Logistic Regression in a Semiparametric Model for Case-Control Data

• Activity Number: 9
• Type: Invited
• Date/Time: Sunday, August 2, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Eric J. Tchetgen*+ and Andrea Rotnitzky and James Robins
• Companies: Harvard University and Universidad Di Tella and Harvard University and Harvard School of Public Health
• Keywords: Doubly robust ; gene-environment independence ; local efficiency ; Influence functions ; Semi-parametric Theory ; gene-environment interaction

Abstract

We propose a new semiparametric framework for making inferences on the parameters indexing a logistic regression under case-control sampling in a model which partially restricts the population density of the regression covariates. Our approach improves on the method proposed by Chatterjee and Carroll (2005) as it yields a broad class of doubly robust estimators, which includes a semiparametric locally-efficient estimator. That is, our estimators remain consistent for the regression parameter, and asymptotically normal in a union model that assumes that at least one, but not necessarily both of two baseline conditional density functions of disjoint subsets of covariates is correctly modeled. At the intersection sub-model of the union model, where both baseline density models are correct, an element of our class of estimators achieves the semiparametric efficiency bound of the model.