Model-Assisted Regression Estimators for Longitudinal Data with Nonignorable Dropout

Estimation with longitudinal Y having nonignorable dropout is considered when the joint distribution of Y and covariate X is nonparametric and the dropout propensity conditional on (Y, X) is parametric. We apply the generalised method of moments to estimate the parameters in the nonignorable dropout propensity based on estimating equations constructed using an instrument Z, which is part of X related to Y but unrelated to the dropout propensity conditioned on Y and other covariates. Population means and other parameters in the nonparametric distribution of Y can be estimated based on inverse propensity weighting with estimated propensity. To improve efficiency, we derive a model-assisted regression estimator making use of information provided by the covariates and previously observed Y-values in the longitudinal setting. The model-assisted regression estimator is protected from model misspecification and is asymptotically normal and more efficient when the working models are correct and some other conditions are satisfied. The finite-sample performance of the estimators is studied through simulation, and an application to the HIV-CD4 data set is also presented as illustration.