin Wang

Abstract: Marginal Structural Models (MSMs), which adopt inverse probability treatment weighting in the estimating equations, are powerful tools to estimate the causal effects of time-varying exposures in the presence of time-dependent confounders. Motivated by the Conservation of Hearing Study (CHEARS) Audiology Assessment Arm (AAA) where repeated hearing measurements were clustered by study participants, time and testing sites, we propose two methods to account for the multi-level correlation structure when fitting the MSMs. The first method directly models the co- variance of the repeated outcomes when solving the weighted generalized estimating equations for MSMs, while the second two-stage analysis approach fits cluster-specific MSMs first and then combines the estimated parameters using mixed effects meta-analysis. Finite sample simulation results suggest that our methods can obtain less biased and more efficient estimates of the parameters by accounting for the multi-level correlation. Moreover, we explore the effects of using fixed or mixed effects model to estimate the treatment probability on the parameter estimates of the MSMs in the presence of unmeasured cluster level confounders. Lastly, we apply our methods to the CHEARS AAA dataset, to estimate the causal effects of aspirin use on hearing loss.