Statistics and Its Interface

Volume 7 (2014)

Number 4

Special Issue on Modern Bayesian Statistics (Part I)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Bayesian semi-parametric joint modeling of biomarker data with a latent changepoint: assessing the temporal performance of Enzyme-Linked Immunosorbent Assay (ELISA) testing for paratuberculosis

Pages: 417 – 438



Michelle Norris (Department of Mathematics and Statistics, California State University, Sacramento, Calif., U.S.A.)

Wesley O. Johnson (Department of Statistics, University of California at Irvine)

Ian A. Gardner (Department of Health Management, Atlantic Veterinary College, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada)


In this paper, we develop a class of semi-parametric statistical models that can be used for the important problem of analyzing longitudinal biomarker data with the purpose of quantifying their diagnostic capabilities, as a function of time from infection. We focus on the complicated problem where there is no gold standard assessment of the actual timing of infection/disease onset (our change point), which provides additional motivation for considering a second, binary test, in order to make it easier to estimate the change points for individuals that become diseased. An important additional feature of our model is its nonparametric part, which allows for distinct biomarker responses to the insult of infection/disease. In our case, the model allows for the possibility of an unknown number of clusters of individuals, each with distinct slopes corresponding to distinct biological reactions. Clusters with steeper slopes would correspond to individuals that could be diagnosed sooner than those with more gradual slopes.


Bayesian semi-parametric approach, change point model, Dirichlet process mixture, longitudinal data, random effects, imperfect reference standard, Johne’s disease

2010 Mathematics Subject Classification

Primary 62P10. Secondary 62G07.

Published 23 December 2014