Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

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 agrees 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. 1 Research supported in part by USPHS grant 5-R01-CA40644 2 Research supported in part by USPHS grants R01-CA51692 and R01-AI31789 3 Research supported in part by National Science Foundation grant DMS-9532039, NIAID grant 2R01 AI29196804, and the Stieltjes Institute. AMS 2000 subject classifications. Primary: 60F05, 60F17; secondary 60J65, 60J70.