On estimating a constrained bivariate random effects model for meta-analysis of test accuracy studies

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Tailored meta-analysis uses setting-specific knowledge for the test positive rate and disease prevalence to constrain the possible values for a test's sensitivity and specificity. The constrained region is used to select those studies relevant to the setting for meta-analysis using an unconstrained bivariate random effects model (BRM). However, sometimes there may be no studies to aggregate, or the summary estimate may lie outside the plausible or “applicable” region. Potentially these shortcomings may be overcome by incorporating the constraints in the BRM to produce a constrained model. Using a penalised likelihood approach we developed an optimisation algorithm based on co-ordinate ascent and Newton-Raphson iteration to fit a constrained bivariate random effects model (CBRM) for meta-analysis. Using numerical examples based on simulation studies and real datasets we compared its performance with the BRM in terms of bias, mean squared error and coverage probability. We also determined the ‘closeness’ of the estimates to their true values using the Euclidian and Mahalanobis distances. The CBRM produced estimates which in the majority of cases had lower absolute mean bias and greater coverage probability than the BRM. The estimated sensitivities and specificity for the CBRM were, in general, closer to the true values than the BRM. For the two real datasets, the CBRM produced estimates which were in the applicable region in contrast to the BRM. When combining setting-specific data with test accuracy meta-analysis, a constrained model is more likely to yield a plausible estimate for the sensitivity and specificity in the practice setting than an unconstrained model.
Original languageEnglish
Pages (from-to)287-299
Number of pages13
JournalStatistical Methods in Medical Research
Issue number2
Early online date7 Jan 2022
Publication statusPublished - 1 Feb 2022

Bibliographical note

Funding Information:
BHW was supported by funding from a Medical Research Council Clinician Scientist award (MR/N007999/1)

Publisher Copyright:
© The Author(s) 2022.


  • Bivariate model
  • penalised likelihood
  • penalty method
  • meta-analysis
  • random effects
  • diagnostic accuracy


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