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Biometrika 1998 85(3):619-630; doi:10.1093/biomet/85.3.619
© 1998 by Biometrika Trust
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Inferences for case-control and semiparametric two-sample density ratio models

JING QIN

Department of Mathematics, University of Maryland College Park, Maryland 20742, U.S.A.jqin{at}math.umd.edu

We consider inference in general binary response regression models under retrospective sampling plans. Prentice & Pyke (1979) discovered that inference for the odds-ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective. We show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions. Also we link casecontrol sampling with a two-sample biased sampling problem, where the ratio of two densities is assumed to take a known parametric form. Connections between this model and the Cox proportional hazards model are pointed out. Large and small sample size behaviour of the proposed estimators is studied.

Key Words: Biased two-sample problem • Case-control data • Multiplicative-intercept risk model • Optimal estimating equation • Retrospective sampling


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