A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems
Article first published online: 2 MAY 2012
© 2012, The International Biometric Society
Volume 68, Issue 4, pages 1103–1112, December 2012
How to Cite
Fong, Y., Wakefield, J., De Rosa, S. and Frahm, N. (2012), A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems. Biometrics, 68: 1103–1112. doi: 10.1111/j.1541-0420.2012.01762.x
- Issue published online: 21 DEC 2012
- Article first published online: 2 MAY 2012
- Received August 2011. Revised January 2012. Accepted February 2012.
- AR(1) process;
- Correlated outliers;
- 5PL curve;
- Dose response curve;
- Multiplex bead array
Summary In the context of a bioassay or an immunoassay, calibration means fitting a curve, usually nonlinear, through the observations collected on a set of samples containing known concentrations of a target substance, and then using the fitted curve and observations collected on samples of interest to predict the concentrations of the target substance in these samples. Recent technological advances have greatly improved our ability to quantify minute amounts of substance from a tiny volume of biological sample. This has in turn led to a need to improve statistical methods for calibration. In this article, we focus on developing calibration methods robust to dependent outliers. We introduce a novel normal mixture model with dependent error terms to model the experimental noise. In addition, we propose a reparameterization of the five parameter logistic nonlinear regression model that allows us to better incorporate prior information. We examine the performance of our methods with simulation studies and show that they lead to a substantial increase in performance measured in terms of mean squared error of estimation and a measure of the average prediction accuracy. A real data example from the HIV Vaccine Trials Network Laboratory is used to illustrate the methods.