Inverse probability weighted estimating equations and multiple imputation are two of the most studied frameworks for dealing with incomplete data in clinical and epidemiological research. We examine the limiting behaviour of estimators arising from inverse probability weighted estimating equations, augmented inverse probability weighted estimating equations, and multiple imputation when the requisite auxiliary models are misspecified. We present specific limiting values for settings involving binary responses and covariates and illustrate the effects of model misspecification using simulations based on data from a breast cancer clinical trial. We demonstrate that the asymptotic bias of the double-robust augmented inverse probability weighted estimator is often smaller than the asymptotic biases of estimators arising from inverse probability weighting or multiple imputation, even when both auxiliary models are misspecified. These asymptotic results are shown to be consistent with empirical results from simulation studies.
Analyses of Incomplete Data with Incorrect Auxiliary Models