Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

Abstract

When outcomes are missing for reasons beyond an investigator's control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the relationships between the covariates and the outcome and use those relationships to predict the missing values. Another is to model the probabilities of missingness given the covariates and incorporate them into a weighted or stratified estimate. Doubly robust (DR) procedures apply both types of model simultaneously and produce a consistent estimate of the parameter if either of the two models has been correctly specified. In this article, we show that DR estimates can be constructed in many ways. We compare the performance of various DR and non-DR estimates of a population mean in a simulated example where both models are incorrect but neither is grossly misspecified. Methods that use inverseprobabilities as weights, whether they are DR or not, are sensitive to misspecification of the propensity model when some estimated propensities are small. Many DR methods perform better than simple inverseprobability weighting. None of the DR methods we tried, however, improved upon the performance of simple regression-based prediction of the missing values. This study does not represent every missing-data problem that will arise in practice. But it does demonstrate that, in at least some settings, two wrong models are not better than one.

Comparison of Propensity Score Methods and Covariate Adjustment

“…[21] As the name implies, this approach offers some robustness to model misspecification either in the PS or the outcome regression model. It is recommended [8,22] when using the propensity score as a covariate to also include individual covariates in the outcome regression model.…”

Transition of care from pre-dialysis prelude to renal replacement therapy: the blueprints of emerging research in advanced chronic kidney disease

“…This weighting aligns the distribution in the linked cohorts of the variables used in the treatment-probability model to match the distribution across different eGFR slopes. These weights can then be used in an outcome-regression model to obtain doubly robust (DR) estimates of effect [67]. DR estimation builds on the PS approach as used by Rosenbaum and Rubin [68] and the inverse probability of weighting (IPW) approach of Robins that is used in marginal structural models (MSM) [69,70].…”

Augmenting propensity score equations to avoid misspecification bias – Evidence from a Monte Carlo simulation

“…Furthermore, we also investigate the consequences of nonadditivity and nonlinearity in the outcome equation for the performance of the modified DW algorithm. To do this, the second simulation structure follows a setup developed by Kang and Schafer (2007) that has been slightly modified for our purposes. In contrast to Simulation 1, this setup includes fewer covariates 6 but allows for nonlinearities and nonadditivity in both the outcome and propensity score equations.…”