## Example 53.1 Stepwise Logistic Regression and Predicted Values

Consider a study on cancer remission (Lee; 1974). The data consist of patient characteristics and whether or not cancer remission occured. The following DATA step creates the data set Remission containing seven variables. The variable remiss is the cancer remission indicator variable with a value of 1 for remission and a value of 0 for nonremission. The other six variables are the risk factors thought to be related to cancer remission.

```data Remission;
input remiss cell smear infil li blast temp;
label remiss='Complete Remission';
datalines;
1   .8   .83  .66  1.9  1.1     .996
1   .9   .36  .32  1.4   .74    .992
0   .8   .88  .7    .8   .176   .982
0  1     .87  .87   .7  1.053   .986
1   .9   .75  .68  1.3   .519   .98
0  1     .65  .65   .6   .519   .982
1   .95  .97  .92  1    1.23    .992
0   .95  .87  .83  1.9  1.354  1.02
0  1     .45  .45   .8   .322   .999
0   .95  .36  .34   .5  0      1.038
0   .85  .39  .33   .7   .279   .988
0   .7   .76  .53  1.2   .146   .982
0   .8   .46  .37   .4   .38   1.006
0   .2   .39  .08   .8   .114   .99
0  1     .9   .9   1.1  1.037   .99
1  1     .84  .84  1.9  2.064  1.02
0   .65  .42  .27   .5   .114  1.014
0  1     .75  .75  1    1.322  1.004
0   .5   .44  .22   .6   .114   .99
1  1     .63  .63  1.1  1.072   .986
0  1     .33  .33   .4   .176  1.01
0   .9   .93  .84   .6  1.591  1.02
1  1     .58  .58  1     .531  1.002
0   .95  .32  .3   1.6   .886   .988
1  1     .6   .6   1.7   .964   .99
1  1     .69  .69   .9   .398   .986
0  1     .73  .73   .7   .398   .986
;
```

The following invocation of PROC LOGISTIC illustrates the use of stepwise selection to identify the prognostic factors for cancer remission. A significance level of 0.3 is required to allow a variable into the model (SLENTRY=0.3), and a significance level of 0.35 is required for a variable to stay in the model (SLSTAY=0.35). A detailed account of the variable selection process is requested by specifying the DETAILS option. The Hosmer and Lemeshow goodness-of-fit test for the final selected model is requested by specifying the LACKFIT option. The OUTEST= and COVOUT options in the PROC LOGISTIC statement create a data set that contains parameter estimates and their covariances for the final selected model. The response variable option EVENT= chooses remiss=1 (remission) as the event so that the probability of remission is modeled. The OUTPUT statement creates a data set that contains the cumulative predicted probabilities and the corresponding confidence limits, and the individual and cross validated predicted probabilities for each observation.

```title 'Stepwise Regression on Cancer Remission Data';
proc logistic data=Remission outest=betas covout;
model remiss(event='1')=cell smear infil li blast temp
/ selection=stepwise
slentry=0.3
slstay=0.35
details
lackfit;
output out=pred p=phat lower=lcl upper=ucl
predprob=(individual crossvalidate);
run;
```
```proc print data=betas;
title2 'Parameter Estimates and Covariance Matrix';
run;
```
```proc print data=pred;
title2 'Predicted Probabilities and 95% Confidence Limits';
run;
```

In stepwise selection, an attempt is made to remove any insignificant variables from the model before adding a significant variable to the model. Each addition or deletion of a variable to or from a model is listed as a separate step in the displayed output, and at each step a new model is fitted. Details of the model selection steps are shown in Outputs 53.1.1 through 53.1.5.

Prior to the first step, the intercept-only model is fit and individual score statistics for the potential variables are evaluated (Output 53.1.1).

