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

• Activity Number: 355
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Norman Breslow*+ and Brad Mc Neney and Jon A. Wellner
• Companies: University of Washington and Simon Frazer University and University of Washington, Seattle
• Keywords: asymptotic ; efficiency ; missing data ; two-phase

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 assessment. 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). 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. Some details are provided for the special case of logistic regression. In related work, we show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient.