Statistics and Its Interface

Volume 2 (2009)

Number 2

Modeling bivariate longitudinal diagnostic outcome data in the absence of a gold standard

Pages: 171 – 185



Ian A. Gardner (Department of Medicine and Epidemiology, University of California at Davis)

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

Michelle Norris (Department of Mathematics and Statistics, California State University, Sacramento)


Diagnostic screening involves testing humans or animals for the presence of disease or infection. For some diseases, a perfect, “gold-standard” test does not exist or is too invasive or expensive to use. Hence, the goals of diagnostic testing may include: quantifying the performance of an imperfect test, diagnosing subjects, and estimating disease prevalence – possibly in the absence of a perfect reference test. To date, most work in this area has focused on cross-sectional data. We extend recent work by developing a model for bivariate longitudinal diagnostic outcomes in the no-gold standard case. We consider the situation where a continuous test and a binary test are repeatedly administered to each subject. For infected subjects, we assume the existence of a changepoint corresponding to time of infection and posit appropriate changes to the model thereafter. This results in a varying-dimensional parameter space since the true infection status of the subjects is unknown. We make inference using Bayesian Markov chain Monte Carlo methods, incorporating the Reversible Jump Markov chain Monte Carlo algorithm of Green for posterior simulation from a varying-dimensional parameter space. We test the model’s performance on simulated data, and then analyze a data set based on Johne’s disease in cattle.


changepoint model, Gibbs sampler, Johne’s disease, longitudinal data, Markov chain Monte Carlo, no-gold standard, reversible jump

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