Modeling continuous diagnostic test data using approximate Dirichlet process distributions

There is now a large literature on the analysis of diagnostic test data. In the absence of a gold standard test, latent class analysis is most often used to estimate the prevalence of the condition of interest and the properties of the diagnostic tests. When test results are measured on a continuous scale, both parametric and nonparametric models have been proposed. Parametric methods such as the commonly used bi-normal model may not fit the data well; nonparametric methods developed to date have been relatively complex to apply in practice, and their properties have not been carefully evaluated in the diagnostic testing context. In this paper, we propose a simple yet flexible Bayesian nonparametric model which approximates a Dirichlet process for continuous data. We compare results from the nonparametric model with those from the bi-normal model via simulations, investigating both how much is lost in using a nonparametric model when the bi-normal model is correct and how much can be gained in using a nonparametric model when normality does not hold. We also carefully investigate the trade-offs that occur between flexibility and identifiability of the model as different Dirichlet process prior distributions are used. Motivated by an application to tuberculosis clustering, we extend our nonparametric model to accommodate two additional dichotomous tests and proceed to analyze these data using both the continuous test alone as well as all three tests together.