LOGISTIC ANALYSIS IN CASE-CONTROL STUDIES UNDER VALIDATION SAMPLING

This paper proposes an analysis of case-control data under a double-sa mpling scheme, when covariates are missing or measured with error at t he first stage of sampling and are validated at the second stage in a subsample. The method combines risk information from both samples. It is derived under the assumptions that (i) the prospective disease inci dence model is of logistic form, (ii) the proxy or partial information takes on finitely many values, and (iii) the error is nondifferential . The method of Prentice & Pyke (1979) is extended to a two-sample des ign to derive an estimating equation for the odds-ratio parameters. It provides an alternative estimator to that given by Breslow & Cain (19 88). Consistency and asymptotic normality of the estimates are derived and a variance formula is presented. Parameters can be estimated by u se of standard packages for quantal-response data. The method can easi ly be extended to the analysis of stratified designs with large strata .