Output 53.1.1 Startup Model
 Stepwise Regression on Cancer Remission Data

The LOGISTIC Procedure

Step 0. Intercept entered:

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

 -2 Log L = 34.372

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept 1 -0.6931 0.4082 2.8827 0.0895

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
9.4609 6 0.1493

Analysis of Effects Eligible for
Entry
Effect DF Score
Chi-Square
Pr > ChiSq
cell 1 1.8893 0.1693
smear 1 1.0745 0.2999
infil 1 1.8817 0.1701
li 1 7.9311 0.0049
blast 1 3.5258 0.0604
temp 1 0.6591 0.4169

In Step 1 (Output 53.1.2), the variable li is selected into the model since it is the most significant variable among those to be chosen (). The intermediate model that contains an intercept and li is then fitted. li remains significant () and is not removed.

Output 53.1.2 Step 1 of the Stepwise Analysis

Step 1. Effect li entered:

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 36.372 30.073
SC 37.668 32.665
-2 Log L 34.372 26.073

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 8.2988 1 0.0040
Score 7.9311 1 0.0049
Wald 5.9594 1 0.0146

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept 1 -3.7771 1.3786 7.5064 0.0061
li 1 2.8973 1.1868 5.9594 0.0146

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
li 18.124 1.770 185.563

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 84.0 Somers' D 0.710
Percent Discordant 13.0 Gamma 0.732
Percent Tied 3.1 Tau-a 0.328
Pairs 162 c 0.855

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
3.1174 5 0.6819

Analysis of Effects Eligible for
Removal
Effect DF Wald
Chi-Square
Pr > ChiSq
li 1 5.9594 0.0146

 Note: No effects for the model in Step 1 are removed.

Analysis of Effects Eligible for
Entry
Effect DF Score
Chi-Square
Pr > ChiSq
cell 1 1.1183 0.2903
smear 1 0.1369 0.7114
infil 1 0.5715 0.4497
blast 1 0.0932 0.7601
temp 1 1.2591 0.2618

In Step 2 (Output 53.1.3), the variable temp is added to the model. The model then contains an intercept and the variables li and temp. Both li and temp remain significant at 0.35 level; therefore, neither li nor temp is removed from the model.

Output 53.1.3 Step 2 of the Stepwise Analysis

Step 2. Effect temp entered:

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 36.372 30.648
SC 37.668 34.535
-2 Log L 34.372 24.648

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 9.7239 2 0.0077
Score 8.3648 2 0.0153
Wald 5.9052 2 0.0522

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept 1 47.8448 46.4381 1.0615 0.3029
li 1 3.3017 1.3593 5.9002 0.0151
temp 1 -52.4214 47.4897 1.2185 0.2697

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
li 27.158 1.892 389.856
temp <0.001 <0.001 >999.999

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 87.0 Somers' D 0.747
Percent Discordant 12.3 Gamma 0.752
Percent Tied 0.6 Tau-a 0.345
Pairs 162 c 0.873

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
2.1429 4 0.7095

Analysis of Effects Eligible for
Removal
Effect DF Wald
Chi-Square
Pr > ChiSq
li 1 5.9002 0.0151
temp 1 1.2185 0.2697

 Note: No effects for the model in Step 2 are removed.

Analysis of Effects Eligible for
Entry
Effect DF Score
Chi-Square
Pr > ChiSq
cell 1 1.4700 0.2254
smear 1 0.1730 0.6775
infil 1 0.8274 0.3630
blast 1 1.1013 0.2940

In Step 3 (Output 53.1.4), the variable cell is added to the model. The model then contains an intercept and the variables li, temp, and cell. None of these variables are removed from the model since all are significant at the 0.35 level.

