Prospective and retrospective analyses under logistic regression models

In logistic case–control studies, Prentice and Pyke (Biometrika 66 (1979) 403–411) showed that valid point estimators of the odds-ratio parameters and their standard errors may be obtained by fitting the prospective logistic regression model to case–control data. Wang and Carroll (Biometrika 80 (1993) 237–241; J. Statist. Plann. Inference 43 (1995) 331–340) generalized Prentice and Pykeʹs (Biometrika 66 (1979) 403–411) results to robust logistic case–control studies. In this paper, we extend the results of Prentice and Pyke (Biometrika 66 (1979) 403–411) and Wang and Carroll (Biometrika 80 (1993) 237–241; J. Statist. Plann. Inference 43 (1995) 331–340) to a class of statistics and a class of unbiased estimating equations. We present some results on simulation and on the analysis of two real datasets.