DeLong, DeLong, and ClarkePearson (1988) report on 49 patients with ovarian cancer who also suffer from an intestinal obstruction. Three (correlated) screening tests are measured to determine whether a patient will benefit from surgery. The three tests are the KG score and two measures of nutritional status: total protein and albumin. The data are as follows:
data roc; input alb tp totscore popind @@; totscore = 10  totscore; datalines; 3.0 5.8 10 0 3.2 6.3 5 1 3.9 6.8 3 1 2.8 4.8 6 0 3.2 5.8 3 1 0.9 4.0 5 0 2.5 5.7 8 0 1.6 5.6 5 1 3.8 5.7 5 1 3.7 6.7 6 1 3.2 5.4 4 1 3.8 6.6 6 1 4.1 6.6 5 1 3.6 5.7 5 1 4.3 7.0 4 1 3.6 6.7 4 0 2.3 4.4 6 1 4.2 7.6 4 0 4.0 6.6 6 0 3.5 5.8 6 1 3.8 6.8 7 1 3.0 4.7 8 0 4.5 7.4 5 1 3.7 7.4 5 1 3.1 6.6 6 1 4.1 8.2 6 1 4.3 7.0 5 1 4.3 6.5 4 1 3.2 5.1 5 1 2.6 4.7 6 1 3.3 6.8 6 0 1.7 4.0 7 0 3.7 6.1 5 1 3.3 6.3 7 1 4.2 7.7 6 1 3.5 6.2 5 1 2.9 5.7 9 0 2.1 4.8 7 1 2.8 6.2 8 0 4.0 7.0 7 1 3.3 5.7 6 1 3.7 6.9 5 1 3.6 6.6 5 1 ;
In the following statements, the NOFIT option is specified in the MODEL statement to prevent PROC LOGISTIC from fitting the model with three covariates. Each ROC statement lists one of the covariates, and PROC LOGISTIC then fits the model with that single covariate. Note that the original data set contains six more records with missing values for one of the tests, but PROC LOGISTIC ignores all records with missing values; hence there is a common sample size for each of the three models. The ROCCONTRAST statement implements the nonparameteric approach of DeLong, DeLong, and ClarkePearson (1988) to compare the three ROC curves, the REFERENCE option specifies that the KG Score curve is used as the reference curve in the contrast, the E option displays the contrast coefficients, and the ESTIMATE option computes and tests each comparison. With ODS Graphics enabled, the plots=roc(id=prob) specification in the PROC LOGISTIC statement displays several plots, and the plots of individual ROC curves have certain points labeled with their predicted probabilities.
ods graphics on; proc logistic data=roc plots=roc(id=prob); model popind(event='0') = alb tp totscore / nofit; roc 'Albumin' alb; roc 'KG Score' totscore; roc 'Total Protein' tp; roccontrast reference('KG Score') / estimate e; run; ods graphics off;
The initial model information is displayed in Output 53.8.1.
Model Information  

Data Set  WORK.ROC 
Response Variable  popind 
Number of Response Levels  2 
Model  binary logit 
Optimization Technique  Fisher's scoring 
Number of Observations Read  43 

Number of Observations Used  43 
Response Profile  

Ordered Value 
popind  Total Frequency 
1  0  12 
2  1  31 
Score Test for Global Null Hypothesis 


ChiSquare  DF  Pr > ChiSq 
10.7939  3  0.0129 
For each ROC model, the model fitting details in Outputs 53.8.2, 53.8.4, and 53.8.6 can be suppressed with the ROCOPTIONS(NODETAILS) option; however, the convergence status is always displayed.
The ROC curves for the three models are displayed in Outputs 53.8.3, 53.8.5, and 53.8.7. Note that the labels on the ROC curve are produced by specifying the ID=PROB option, and are the predicted probabilities for the cutpoints.
Model Convergence Status 

Convergence criterion (GCONV=1E8) satisfied. 
Model Fit Statistics  

Criterion  Intercept Only 
Intercept and Covariates 
AIC  52.918  49.384 
SC  54.679  52.907 
2 Log L  50.918  45.384 
Testing Global Null Hypothesis: BETA=0  

Test  ChiSquare  DF  Pr > ChiSq 
Likelihood Ratio  5.5339  1  0.0187 
Score  5.6893  1  0.0171 
Wald  4.6869  1  0.0304 
Analysis of Maximum Likelihood Estimates  

