Integrated Environmental Assessment and Management — Volume 10, Number 1—pp. 149 © 2013 SETAC
149
Assessing the Predictive Performance of Risk‐Based Water Quality Criteria Using Decision Error Estimates from Receiver Operating Characteristics (ROC) Analysis Douglas B McLaughliny yNational Council for Air and Stream Improvement, Western Michigan University, Kalamazoo, Michigan, USA
McLaughlin DB. 2012. Assessing the predictive performance of risk‐based water quality criteria using decision error estimates from Receiver Operating Characteristics (ROC) analysis. Integr Environ Assess Manag 8:674–684. Formulae for the FPE and FNE error rates were incorrect as originally published in Table 2. The correct formulae are: FPE ¼ n(FP)/[n(TN) þ n(FP)]; FNE ¼ n(FN)/[n(FN) þ n(TP)] as presented here in the corrected table.
Indicator (stressor) Attaining
Nonattaining
Total count
n(FN)
n(TP)
250þ251 ¼ 501
250
251
n(TN)
n(FP)
252
248
250þ252 ¼ 502
251þ248 ¼ 499
Actual (response) Nonattaining
Attaining
Total count
252þ248 ¼ 500
1001
Prevalence ¼ (n(TP)þn(FN))/(n(TP)þn(FP)þn(FN)þn(TN)) ¼ 501/1001 0.5 Nonerror rates: Sp ¼ n(TN)/[n(TN)þn(FP)] ¼ 252/500 0.5. Se ¼ n(TP)/[n(FN)þn(TP)] ¼ 251/501 0.5. PPV ¼ n(TP)/[n(TP)þn(FP)] ¼ 251/499 0.5. NPV ¼ n(TN)/[n(TN)þn(FN)] ¼ 252/502 0.5. Accuracy ¼ 1/2(SpþSe) ¼ (n(TP)þn(TN))/(n(TP)þn(FP)þn(FN)þn(TN)). ¼(251þ252)/1001 0.5. Error rates: FPE ¼ n(FP)/[n(TN)þn(FP)] ¼ 1Sp ¼ 248/500 0.5. FNE ¼ n(FN)/[n(FN)þn(TP)] ¼ 1Se ¼ 250/501 0.5. PPE ¼ n(FP)/[n(FP)þn(TP)] ¼ 1PPV ¼ 248/499 0.5. NPE ¼ n(FN)/[n(FN)þn(TN)] ¼ 1NPV ¼ 250/502 0.5. a Counts are chosen to help illustrate the calculation of each term. FN ¼ false negative; FNE ¼ false negative error; FP ¼ false positive; FPE ¼ false positive error; NPE ¼ negative predictive error; NPV ¼ negative predictive value; PPE ¼ positive predictive error; PPV ¼ positive predictive value; ROC ¼ receiver operating characteristics; Se ¼ sensitivity; Sp ¼ specificity; TN ¼ true negative; TP ¼ true positive.
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ieam.1505
Corrigendum
Table 2. Performance metrics (after Linnet 1988) and example calculations for a 2 2 contingency table (i.e., error matrix) for ROC analysis with quadrant counts and ROC terms calculated for a hypothetical situation involving uncorrelated stressor and response variables, with total n ¼ 1001 data pairs, and Ythr, and Xc set at the median values for each variablea
149
Assessing the Predictive Performance of Risk‐Based Water Quality Criteria Using Decision Error Estimates from Receiver Operating Characteristics (ROC) Analysis Douglas B McLaughliny yNational Council for Air and Stream Improvement, Western Michigan University, Kalamazoo, Michigan, USA
McLaughlin DB. 2012. Assessing the predictive performance of risk‐based water quality criteria using decision error estimates from Receiver Operating Characteristics (ROC) analysis. Integr Environ Assess Manag 8:674–684. Formulae for the FPE and FNE error rates were incorrect as originally published in Table 2. The correct formulae are: FPE ¼ n(FP)/[n(TN) þ n(FP)]; FNE ¼ n(FN)/[n(FN) þ n(TP)] as presented here in the corrected table.
Indicator (stressor) Attaining
Nonattaining
Total count
n(FN)
n(TP)
250þ251 ¼ 501
250
251
n(TN)
n(FP)
252
248
250þ252 ¼ 502
251þ248 ¼ 499
Actual (response) Nonattaining
Attaining
Total count
252þ248 ¼ 500
1001
Prevalence ¼ (n(TP)þn(FN))/(n(TP)þn(FP)þn(FN)þn(TN)) ¼ 501/1001 0.5 Nonerror rates: Sp ¼ n(TN)/[n(TN)þn(FP)] ¼ 252/500 0.5. Se ¼ n(TP)/[n(FN)þn(TP)] ¼ 251/501 0.5. PPV ¼ n(TP)/[n(TP)þn(FP)] ¼ 251/499 0.5. NPV ¼ n(TN)/[n(TN)þn(FN)] ¼ 252/502 0.5. Accuracy ¼ 1/2(SpþSe) ¼ (n(TP)þn(TN))/(n(TP)þn(FP)þn(FN)þn(TN)). ¼(251þ252)/1001 0.5. Error rates: FPE ¼ n(FP)/[n(TN)þn(FP)] ¼ 1Sp ¼ 248/500 0.5. FNE ¼ n(FN)/[n(FN)þn(TP)] ¼ 1Se ¼ 250/501 0.5. PPE ¼ n(FP)/[n(FP)þn(TP)] ¼ 1PPV ¼ 248/499 0.5. NPE ¼ n(FN)/[n(FN)þn(TN)] ¼ 1NPV ¼ 250/502 0.5. a Counts are chosen to help illustrate the calculation of each term. FN ¼ false negative; FNE ¼ false negative error; FP ¼ false positive; FPE ¼ false positive error; NPE ¼ negative predictive error; NPV ¼ negative predictive value; PPE ¼ positive predictive error; PPV ¼ positive predictive value; ROC ¼ receiver operating characteristics; Se ¼ sensitivity; Sp ¼ specificity; TN ¼ true negative; TP ¼ true positive.
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ieam.1505
Corrigendum
Table 2. Performance metrics (after Linnet 1988) and example calculations for a 2 2 contingency table (i.e., error matrix) for ROC analysis with quadrant counts and ROC terms calculated for a hypothetical situation involving uncorrelated stressor and response variables, with total n ¼ 1001 data pairs, and Ythr, and Xc set at the median values for each variablea
