Semiparametric regression for repeated outcomes with nonignorable nonresponse

We consider inference about the parameter beta* indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values; that is, nonresponse is nonignorable. We propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal (CAN) for estimating beta* when the response probabilities can be parametrically modeled and a CAN estimator exists. The proposed estimators do not require full specification of a parametric likelihood, and their computation does not require numerical integration. Our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse. We show that our class essentially consists of all CAN estimators of beta*. We also show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model. When the model for nonresponse is richly parameterized, joint estimation of the regression parameter beta* and the nonresponse model parameter tau* which encodes the magnitude of nonignorable selection bias, may be difficult or impossible. Therefore we propose regarding the selection bias parameter tau* as known, rather than estimating it from the data. We then perform a sensitivity analysis that examines how inference concerning the regression parameter beta* changes as we vary tau* over a range of plausible values. We apply our approach to the analysis of ACTG Trial 002, an AIDS clinical trial.