Fitting regression models to case-control data by maximum likelihood. (English) Zbl 1058.62505

Summary: We consider fitting categorical regression models to data obtained by either stratified or nonstratified case-control, or response selective, sampling from a finite population with known population totals in each response category. With certain models, such as the logistic with appropriate constant terms, a method variously known as conditional maximum likelihood (Breslow and Cain, 1988) or pseudo-conditional likelihood (Wild, 1991), which involves the prospective fitting of a pseudo-model, results in maximum likelihood estimates of case-control data. We extend these results by showing the maximum likelihood estimates for any model can be found by iterating this process with a simple updating of offset parameters. Attention is also paid to estimation of the asymptotic covariance matrix. One benefit of the results of this paper is the ability to obtain maximum likelihood estimates of the parameters of logistic models for stratified case-control studies, using an ordinary logistic regression program, even when the stratum constants are modelled.


62D05 Sampling theory, sample surveys
62F10 Point estimation
62J12 Generalized linear models (logistic models)
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