Open Access Open Badges Research article

Meta-analysis and meta-modelling for diagnostic problems

Suphada Charoensawat1, Walailuck Böhning2, Dankmar Böhning3* and Heinz Holling2

Author Affiliations

1 Health Sciences Program Udon Thani Rajabhat University, Udon Thani, Thailand

2 Statistics and Quantitative Methods, Faculty of Psychology and Sport Science, University of Münster, Münster, Germany

3 Southampton Statistical Sciences Research Institute, Mathematics and Medical Statistics, University of Southampton, Southampton SO17 1BJ, UK

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BMC Medical Research Methodology 2014, 14:56  doi:10.1186/1471-2288-14-56

Published: 24 April 2014



A proportional hazards measure is suggested in the context of analyzing SROC curves that arise in the meta–analysis of diagnostic studies. The measure can be motivated as a special model: the Lehmann model for ROC curves. The Lehmann model involves study–specific sensitivities and specificities and a diagnostic accuracy parameter which connects the two.


A study–specific model is estimated for each study, and the resulting study-specific estimate of diagnostic accuracy is taken as an outcome measure for a mixed model with a random study effect and other study-level covariates as fixed effects. The variance component model becomes estimable by deriving within-study variances, depending on the outcome measure of choice. In contrast to existing approaches – usually of bivariate nature for the outcome measures – the suggested approach is univariate and, hence, allows easily the application of conventional mixed modelling.


Some simple modifications in the SAS procedure proc mixed allow the fitting of mixed models for meta-analytic data from diagnostic studies. The methodology is illustrated with several meta–analytic diagnostic data sets, including a meta–analysis of the Mini–Mental State Examination as a diagnostic device for dementia and mild cognitive impairment.


The proposed methodology allows us to embed the meta-analysis of diagnostic studies into the well–developed area of mixed modelling. Different outcome measures, specifically from the perspective of whether a local or a global measure of diagnostic accuracy should be applied, are discussed as well. In particular, variation in cut-off value is discussed together with recommendations on choosing the best cut-off value. We also show how this problem can be addressed with the proposed methodology.

Diagnostic accuracy; Mixed modelling; Random effects modelling; Cut-off value modelling; SROC modelling