On the semi-parametric efficiency of logistic regression under case-control sampling. (English) Zbl 0965.62033

Breslow, Norman E.; Robins, James M.; Wellner, Jon A.

Bernoulli 6, No. 3, 447-455 (2000).

Summary: Using modern theory for semi-parametric models, we provide details for an argument of J.M. Robins et al. [J. Am. Stat. Assoc. 89, No. 427, 846-866 (1994; Zbl 0815.62043)] showing efficiency of the standard logistic regression estimator applied to data from case-control studies. Our elaboration of this argument, and of a related one by P.J. Bickel et al. [Efficient and adaptive estimation for semiparametric models. (1993; Zbl 0786.62001)], includes a constructive new proof of the result.

MSC:

62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference
62J12	Generalized linear models (logistic models)

Keywords:

biased sampling; epidemiology; influence function

Citations:

Zbl 0815.62043; Zbl 0786.62001