Effects of Model Selection in Estimating Variance of Regression Slope for Heteroscedastic Bivariate Models. Examples from Nutritional Epidemiology.

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Epidemiology*
• Author(s): Simon Rosenfeld*+ and Victor Kipnis
• Affiliation(s): National Cancer Institute and National Cancer Institute
• Keywords: Box-Cox power transformation ; heteroscedastic models ; sandwich estimator ; deviation from normality ; bootstrap estimator ; weighted regression

Abstract

A traditional approach to modeling association between dichotomous outcome Y and exposure variables X is based on the logistic regression model. Often, the exposure variables are not directly measurable and instead, a vector of surrogate variables W is observed. To adjust for exposure measurement error, the calibration sub-study is carried out where both the surrogate and exposure variables are available. Presicion of calibration depends on specification of the regression E( X|W). Traditionally, it is assumed that this regression is linear and homoscedastic. However, in reality the joint distribution of X and W are very far from normality, and this assumption often results in overly optimistic estimates of confidence limits for the estimated relative risk. Using Monte Carlo simulation, we compare several strategies for estimating the variance of regression slope, i.e., OLS, Box-Cox transformation, sandwich estimator, bootstrap estimator and weighted regression. It is shown that in samples of moderate size, all of the strategies produce biased results. Examples from nutritional data show that the least biased approach is the Box-Cox power transformation.