Regression with Error in Both Variables: Adjustment via Nonlinear Transformation of Replicates

• Activity Number: 198
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Peter Holck*+ and John Grove
• Companies: University of Hawaii and University of Hawaii, Manoa
• Keywords: measurement-error ; bias

Abstract

It is well known that a biased estimate of ß may result when modeling the relation of Y to an explanatory variable X having random measurement error. The usual adjustment for the attenuated ß estimate is to multiply ß-hat by the inverse of the reliability coefficient of X. Under restrictions of normally distributed X and homoscedastic measurement error, this adjustment is optimal (minimum variance ß-hat) and equivalent to the resulting regression coefficient of Y regressed on E(X|Z), where Z is the measured value of X; E(X|Z) is then linear in Z. However, we show a method for substantial improvement in ß estimation when normality assumptions are not valid. Using estimation of E(X|Z) based on replicate measurements and nonlinear modeling of E(Z1|Z2), we obtain ß estimates with reduced MSE and greater power. Simulated data illustrate this improvement when X is binary and measurement error is heteroscedastic, with less improvement when measurement error is homoscedastic. This adjustment method does no harm: When normality assumptions are valid, it is comparable to the usual reliability coefficient adjustment. We also provide recommendations to maximize performance of the method.