IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i11p1310-d570380.html
   My bibliography  Save this article

Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Johny Pambabay-Calero & Sergio Bauz-Olvera & Ana Nieto-Librero & Ana Sánchez-García & Puri Galindo-Villardón, 2021. "Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions," Mathematics, MDPI, vol. 9(11), pages 1-20, June.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1310-:d:570380
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/11/1310/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/11/1310/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    2. Mauricio Huerta & Víctor Leiva & Camilo Lillo & Marcelo Rodríguez, 2018. "A beta partial least squares regression model: Diagnostics and application to mining industry data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(3), pages 305-321, May.
    3. V. Dukic & C. Gatsonis, 2003. "Meta-analysis of Diagnostic Test Accuracy Assessment Studies with Varying Number of Thresholds," Biometrics, The International Biometric Society, vol. 59(4), pages 936-946, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xue-Ying Xu & Hong Kong & Rui-Xiang Song & Yu-Han Zhai & Xiao-Fei Wu & Wen-Si Ai & Hong-Bo Liu, 2014. "The Effectiveness of Noninvasive Biomarkers to Predict Hepatitis B-Related Significant Fibrosis and Cirrhosis: A Systematic Review and Meta-Analysis of Diagnostic Test Accuracy," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-16, June.
    2. Lu Yang & Claudia Czado, 2022. "Two‐part D‐vine copula models for longitudinal insurance claim data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1534-1561, December.
    3. Kolev, Nikolai, 2016. "Characterizations of the class of bivariate Gompertz distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 173-179.
    4. Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
    5. Gery Geenens, 2024. "(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem," Mathematics, MDPI, vol. 12(3), pages 1-7, January.
    6. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.
    7. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    8. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    9. repec:hal:wpaper:hal-00746251 is not listed on IDEAS
    10. Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    11. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    13. Adelchi Azzalini & Marc G. Genton, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 198-202, August.
    14. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," Economic Research Papers 270232, University of Warwick - Department of Economics.
    15. M. Mesfioui & T. Bouezmarni & M. Belalia, 2023. "Copula-based link functions in binary regression models," Statistical Papers, Springer, vol. 64(2), pages 557-585, April.
    16. Serge Darolles & Gaëlle Le Fol & Yang Lu & Ran Sun, 2018. "Bivariate integer-autoregressive process with an application to mutual fund flows," Post-Print hal-04590149, HAL.
    17. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    18. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    19. Fantazzini, Dean, 2020. "Discussing copulas with Sergey Aivazian: a memoir," MPRA Paper 102317, University Library of Munich, Germany.
    20. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Stat Trek. An interview with Christian Genest," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-14, May.
    21. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1310-:d:570380. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.