Bayesian analysis of prevalence with covariates using simulation-based techniques: applications to HIV screening

Abstract

Ignoring the limited precision of medical diagnostic tests can incur serious bias in prevalence estimation. Conversely, treating the values of sensitivity and specificity as constants, as in most studies, inevitably underestimates the variability of prevalence estimates. Bayesian inference provides a natural framework with which to integrate the variability in the estimates of sensitivity and specificity with estimation of prevalence. However, the resulting model becomes quite complicated and presents a computational challenge. Recently, Mendoza‐Blanco et al. proposed a missing‐data approach with simulation‐based techniques to deal with the computational difficulties. Although their approach is quite effective in reducing the computational complexity into manageable tasks, their developed methodology is not general enough for modelling the effects of covariates in prevalence estimation. In this paper, we extend their work in this direction by combining their missing‐data approach with a latent variable technique for modelling discrete data. The present work also generalizes the methods of Albert and Chib for Bayesian analysis of binary response data with errors in the response. We illustrate the methodology with several real data examples extracted from the literature. Copyright © 1999 John Wiley & Sons, Ltd.

Classification of Ipsilateral Breast Tumor Recurrences After Breast Conservation Therapy Can Predict Patient Prognosis and Facilitate Treatment Planning

“…We used Tu’s method 23 to obtain estimated sensitivity and specificity values for each method. Method 2 had higher sensitivity but lower specificity than method 1.…”

“…This assumption may not always be true since markers may change due to clonal evolution. Although Tu’s method 23 provides the corrected coefficient estimates and allows for uncertainty in test sensitivity and specificity values, the estimates can be further improved by incorporating additional survival information that is correlated with the classification status. In the future, working with statisticians to develop a methodological framework that provides more accurate estimates of sensitivity and specificity values for each classification method will help clinicians decide which method to use on the basis of the sensitivity-specificity trade-off.…”

“…22 Tu et al proposed a Bayesian model that incorporates the test sensitivity and specificity into the likelihood function to quantify the effects of covariates on event probability. 23 Their approach has been used in several publications and has the advantages that a relatively broad family of link functions is easily accommodated, data resulting from multiple screening tests and/or pooled samples can be modeled, and the effect of covariates assessed. 24, 25 In this study, we used Tu’s method to test the sensitivity and specificity of each method.…”

Bayesian Estimation for Diagnostic Testing of Biosecurity Risk Material in the Absence of a Gold Standard when Test Data are Incomplete

“…Other extensions to this paper also exist, including an extension to the case of three diagnostic tests (Scott et al 2008) and the case of two populations with different prevalence values but the same diagnostic tests (Johnson et al 2001). It is also possible to incorporate covariates into the estimation (Epstein et al 1996;Tu et al 1999;Lewis et al 2012) and to estimate sample size for this and related methods (Beavers and Stamey 2012). There may also be value in the use of second-order simulation to better understand the sources of uncertainty in the estimated posterior distributions (e.g.…”

Binomial regression with a misclassified covariate and outcome

“…23 When no gold standard, but two imperfect measures are available, one can account for the misclassification using a maximum likelihood approach. 24 Because the likelihood function often involves complicated integrations that a closed form is unavailable for most models, the expectation–maximization algorithm 17 and Bayesian inference using Markov chain Monte Carlo (MCMC) methods 5,6,25,26 have been widely used to correct for misclassification. There are several advantages of using Bayesian inference framework: (a) the approximation of the integrals in the likelihood is not required, and the unobserved variables can be sampled along with the model parameters from their full posterior distribution; (b) the available prior information of some parameters can be readily incorporated; and (c) with the development of BUGS projects, 27 the implementation in OpenBUGS is made simple by specifying the likelihood function and the prior distribution of all unknown parameters.…”