Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error
Article first published online: 10 AUG 2009
© 2009, The International Biometric Society
Volume 66, Issue 2, pages 444–454, June 2010
How to Cite
Sinha, S., Mallick, B. K., Kipnis, V. and Carroll, R. J. (2010), Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error. Biometrics, 66: 444–454. doi: 10.1111/j.1541-0420.2009.01309.x
- Issue published online: 1 JUN 2010
- Article first published online: 10 AUG 2009
- Received December 2008. Revised May 2009. Accepted May 2009.
- Dirichlet process prior;
- Gibbs sampling;
- Measurement error;
- Metropolis–Hastings algorithm;
- Partly linear model
Summary: We propose a semiparametric Bayesian method for handling measurement error in nutritional epidemiological data. Our goal is to estimate nonparametrically the form of association between a disease and exposure variable while the true values of the exposure are never observed. Motivated by nutritional epidemiological data, we consider the setting where a surrogate covariate is recorded in the primary data, and a calibration data set contains information on the surrogate variable and repeated measurements of an unbiased instrumental variable of the true exposure. We develop a flexible Bayesian method where not only is the relationship between the disease and exposure variable treated semiparametrically, but also the relationship between the surrogate and the true exposure is modeled semiparametrically. The two nonparametric functions are modeled simultaneously via B-splines. In addition, we model the distribution of the exposure variable as a Dirichlet process mixture of normal distributions, thus making its modeling essentially nonparametric and placing this work into the context of functional measurement error modeling. We apply our method to the NIH-AARP Diet and Health Study and examine its performance in a simulation study.