ON ROBUST ESTIMATION IN LOGISTIC CASE-CONTROL STUDIES

Consider a logistic regression model under case-control sampling. Prentice & Pyke (1979) showed that the logistic slope estimates with case-control sampling may be estimated from a standard prospective logistic regression program and that the resulting standard errors are asymptotically correct. Since logistic regression estimates are nonrobust, we propose and analyze robust estimates of the slope parameters. We focus specifically on estimates which downweight observations on one of three factors: (i) leverage, (ii) extreme fitted values, and (iii) likelihood of misclassification. In the prospective framework, all these estimates have easily computed asymptotic covariance matrices. We compute the asymptotic distribution theory for such robust estimates under the case-control sampling scheme, showing that they are consistent and asymptotically normally distributed. In addition, we show that the prospective formulae for asymptotic covariance estimates may be used without modification in case-control studies.