Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators

Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate L-t and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of L-t when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.