ANALYSIS OF SEMIPARAMETRIC REGRESSION-MODELS WITH NON-IGNORABLE NONRESPONSE

In this article we consider the problem of making inferences about the parameter beta(0) indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables (outcome or covar iates) are missing for some study subjects and the probability of non- response depends upon both observed and unobserved data values, that i s, non-response is non-ignorable, We propose a new class of inverse pr obability of censoring weighted estimators that are consistent and asy mptotically normal (CAN) for estimating beta(0) when the non-response probabilities can be parametrically modelled and a CAN estimator exist s. The proposed estimators do not require full specification of the li kelihood and their computation does not require numerical integration. We show that the asymptotic variance of the optimal estimator in our class attains the semi-parametric variance bound for the model, In som e models, no CAN estimator of beta(0) exists. We provide a general alg orithm for determining when CAN estimators of beta(0) exist. Our resul ts follow after specializing a general representation described in the article for the efficient score and the influence function of regular , asymptotically linear estimators in an arbitrary semi-parametric mod el with non-ignorable non-response in which the probability of observi ng complete data is bounded away from zero and the non-response probab ilities can be parametrically modelled.