Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

Johny Pambabay-Calero, Sergio Bauz-Olvera, Ana Nieto-Librero, Ana Sánchez-García and Puri Galindo-Villardón
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Johny Pambabay-Calero: Faculty of Natural Sciences and Mathematics, ESPOL, Polytechnic University, Guayaquil 090101, Ecuador
Sergio Bauz-Olvera: Faculty of Natural Sciences and Mathematics, ESPOL, Polytechnic University, Guayaquil 090101, Ecuador
Ana Nieto-Librero: Department of Statistics, Instituto de Investigación Biomédica de Salamanca (IBSAL), University of Salamanca, 37008 Salamanca, Spain
Ana Sánchez-García: INICO, Faculty of Education, University of Salamanca, 37008 Salamanca, Spain
Puri Galindo-Villardón: Department of Statistics, Instituto de Investigación Biomédica de Salamanca (IBSAL), University of Salamanca, 37008 Salamanca, Spain

Mathematics, 2021, vol. 9, issue 11, 1-20

Abstract: Models implemented in statistical software for the precision analysis of diagnostic tests include random-effects modeling (bivariate model) and hierarchical regression (hierarchical summary receiver operating characteristic). However, these models do not provide an overall mean, but calculate the mean of a central study when the random effect is equal to zero; hence, it is difficult to calculate the covariance between sensitivity and specificity when the number of studies in the meta-analysis is small. Furthermore, the estimation of the correlation between specificity and sensitivity is affected by the number of studies included in the meta-analysis, or the variability among the analyzed studies. To model the relationship of diagnostic test results, a binary covariance matrix is assumed. Here we used copulas as an alternative to capture the dependence between sensitivity and specificity. The posterior values were estimated using methods that consider sampling algorithms from a probability distribution (Markov chain Monte Carlo), and estimates were compared with the results of the bivariate model, which assumes statistical independence in the test results. To illustrate the applicability of the models and their respective comparisons, data from 14 published studies reporting estimates of the accuracy of the Alcohol Use Disorder Identification Test were used. Using simulations, we investigated the performance of four copula models that incorporate scenarios designed to replicate realistic situations for meta-analyses of diagnostic accuracy of the tests. The models’ performances were evaluated based on p -values using the Cramér–von Mises goodness-of-fit test. Our results indicated that copula models are valid when the assumptions of the bivariate model are not fulfilled.

Keywords: copula function; binary covariance; Bayesian hierarchical model; Markov chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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