A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests

Abstract

For a particular disease, there may be two diagnostic tests developed, where each of the tests is subject to several studies. A quadrivariate generalised linear mixed model (GLMM) has been recently proposed to joint meta-analyse and compare two diagnostic tests. We propose a D-vine copula mixed model for joint meta-analysis and comparison of two diagnostic tests. Our general model includes the quadrivariate GLMM as a special case and can also operate on the original scale of sensitivities and specificities. The method allows the direct calculation of sensitivity and specificity for each test, as well as the parameters of the summary receiver operator characteristic (SROC) curve, along with a comparison between the SROCs of each test. Our methodology is demonstrated with an extensive simulation study and illustrated by meta-analysing two examples where two tests for the diagnosis of a particular disease are compared. Our study suggests that there can be an improvement on GLMM in fit to data since our model can also provide tail dependencies and asymmetries.

Keywords

Copula mixed model generalised linear mixed model sensitivity/specificity SROC vines

Get full access to this article

View all access options for this article.

References

Jackson

Riley

White

. Multivariate meta-analysis: potential and promise. Stat Med 2011; 30: 2481–2498.

Mavridis

Salanti

. A practical introduction to multivariate meta-analysis. Stat Meth Med Res 2013; 22: 133–158.

Nie

Cole

, et al. Statistical methods for multivariate meta-analysis of diagnostic tests: an overview and tutorial. Stat Meth Med Res 2016; 25: 1596–1619.

Takwoingi

Leeflang

Deeks

. Empirical evidence of the importance of comparative studies of diagnostic test accuracy. Ann Intern Med 2013; 158: 544–554.

Siadaty

Shu

. Proportional odds ratio model for comparison of diagnostic tests in meta-analysis. BMC Med Res Methodol 2004; 4: 27–27.

Tatsioni

Zarin

Aronson

, et al. Challenges in systematic reviews of diagnostic technologies. Ann Intern Med 2005; 142: 1048–1055.

Leeflang

Deeks

Gatsonis

, et al. Systematic reviews of diagnostic test accuracy. Ann Intern Med 2008; 149: 889–897.

Chu

Cole

. Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalized linear mixed model approach. J Clin Epidemiol 2006; 59: 1331–1332.

Trikalinos

Hoaglin

Small

, et al. Methods for the joint meta-analysis of multiple tests. Res Synth Meth 2014; 5: 294–312.

10.

Hoyer

Kuss

. Meta-analysis for the comparison of two diagnostic tests to a common gold standard: a generalized linear mixed model approach. Stat Meth Med Res 2018; 27: 1410–1421.

11.

Nikoloulopoulos

. A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence. Stat Meth Med Res 2017; 26: 2270–2286.

12.

Hoyer

Kuss

. Meta-analysis for the comparison of two diagnostic tests–a new approach based on copulas. Stat Med 2018; 37: 739–748.

13.

Joe

. Multivariate models and dependence concepts, London, UK: Chapman & Hall, 1997.

14.

Joe

. Dependence modeling with copulas, London, UK: Chapman & Hall, 2014.

15.

Nelsen

. An introduction to copulas, New York, NY: Springer-Verlag, 2006.

16.

Sklar

. Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 1959; 8: 229–231.

17.

Nikoloulopoulos

Joe

. Factor copula models for item response data. Psychometrika 2015; 80: 126–150.

18.

Joe

Nikoloulopoulos

. Tail dependence functions and vine copulas. J Multivariate Analys 2010; 101: 252–270.

19.

Nikoloulopoulos

Joe

. Vine copulas with asymmetric tail dependence and applications to financial return data. Computat Stat Data Analys 2012; 56: 659–3673.

20.

Joe H. Families of m-variate distributions with given margins and

m (m - 1) / 2

bivariate dependence parameters. In: Rüschendorf L, Schweizer B and Taylor M (eds) Distributions with fixed marginals and related topics, vol. 28. Hayward, CA: Institute of Mathematical Statistics, pp.120–141.

21.

Nikoloulopoulos

. A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution. Stat Med 2015; 34: 3842–3865.

22.

Kuss

Hoyer

Solms

. Meta-analysis for diagnostic accuracy studies: a new statistical model using beta-binomial distributions and bivariate copulas. Stat Med 2014; 33: 17–30.

23.

Nikoloulopoulos

. Comment on ‘A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence’. Stat Meth Med Res 2016; 25: 988–991.

24.

Nash

. Compact numerical methods for computers: linear algebra and function minimisation, 2nd ed. New York, NY: Hilger, 1990.

25.

Stroud

Secrest

. Gaussian quadrature formulas, Englewood Cliffs, NJ: Prentice-Hall, 1966.

26.

Nikoloulopoulos

. Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests. Stat Meth Med Res 2018; 27: 2540–2553.

27.

Nikoloulopoulos

. On composite likelihood in bivariate meta-analysis of diagnostic test accuracy studies. AStA Adv Stat Analys 2018; 102: 211–227.

28.

Nishimura

Sugiyama

Kogata

, et al. Meta-analysis: diagnostic accuracy of anti-cyclic citrullinated peptide antibody and rheumatoid factor for rheumatoid arthritis. Ann Intern Med 2007; 146: 797–808.

29.

Bennett

Guo

Dharmage

. Hba1c as a screening tool for detection of type 2 diabetes: a systematic review. Diab Med 2007; 24: 333–343.

30.

Kodama

Horikawa

Fujihara

, et al. Use of high-normal levels of haemoglobin a1c and fasting plasma glucose for diabetes screening and for prediction: a meta-analysis. Diab/Metab Res Rev 2013; 29: 680–692.

31.

Dimou

Adam

Bagos

. A multivariate method for meta-analysis and comparison of diagnostic tests. Stat Med 2016; 35: 3509–3523.

32.

Hua

Joe

. Tail order and intermediate tail dependence of multivariate copulas. J Multivariate Analys 2011; 102: 1454–1471.

33.

Nikoloulopoulos AK. CopulaREMADA: Copula mixed effect models for multivariate meta-analysis of diagnostic test accuracy studies, R package version 1.1, 2018. https://CRAN.R-project.org/package=CopulaREMADA.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.07 MB