Empirical Bayes-Type Shrinkage Estimators for Evaluating Multiple Exposures in Epidemiology Studies

• Activity Number: 26
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jaya Satagopan*+ and Qin Zhou and Susan Oliveria and Stephen Dusza and Martin Weinstock and Marianne Berwick and Allan Halpern
• Companies: Memorial Sloan-Kettering Cancer Center and Memorial Sloan-Kettering Cancer Center and Memorial Sloan-Kettering Cancer Center and Memorial Sloan-Kettering Cancer Center and Brown University and University of New Mexico and Memorial Sloan-Kettering Cancer Center
• Keywords: exchangeability ; empirical Bayes ; minimum risk ; random effects

Abstract

Epidemiology studies increasingly examine multiple exposures in relation to disease by selecting the exposures of interest in a thematic manner. For example, sun exposure, sunburn and sun protection behavior could be themes for an investigation of sun-related exposures. Several studies now use predefined linear combinations of the exposures pertaining to the themes to estimate the effects of the individual exposures. Such analyses may improve the precision of the exposure effects, but they can lead to inflated bias and type I errors when the linear combinations are inaccurate. We investigate empirical Bayes-type shrinkage estimators and preliminary test estimators as alternative approaches when it is desirable to exploit the thematic choice of exposures, but the accuracy of the predefined linear combinations is unknown. We show that the two estimator are intimately related under certain assumptions, and identify a robust empirical Bayes type shrinkage estimator for use in practical settings. These methods are illustrated using data from the 'Study of nevi in children', where the exposures are the individual questionnaire items and the outcome is log(total back naevus count).