Receiver Operating Characteristic Curve Analysis of Beach Water Quality Indicator Variables

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Abstract
Receiver operating characteristic (ROC) curve analysis is a simple and effective means to compare the accuracies of indicator variables of bacterial beach water quality. The indicator variables examined in this study were previous day's Enterococcus density and antecedent rainfall at 24, 48, and 96 h. Daily Enterococcus densities and 15-min rainfall values were collected during a 5-year (1996 to 2000) study of four Boston Harbor beaches. The indicator variables were assessed for their ability to correctly classify water as suitable or unsuitable for swimming at a maximum threshold Enterococcus density of 104 CFU/100 ml. Sensitivity and specificity values were determined for each unique previous day's Enterococcus density and antecedent rainfall volume and used to construct ROC curves. The area under the ROC curve was used to compare the accuracies of the indicator variables. Twenty-four-hour antecedent rainfall classified elevated Enterococcus densities more accurately than previous day's Enterococcus density ( P = 0.079). An empirically derived threshold for 48-h antecedent rainfall, corresponding to a sensitivity of 0.75, was determined from the 1996 to 2000 data and evaluated to ascertain if the threshold would produce a 0.75 sensitivity with independent water quality data collected in 2001 from the same beaches.