EFFICIENCY COMPARISONS IN MULTIVARIATE MULTIPLE-REGRESSION WITH MISSING OUTCOMES

We consider a Follow-up study in which an outcome variable is to be me asured at fixed time points and covariate values are measured prior to start of follow-up. We assume that the conditional mean of the outcom e given the covariates is a linear function of the covariates and is i ndexed by occasion-specific regression parameters. In this paper we st udy the asymptotic properties of several frequently used estimators of the regression parameters, namely the ordinary least squares (OLS), t he generalized least squares (GLS), and the generalized estimating equ ation (GEE) estimators when the complete vector of outcomes is not alw ays observed, the missing data patterns are monotone and the data are missing completely at random (MCAR) in the sense defined by Rubin [11] . We show that when the covariance of the outcome given the covariates is constant, as opposed to tile nonmissing data case: (a) the GLS est imator is more efficient than the OLS estimator, (b) the GLS estimator is inefficient, and (c) the semiparametric efficient estimator in a m odel that imposes linear restrictions only on the conditional mean of the last occasion regression can be less efficient than the efficient estimator in a model that imposes linear restrictions on the condition al means of all the outcomes. We provide formulae and calculations of the asymptotic relative efficiencies of the considered estimators in t hree important cases: (1) for the estimators of the occasion-specific means, (2) for estimators of occasion-specific mean differences, and ( 3) for estimators of occasion-specific dose-response model parameters. (C) 1997 Academic Press.