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ANALYSIS OF SEMI-PARAMETRIC REGRESSION MODELS WITH NON-IGNORABLE NON-RESPONSE

โœ Scribed by ANDREA ROTNITZKY; JAMES ROBINS

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
427 KB
Volume
16
Category
Article
ISSN
0277-6715

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โœฆ Synopsis

In this article we consider the problem of making inferences about the parameter indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables (outcome or covariates) are missing for some study subjects and the probability of non-response depends upon both observed and unobserved data values, that is, non-response is non-ignorable. We propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal (CAN) for estimating when the non-response probabilities can be parametrically modelled and a CAN estimator exists. The proposed estimators do not require full specification of the likelihood 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 some models, no CAN estimator of exists. We provide a general algorithm for determining when CAN estimators of exist. Our results 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 model with non-ignorable non-response in which the probability of observing complete data is bounded away from zero and the non-response probabilities can be parametrically modelled.

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