| Abstract: | Prentice and Pyke (1979) showed that the logistic slope estimates with case-control sampling may be estimated from a standard prospective logistic regression and that the resulting standard errors are asymptotically correct. We extend the results to (i) robustness in classical case-control studies; (ii) robust case-control studies with response-dependent weights; (iii) robustness in measurement error case-control studies; (iv) likelihoods in measurement error case-control studies. In (i), we consider robustness with Mallows-type weights which downweigh high-leverage points. In (ii), we investigate the proposal of Kunsch, Stefanski and Carroll (1989) whose weights depend on case-control status. In (iii), we apply the methods of Simpson, Ruppert and Carroll (1992) and Carroll and Pederson (1993) to the case when the true predictor is an unobserved continuous random variable and in its place a surrogate is observed with nondifferential measurement error. In (iv), we compare our method with a conditional likelihood due to Satten and Kupper (1993). In all applications, estimated standard errors obtained by formulae for prospective analysis are asymptotically correct. |
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