Regression-based Adjustment for Time-varying Confounders

Abstract

Social scientists are often interested in estimating the marginal effects of a time-varying treatment on an end-of-study continuous outcome. With observational data, estimating these effects is complicated by the presence of time-varying confounders affected by prior treatments, which may lead to bias in conventional regression and matching estimators. In this situation, inverse-probability-of-treatment-weighted (IPTW) estimation of a marginal structural model remains unbiased if treatment assignment is sequentially ignorable and the conditional probability of treatment is correctly modeled, but this method is not without limitations. In particular, it is difficult to use with continuous treatments, and it is relatively inefficient. This article explores using an alternative regression-based method—regression-with-residuals (RWR) estimation of a constrained structural nested mean model—that may overcome some of these limitations in practice. It is unbiased for the marginal effects of a time-varying treatment if treatment assignment is sequentially ignorable, the treatment effects of interest are invariant across levels of the confounders, and a model for the conditional mean of the outcome is correctly specified. The performance of RWR estimation relative to IPTW estimation is evaluated with a series of simulation experiments and with an empirical example based on longitudinal data from the Panel Study of Income Dynamics. Results indicate that it may outperform IPTW estimation in certain situations.