Nonparametric Regression in the Secondary Analysis of the Case-Control Studies

• Activity Number: 252
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shahina Rahman*+ and Raymond J. Carroll
• Companies: Texas A&M University and Texas A&M University
• Keywords: Case-control samples ; Heteroscedastic ; Nonparametric kernel-type regression ; Rare disease ; Secondary analysis

Abstract

The case-control study has pointed to many important discoveries in epidemiology. The primary analysis of case-control studies focuses on the relationship between disease (D) and a set of covariates of interest (Y,X). This article focuses on the secondary application in order to investigate the interrelationship between the covariates. The standard statistical analysis of secondary variables, while ignoring the case-control sampling scheme, can be extremely misleading for rare diseases. The common practice then is to regress Y on X using the controls only. Previous work has been done assuming a parametric distribution for Y given X with homoscedastic error with no distributional assumption on X. In this article, we introduce a novel nonparametric methodology based on a kernel-type estimator without any assumption about the distribution of Y given X and allow the error to be heteroscedastic. We show our estimator is consistent for rare diseases while successfully utilizing both the cases and controls in our method and thereafter demonstrate the substantial increase in efficiency over the standard practice of using only the controls.