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

Abstract

SUMMARYIgnoring the limited precision of medical diagnostic tests can incur serious bias in prevalence estimation. Conversely, treating the values of sensitivity and speciÿcity 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 speciÿcity 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 di culties. Although their approach is quite e ective in reducing the computational complexity into manageable tasks, their developed methodology is not general enough for modelling the e ects 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.

Bias, efficiency, and agreement for group-testing regression models

“…Xie [19] treats the individual responses as unobserved and uses an expectation-maximisation (EM) algorithm to find the maximum likelihood estimates. Tu et al [20] suggests a Bayesian approach for modeling, but like Farrington [17], make the restrictive assumption that covariate values are identical within groups.…”

Rank‐preserving regression: a more robust rank regression model against outliers

“…If the error term in the linear model follows other distributions such as the t distribution, then the probit t link will ensure the same interpretation for the parameters. However, the use of different popular links generally does not have much impact on the parameters, because the probit, the probit t , and the logit link …”

A Bayesian model for misclassified binary outcomes and correlated survival data with applications to breast cancer

“…In addition, Magder and Hughes [16] treated test sensitivity and specificity as fixed values and did not account for their uncertainty. To address this issue and to model the covariate effects in prevalence estimation, researchers have proposed various Bayesian models that use likelihood functions that are based on observed and latent variables [17][18][19] or observed variables only [20]. A unique feature of our proposed method is that the likelihood formulation incorporates both the test sensitivity and specificity and the correlated survival information, thus improving the estimation of the covariate effects on the probability of IBTR's being NP and the diagnostic test accuracy.…”

“…This assumption will be relaxed in Section 2.2. The likelihood formulation involves only the binomial regression with misclassified outcome and is essentially identical to model (2) of Tu et al [17] or model (2) of McInturff et al [20].…”