# Modernising Receiver Operating Characteristic (ROC) Curves +
## 2 Related Work  
Traditional ROC curves have not been without their critics. It has been claimed that separate information about TPR (sensitivity) and FPR (1--specificity, fall-out) is lost in the making of an ROC plot, and no distinction is made for differences in device-specific _SL_[10]. As explained in Appendix A.1, better performing device types are considered to be those whose ROC curves lie furthest towards the left-hand, upper corner of the plots, but that procedure has been criticised as being only a relative judgment [3].  
The limitations in interpretation due to the non-linearity of ROC curves have provoked, over the years, some suggestions about linearisation. For instance, early work by [PERSON] [11] included the making of plots of ROC curves on log-log axes. [PERSON] [12] later proposed the linearisation of ROC curves by making plots of log-odds ratios (logits) on both plot axes instead of the non-linear % metrics TPR, FPR and _AUC_ of traditional ROC curves (Figure 1), but [PERSON] apparently did not express these in terms of the Rasch model.  
As explained in the introduction, much of that ROC work has been kept to CTT and many have been reluctant to adopt modern test theory (Section 1 and Appendix A.1), despite the latter's development being concurrent with ROC use over the decades.  
There has been some recent work which has included modern measurement theory, demonstrating improved diagnostic performance when Rasch-compensated metrics are used to plot traditional ROC curves. [PERSON] et al. (2013), for instance, considered the interpretations of standard ROC approaches with Rasch modelling, comparing test sensitivity, specificity, and likelihood ratios with the logit (and probability) estimates of the Rasch model, using the entire set of their available data (for the case of mechanical knee examinations). They demonstrated significant correlations between traditional approaches and Rasch model estimates and found that, for instance, positive likelihood ratios were significantly correlated with the probability values of a positive diagnosis from the Rasch model.  
The diagnostic and demographic variables associated with the known differences in heart failure severity, with the potential for impacting the risk of intensive care unit admission, were included in another Rasch analysis by [PERSON] and [PERSON] (1994) intended as an aid in modelling the diagnostic process ([PERSON] and [PERSON], 1994; [PERSON], 1995). They compared ROC curves based on their unadjusted heart failure severity measures with ROC curves for the Rasch regression adjusted heart failure severity measures in which there is an improvement in _AUC_ from 0.63 to 0.76, respectively, with the Rasch-adjusted measures. In a final comment, [PERSON] and [PERSON] (1994) mention that the Rasch regression concept ([PERSON] and [PERSON], 1994; [PERSON], 1995) raises the possibility of using the log-odds ratios built into the heart failure severity measures (adjusted or unadjusted) as estimates of related outcome likelihoods.  
In an even more recent work published during the writing of this manuscript, reference ([PERSON] and [PERSON], 1994) reports on summary receiver operating characteristic (sROC) curves which are constructed using a regression model logit-TPR over logit-FPR.  
Despite these recent advances, as far as we are aware, none of this recent work or others have explicitly addressed both of these limitations--i.e., counted fractions (Appendix A.1) and a lack of separation ability/difficulty (Appendix A.2)--and ROC curves have continued almost exclusively to be analysed in the traditional way.  
Figure 1: Traditional ROC curves for the five device types used for pregnancy testing.