Meta-Analysis in DTA with Hierarchical Models Bivariate and HSROC: Simulation Study

  • Sergio A. Bauz-OlveraEmail author
  • Johny J. Pambabay-Calero
  • Ana B. Nieto-Librero
  • Ma. Purificación Galindo-Villardón
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 301)


In meta-analysis for diagnostic test accuracy (DTA), summary measures such as sensitivity, specificity, and odds ratio are used. However, these measures may not be adequate to integrate studies with low prevalence, which is why statistical modeling based on true positives and false positives is necessary. In this context, there are several statistical methods, the first of which is a bivariate random effects model, part of the assumption that the logit of sensitivity and specificity follow a bivariate normal distribution, the second, refers to the HSROC or hierarchical model, is similar to bivariate, with the particularity that it directly models the sensitivity and specificity relationship through cut points. Using simulations, we investigate the performance of hierarchical models, varying their parameters and hyperparameters and proposing a better management of variability within and between studies. The results of the simulated data are analyzed according to the criterion of adjustment of the models and estimates of their parameters.


Diagnostic precision Meta-analysis HSROC model Bivariate model Low prevalence 


  1. 1.
    Midgette, A.S., Stukel, T.A., Littenberg, B.: A meta-analytic method for summarizing diagnostic test performances: receiver-operating-characteristic-summary point estimates. Med. Decis. Mak. 13(3), 253–257 (1993)CrossRefGoogle Scholar
  2. 2.
    Moses, L.E., Shapiro, D., Littenberg, B.: Combining independent studies of a diagnostic test into a summary ROC curve: data-analytic approaches and some additional considerations. Stat. Med. 12(14), 1293–1316 (1993)CrossRefGoogle Scholar
  3. 3.
    Reitsma, J.B., Glas, A.S., Rutjes, A.W., Scholten, R.J., Bossuyt, P.M., Zwinderman, A.H.: Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. J. Clin. Epidemiol. 58(10), 982–990 (2005)CrossRefGoogle Scholar
  4. 4.
    Rutter, C.M., Gatsonis, C.A.: A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Stat. Med. 20(19), 2865–2884 (2001)CrossRefGoogle Scholar
  5. 5.
    Arends, L.R., Hamza, T.H., Van Houwelingen, J.C., Heijenbrok-Kal, M.H., Hunink, M.G.M., Stijnen, T.: Bivariate random effects meta-analysis of ROC curves. Med. Decis. Mak. 28(5), 621–638 (2008)CrossRefGoogle Scholar
  6. 6.
    Harbord, R.M., Deeks, J.J., Egger, M., Whiting, P., Sterne, J.A.: A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics 8(2), 239–251 (2006)CrossRefGoogle Scholar
  7. 7.
    Kotz, S., Balakrishnan, N., Johnson, N.L.: Bivariate and trivariate normal distributions. Contin. Multivar. Distrib. 1, 251–348 (2000)Google Scholar
  8. 8.
    Van Houwelingen, H.C., Arends, L.R., Stijnen, T.: Advanced methods in meta-analysis: multivariate approach and meta-regression. Stat. Med. 21(4), 589–624 (2002)CrossRefGoogle Scholar
  9. 9.
    Chu, H., Guo, H., Zhou, Y.: Bivariate random effects meta-analysis of diagnostic studies using generalized linear mixed models. Med. Decis. Mak. 30(4), 499–508 (2010)CrossRefGoogle Scholar
  10. 10.
    Macaskill, P.: Empirical Bayes estimates generated in a hierarchical summary ROC analysis agreed closely with those of a full Bayesian analysis. J. Clin. Epidemiol. 57(9), 925–932 (2004)CrossRefGoogle Scholar
  11. 11.
    Chappell, F.M., Raab, G.M., Wardlaw, J.M.: When are summary ROC curves appropriate for diagnostic meta-analyses? Stat. Med. 28(21), 2653–2668 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kriston, L., Hölzel, L., Weiser, A.K., Berner, M.M., Härter, M.: Meta-analysis: are 3 questions enough to detect unhealthy alcohol use? Ann. Intern. Med. 149(12), 879–888 (2008)CrossRefGoogle Scholar
  13. 13.
    Bachmann, L.M., Puhan, M.A., Ter Riet, G., Bossuyt, P.M.: Sample sizes of studies on diagnostic accuracy: literature survey. Bmj 332(7550), 1127–1129 (2006)CrossRefGoogle Scholar
  14. 14.
    Doebler, P., Holling, H.: Meta-analysis of diagnostic accuracy with mada. Reterieved at: (2015)
  15. 15.
    Dendukuri, N., Schiller, I., Joseph, L., Pai, M.: Bayesian meta-analysis of the accuracy of a test for tuberculous pleuritis in the absence of a gold standard reference. Biometrics 68(4), 1285–1293 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Grycuk, R., Gabryel, M., Scherer, R., Voloshynovskiy, S.: Multi-layer architecture for storing visual data based on WCF and microsoft SQL server database. In: International Conference on Artificial Intelligence and Soft Computing, pp. 715–726. Springer, Cham (2015)CrossRefGoogle Scholar
  17. 17.
    Sheu, C.F., Chen, C.T., Su, Y.H., Wang, W.C.: Using SAS PROC NLMIXED to fit item response theory models. Behav. Res. Methods 37(2), 202–218 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sergio A. Bauz-Olvera
    • 1
    Email author
  • Johny J. Pambabay-Calero
    • 2
  • Ana B. Nieto-Librero
    • 3
    • 4
  • Ma. Purificación Galindo-Villardón
    • 3
    • 4
  1. 1.Facultad de Ciencias de la VidaEscuela Superior Politécnica del LitoralGuayaquilEcuador
  2. 2.Facultad de Ciencias Naturales y MatemáticasEscuela Superior Politécnica del LitoralGuayaquilEcuador
  3. 3.Dpto. de Estadística, Facultad de MedicinaUniversidad de SalamancaSalamancaSpain
  4. 4.Instituto de Investigación Biomédica (IBSAL)SalamancaSpain

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