Analyzing receiver operating characteristic curves to compare medical diagnostic tests

ABSTRACT

One exposes with diagnosis problems when she or he does an experiment or modeling to predict and allocate objects or persons to certain groups. For example in medicine in order to discriminate diabetes or cancers [level 2 of prevention] different criterions or indices can used. The simplest status is allocating objects to two possible categories, therefore one can measure a test variable in ordinal or continuous scale and regarding an appropriate cut-off in range of test variable and sensitivity, specificity and value of loss function, he or she can determine objects for each category. A suitable and single value index to evaluate test variable is A, area under receiver operating characteristic [ROC] curve. Since probably there are several test variables that measured on a unique sample, so there are natural correlations between A's. When one wants to compare and select the best test [s] among them, ignoring of these correlations can lead to confused results. We have detailed a method to compute A's and their variance-covariance matrix and introduced an adequate statistical test to compare them also using a set of simulated data have showed effectiveness of correlations on statistical results. For applied purposes we have prepared a software package using Delphi5. Based on simulated data for two indices we found A[1] = 0.660, SE[A[1]] = 0.054, A[2] -0.49, SE [A[2]] - 0.06. By ignoring correlations between A[1], A[2] we computed Z =2.1, it leads to reject equality of As in a alpha = 0.05 level, otherwise by regarding correlation, Z =1.92 and equality will accept. Ignoring correlation between As can lead to incorrect results: