3D ROC analysis for detection software used in water monitoring

Under the U.S. Army sponsored Joint Service Agent Water Monitor (JSAWM) program, developing hand-held assays using tickets for chemical/biological agent detection has been of major interest. One of keys to success is to develop detection algorithms that not only can effectively detect the presence of various agents, but also can quantify the detected agents. This paper presents a recent development of detection software that can perform 3-dimensional (3D) receiver operating characteristics (ROC) analysis which is based on quantified agent concentration. The ROC curves have been widely used in communications, signal processing and medical communities to evaluate the effectiveness of a detection technique. It generally formulates a signal detection problem as a binary composite hypothesis testing problem with the null hypothesis and the alternative hypothesis represents the case of no signal and the case of signal presence respectively. The ROC curve is then plotted based on the detection probability (power) P _D versus the false alarm probability, P _F. Unfortunately, such a two-dimensional (2D) (P _D,P _F)-based ROC curve does not factor in the concentration detected in an agent signal which is a crucial parameter in chemical/biological agent detection. The proposed 3D ROC analysis is developed from such a need. It includes an additional parameter, referred to as threshold t, which is used to threshold the detected agent signal concentration. Consequently, a different value of t results in a different 2D ROC curve. In order to take into account the thresholding factor t, a 3D ROC curve is derived and plotted based on three parameters, (P _D,P _F,t). As a result of the 3D ROC curve, three 2D ROC curves can be also derived. One is the conventional 2D (P _D,P _F)-ROC curve. Another is a 2D (P _D,t)-ROC curve which describes the relationship between P _D and the threshold value t. A third one is a 2D (P _F,t)-ROC curve which shows the effect of the threshold value t on P _F. The utility of the proposed 3D ROC analysis will be demonstrated by the detection software developed by the UMBC for the tickets used in HHA for water monitoring.