- Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling
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- Abstract:
Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.
- Suggested Citation:
- Norm Breslow, Brad McNeney, and Jon A. Wellner,
"Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling"
(February 22, 2002).
UW Biostatistics Working Paper Series.
Working Paper 183.
http://www.bepress.com/uwbiostat/paper183