Regression-Based Adjustment for Time-Varying Confounders
Geoff Wodtke, University of Toronto
UT Sociology Working Paper No. 2017-01
Keywords: marginal structural models, structural nested mean models, inverse probability of treatment weighting, regression with residuals, time-varying confounders
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, the inverse-probability-of-treatment-weighted (IPTW) estimator 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 proposes an alternative regression-based estimator – two-stage regression-with-residuals (RWR) – 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 the RWR estimator relative to the IPTW estimator 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 the IPTW estimator, at least in certain situations.