Estimation of Regression Coefficients When Some Regressors are not Always Observed

Bibliographic Data

ID23316241
AuthorsJames M Robins (0000-0001-6609-209X, a Harvard School of Public Health , Boston , MA , 02115), Andrea Rotnitzky (0009-0009-7272-6832, a Harvard School of Public Health , Boston , MA , 02115), Lue Ping Zhao (0000-0002-1387-7165, Fred Hutch Cancer Center)
Year1994
Volume89
Issue427
Pages846-866
Publication date1994-09-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueJournal of the American Statistical Association (JOURNAL)
Journal identifiersISSN: 0162-1459 • E-ISSN: 1537-274X
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/01621459.1994.10476818
OpenAlexW2039811614
LanguageEN
Citations received142
References cited39

In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0 of the conditional mean model when the data are missing at random in the sense of Rubin and the missingness probabilities are either known or can be parametrically modeled. We show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0, and then deriving a representation for the efficient score, the semiparametric variance bound, and the influence function of any regular, asymptotically linear estimator in this more general estimation problem. Because the optimal estimator depends on the unknown probability law generating the data, we propose locally and globally adaptive semiparametric efficient estimators. We compare estimators in our class with previously proposed estimators. We show that each previous estimator is asymptotically equivalent to some, usually inefficient, estimator in our class. This equivalence is a consequence of a proposition stating that every regular asymptotic linear estimator of α0 is asymptotically equivalent to some estimator in our class. We compare various estimators in a small simulation study and offer some practical recommendations.

Asymptotic distribution · Bounded function · Conditional expectation · Consistent estimator · Delta method · Efficient estimator · Estimating equations · Estimator · Minimum-variance unbiased estimator · Missing data · Semiparametric model · Semiparametric regression · Statistics · Advanced Statistical Methods and Models · Applied Mathematics · Mathematics · Statistical Methods and Bayesian Inference · Statistical Methods and Inference