On the use of partial area under the ROC curve for comparison of two diagnostic tests

Evaluation of diagnostic performance is typically based on the receiver operating characteristic (ROC) curve and the area under the curve (AUC) as its summary index. The partial area under the curve (pAUC) is an alternative index focusing on the range of practical/clinical relevance. One of the problems preventing more frequent use of the pAUC is the perceived loss of efficiency in cases of noncrossing ROC curves. In this paper, we investigated statistical properties of comparisons of two correlated pAUCs. We demonstrated that outside of the classic model there are practically reasonable ROC types for which comparisons of noncrossing concave curves would be more powerful when based on a part of the curve rather than the entire curve. We argue that this phenomenon stems in part from the exclusion of noninformative parts of the ROC curves that resemble straight‐lines. We conducted extensive simulation studies in families of binormal, straight‐line, and bigamma ROC curves. We demonstrated that comparison of pAUCs is statistically more powerful than comparison of full AUCs when ROC curves are close to a “straight line”. For less flat binormal ROC curves an increase in the integration range often leads to a disproportional increase in pAUCs’ difference, thereby contributing to an increase in statistical power. Thus, efficiency of differences in pAUCs of noncrossing ROC curves depends on the shape of the curves, and for families of ROC curves that are nearly straight‐line shaped, such as bigamma ROC curves, there are multiple practical scenarios in which comparisons of pAUCs are preferable.     

Altitudinal distribution limits of aquatic macroinvertebrates: an experimental test in a tropical alpine stream

1. Temperature and oxygen are recognised as the main drivers of altitudinal limits of species distributions. However, the two factors are linked, and both decrease with altitude, why their effects are difficult to disentangle. 2. This was experimentally addressed using aquatic macroinvertebrates; larvae of Andesiops (Ephemeroptera), Claudioperla, (Plecoptera), Scirtes (Coleoptera) and Anomalocosmoecus (Trichoptera), and the amphipod Hyalella in an Ecuadorian glacier‐fed stream (4100–4500 m a.s.l.). The following were performed: (i) quantitative benthic sampling at three sites to determine altitudinal patterns in population densities, (ii) transplants of the five taxa upstream of their natural altitudinal limit to test the short‐term (14 days) effect on survival, and (iii) in situ experiments of locomotory activity as a proxy for animal response to relatively small differences in temperature (5 °C vs. 10 °C) and oxygen saturation (55% vs. 62%). 3. The transplant experiment reduced survival to a varying degree among taxa, but Claudioperla survived well at a site where it did not naturally occur. In the in situ experiment, Scirtes and Hyalella decreased their activity at lower oxygen saturation, whereas Andesiops and Anomalocosmoecus did so at a low temperature. The decrease in activity from a high to a low temperature and oxygen for the five taxa was significantly correlated with their mortality in the transplant experiment. 4. Together the present experiments indicate that even relatively small differences in temperature and oxygen may produce effects explaining ecological patterns, and depending on the taxon, either water temperature or oxygen saturation, without clear interacting effects, are important drivers of altitudinal limits.