On information matrices in case-control studies

In this paper we investigate the properties of the information matrices and asymptotic covariances of the constrained maximum likelihood estimates (MLE) in case-control studies. Since in a case-control study samples are stratified on case-control status, the sampling scheme is different from the usual simple random sampling. It is shown that the relationship between the information and asymptotic covariances of the MLEs in the usual unconstrained likelihood theory applies to case-control studies. Furthermore, this property holds in nondifferential measurement error models.