Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

Johny Pambabay-Calero,Ana Sánchez-García,Ana Nieto-Librero,Sergio Bauz-Olvera,Puri Galindo-Villardón

doi:10.3390/math9111310

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.

Highlights

The exponential growth of the medical literature and the increasingly widespread use of information and communication technologies, together with the dispersion of scientific literature, make it difficult for researchers and health professionals to access relevant information
We used statistical tests based on measures such as the chi-square, Cook distance, and Mahalanobis distance [38,39]
Definitions, implications, and methodologies were presented for the development of models for meta-analyses of diagnostic tests associated with copulas applied to a particular data set, previous studies [41,42] noted that it might be difficult to estimate copulas from a dataset, especially for count data

Summary

Introduction

The exponential growth of the medical literature and the increasingly widespread use of information and communication technologies, together with the dispersion of scientific literature, make it difficult for researchers and health professionals to access relevant information. Meta-analysis is a quantitative statistical analysis of several separate but similar experiments or studies, to test the pooled data for statistical significance that uses statistical models to estimate the results of several studies in a single measure [1]. The correct diagnosis of disease is of primary interest in psychology and medicine. Diagnostic tests are medical tests that detect the condition of a patient who is at risk of developing a disease [2]. As many of the results of diagnostic tests are based on a single biomarker, such results will not always lead to a correct diagnosis [3]. Meta-analysis is critical for investigating the available information on the accuracy of a diagnostic test [4,5]

Methods

Results

Conclusion