Parameter  DF  Estimate  Standard Error 
Wald ChiSquare 
Pr > ChiSq 
Intercept  1  2.4646  1.5913  2.3988  0.1214 
alb  1  1.0520  0.4859  4.6869  0.0304 
Odds Ratio Estimates  

Effect  Point Estimate  95% Wald Confidence Limits 

alb  0.349  0.135  0.905 
Model Convergence Status 

Convergence criterion (GCONV=1E8) satisfied. 
Model Fit Statistics  

Criterion  Intercept Only 
Intercept and Covariates 
AIC  52.918  46.262 
SC  54.679  49.784 
2 Log L  50.918  42.262 
Testing Global Null Hypothesis: BETA=0  

Test  ChiSquare  DF  Pr > ChiSq 
Likelihood Ratio  8.6567  1  0.0033 
Score  8.3613  1  0.0038 
Wald  6.3845  1  0.0115 
Analysis of Maximum Likelihood Estimates  

Parameter  DF  Estimate  Standard Error 
Wald ChiSquare 
Pr > ChiSq 
Intercept  1  2.1542  1.2477  2.9808  0.0843 
totscore  1  0.7696  0.3046  6.3845  0.0115 
Odds Ratio Estimates  

Effect  Point Estimate  95% Wald Confidence Limits 

totscore  0.463  0.255  0.841 
Model Convergence Status 

Convergence criterion (GCONV=1E8) satisfied. 
Model Fit Statistics  

Criterion  Intercept Only 
Intercept and Covariates 
AIC  52.918  51.794 
SC  54.679  55.316 
2 Log L  50.918  47.794 
Testing Global Null Hypothesis: BETA=0  

Test  ChiSquare  DF  Pr > ChiSq 
Likelihood Ratio  3.1244  1  0.0771 
Score  3.1123  1  0.0777 
Wald  2.9059  1  0.0883 
Analysis of Maximum Likelihood Estimates  

Parameter  DF  Estimate  Standard Error 
Wald ChiSquare 
Pr > ChiSq 
Intercept  1  2.8295  2.2065  1.6445  0.1997 
tp  1  0.6279  0.3683  2.9059  0.0883 
Odds Ratio Estimates  

Effect  Point Estimate  95% Wald Confidence Limits 

tp  0.534  0.259  1.099 
All ROC curves being compared are also overlaid on the same plot, as shown in Output 53.8.8.
Output 53.8.9 displays the association statistics, and displays the area under the ROC curve along with its standard error and a confidence interval for each model in the comparison. The confidence interval for Total Protein contains 0.50; hence it is not significantly different from random guessing, which is represented by the diagonal line in the preceding ROC plots.
ROC Association Statistics  

ROC Model  MannWhitney  Somers' D (Gini) 
Gamma  Taua  
Area  Standard Error 
95% Wald Confidence Limits 

Albumin  0.7366  0.0927  0.5549  0.9182  0.4731  0.4809  0.1949 
KG Score  0.7258  0.1028  0.5243  0.9273  0.4516  0.5217  0.1860 
Total Protein  0.6478  0.1000  0.4518  0.8439  0.2957  0.3107  0.1218 
Output 53.8.10 shows that the contrast used ’KG Score’ as the reference level. This table is produced by specifying the E option in the ROCCONTRAST statement.
ROC Contrast Coefficients  

ROC Model  Row1  Row2 
Albumin  1  0 
KG Score  1  1 
Total Protein  0  1 
Output 53.8.11 shows that the 2degreesoffreedom test that the ’KG Score’ is different from at least one other test is not significant at the 0.05 level.
ROC Contrast Test Results  

Contrast  DF  ChiSquare  Pr > ChiSq 
Reference = KG Score  2  2.5340  0.2817 
Output 53.8.12 is produced by specifying the ESTIMATE option in the ROCCONTRAST statement. Each row shows that the curves are not significantly different.
ROC Contrast Estimation and Testing Results by Row  

Contrast  Estimate  Standard Error 
95% Wald Confidence Limits 
ChiSquare  Pr > ChiSq  
Albumin  KG Score  0.0108  0.0953  0.1761  0.1976  0.0127  0.9102 
Total Protein  KG Score  0.0780  0.1046  0.2830  0.1271  0.5554  0.4561 