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Abstract
Background: Meta-analysis of diagnostic accuracy studies is more technically challenging than that of studies of interventions. A number of different, and apparently divergent, methods for meta-analysis of diagnostic studies have been proposed. Formulation of recommendations for Cochrane reviewers is difficult because of the apparently distinct theoretical basis and interpretation of these methods.
Summary ROC (SROC) curves may be fitted using simple linear regression [Littenberg & Moses, Med Decis Making 1993]. However, this has questionable validity as the assumptions behind linear regression are violated. Two more sophisticated models have been proposed: the hierarchical SROC (HSROC) model [Rutter & Gatsonis, Stat Med 2001], and bivariate random-effects meta-analysis [van Houwelingen et al., Stat Med 2002]. They are parameterised differently: HSROC models variability in test accuracy and threshold, while the bivariate method models variability in sensitivity and specificity plus their correlation.
Results: These two models can be shown to be very closely related, and often identical. In the absence of study-level covariates, they are different parameterisations of the same model. A consistent estimate of the summary operating point can be found by independent analyses of sensitivity and specificity, assuming their logits have a normal distribution.
The bivariate model allows inclusion of covariates that affect sensitivity and/or specificity, while the HSROC model allows covariates that affect accuracy and/or threshold. Models that allow a covariate to affect both are equivalent. However, the HSROC model can be more easily extended to include a covariate to affect the degree of asymmetry of the SROC curve. This would be necessary for formal comparison of groups of studies whose SROC curves intersect. Apparent discrepancies in results can arise from differences in software, particularly if the software does not model the binomial structure. Problems can arise when there are few studies.
Conclusions: The HSROC and bivariate methods are identical in many situations. Recognition of this may allow simplification of recommendations to Cochrane reviewers, and use of a wider range of statistical software.
Summary ROC (SROC) curves may be fitted using simple linear regression [Littenberg & Moses, Med Decis Making 1993]. However, this has questionable validity as the assumptions behind linear regression are violated. Two more sophisticated models have been proposed: the hierarchical SROC (HSROC) model [Rutter & Gatsonis, Stat Med 2001], and bivariate random-effects meta-analysis [van Houwelingen et al., Stat Med 2002]. They are parameterised differently: HSROC models variability in test accuracy and threshold, while the bivariate method models variability in sensitivity and specificity plus their correlation.
Results: These two models can be shown to be very closely related, and often identical. In the absence of study-level covariates, they are different parameterisations of the same model. A consistent estimate of the summary operating point can be found by independent analyses of sensitivity and specificity, assuming their logits have a normal distribution.
The bivariate model allows inclusion of covariates that affect sensitivity and/or specificity, while the HSROC model allows covariates that affect accuracy and/or threshold. Models that allow a covariate to affect both are equivalent. However, the HSROC model can be more easily extended to include a covariate to affect the degree of asymmetry of the SROC curve. This would be necessary for formal comparison of groups of studies whose SROC curves intersect. Apparent discrepancies in results can arise from differences in software, particularly if the software does not model the binomial structure. Problems can arise when there are few studies.
Conclusions: The HSROC and bivariate methods are identical in many situations. Recognition of this may allow simplification of recommendations to Cochrane reviewers, and use of a wider range of statistical software.
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