Methods for performing meta-analyses regarding diagnostic tests are still being debated in the literature and new statistical developments are underway (Eusebi et al. 2014). Three main models exist. The first one corresponds to a fixed effect model whereas the other two are random effect models. These last two are based on a hierarchical model, taking into account the variability present within studies and between studies. Exact mathematical details for each model discussed are provided in Appendix III.
The Moses-Littenberg model (Littenberg et al. 1990; Moses et al. 1993) has been extensively used for meta-analyses of DTA (Holling et al. 2012).
However, it is principally a fixed effect model, whereas for many such analyses a random effect model is required. It allows the performance of SROC curves in an exploratory approach. As a fixed effect model, it does not take into account and does not consider the variability between studies.
Due to its evident simplicity (it notably does not integrate the inter-study variability), this model can, in some circumstances, produce very different SROC curves compared to the hierarchical model described below (Harbord et al. 2008). The Cochrane Collaboration recommends careful use of this model which should be limited to preliminary analyses. Confidence intervals in statistics estimates or investigations of heterogeneity should not be studied with this model. 19
The Bivariate model (Reitsma et al. 2009) estimates the summary parameters: sensitivity and specificity across primary studies. It is presented in the Cochrane Handbook (Macaskill et al. 2010) and in the article of Leeflang et al. 2014 as a method of choice.
In this method, following Chu & Cole et al. 2006, the within study variability is modelled through binomial distributions, one for sensitivity and the other for specificity. These distributions are treated jointly since estimates of sensitivity and specificity, within each study, are non-independent.
To deal with variability in positivity cutpoint values, Rutter and Gatsonis. 2001 developed the hierarchal SROC (HSROC) model. It produces a SROC in which each study provides only one pair of values for sensitivity and specificity. It is presented in the Cochrane Handbook (Macaskill et al. 2010) and in the article by Leeflang et al. 2014 as a method of choice to obtain SROC curves.