Output 53.1.4 Step 3 of the Stepwise Analysis

Step 3. Effect cell entered:

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 36.372 29.953
SC 37.668 35.137
-2 Log L 34.372 21.953

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 12.4184 3 0.0061
Score 9.2502 3 0.0261
Wald 4.8281 3 0.1848

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept 1 67.6339 56.8875 1.4135 0.2345
cell 1 9.6521 7.7511 1.5507 0.2130
li 1 3.8671 1.7783 4.7290 0.0297
temp 1 -82.0737 61.7124 1.7687 0.1835

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
cell >999.999 0.004 >999.999
li 47.804 1.465 >999.999
temp <0.001 <0.001 >999.999

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 88.9 Somers' D 0.778
Percent Discordant 11.1 Gamma 0.778
Percent Tied 0.0 Tau-a 0.359
Pairs 162 c 0.889

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
0.1831 3 0.9803

Analysis of Effects Eligible for
Removal
Effect DF Wald
Chi-Square
Pr > ChiSq
cell 1 1.5507 0.2130
li 1 4.7290 0.0297
temp 1 1.7687 0.1835

 Note: No effects for the model in Step 3 are removed.

Analysis of Effects Eligible for
Entry
Effect DF Score
Chi-Square
Pr > ChiSq
smear 1 0.0956 0.7572
infil 1 0.0844 0.7714
blast 1 0.0208 0.8852

Finally, none of the remaining variables outside the model meet the entry criterion, and the stepwise selection is terminated. A summary of the stepwise selection is displayed in Output 53.1.5.

Output 53.1.5 Summary of the Stepwise Selection
Summary of Stepwise Selection
Step Effect DF Number
In
Score
Chi-Square
Wald
Chi-Square
Pr > ChiSq
Entered Removed
1 li   1 1 7.9311   0.0049
2 temp   1 2 1.2591   0.2618
3 cell   1 3 1.4700   0.2254

Results of the Hosmer and Lemeshow test are shown in Output 53.1.6. There is no evidence of a lack of fit in the selected model .

Output 53.1.6 Display of the LACKFIT Option
Partition for the Hosmer and Lemeshow Test
Group Total remiss = 1 remiss = 0
Observed Expected Observed Expected
1 3 0 0.00 3 3.00
2 3 0 0.01 3 2.99
3 3 0 0.19 3 2.81
4 3 0 0.56 3 2.44
5 4 1 1.09 3 2.91
6 3 2 1.35 1 1.65
7 3 2 1.84 1 1.16
8 3 3 2.15 0 0.85
9 2 1 1.80 1 0.20

Hosmer and Lemeshow Goodness-of-Fit
Test
Chi-Square DF Pr > ChiSq
6.2983 7 0.5054

The data set betas created by the OUTEST= and COVOUT options is displayed in Output 53.1.7. The data set contains parameter estimates and the covariance matrix for the final selected model. Note that all explanatory variables listed in the MODEL statement are included in this data set; however, variables that are not included in the final model have all missing values.

Output 53.1.7 Data Set of Estimates and Covariances
 Stepwise Regression on Cancer Remission Data Parameter Estimates and Covariance Matrix

Obs _LINK_ _TYPE_ _STATUS_ _NAME_ Intercept cell smear infil li blast temp _LNLIKE_
1 LOGIT PARMS 0 Converged remiss 67.63 9.652 . . 3.8671 . -82.07 -10.9767
2 LOGIT COV 0 Converged Intercept 3236.19 157.097 . . 64.5726 . -3483.23 -10.9767
3 LOGIT COV 0 Converged cell 157.10 60.079 . . 6.9454 . -223.67 -10.9767
4 LOGIT COV 0 Converged smear . . . . . . . -10.9767
5 LOGIT COV 0 Converged infil . . . . . . . -10.9767
6 LOGIT COV 0 Converged li 64.57 6.945 . . 3.1623 . -75.35 -10.9767
7 LOGIT COV 0 Converged blast . . . . . . . -10.9767
8 LOGIT COV 0 Converged temp -3483.23 -223.669 . . -75.3513 . 3808.42 -10.9767

The data set pred created by the OUTPUT statement is displayed in Output 53.1.8. It contains all the variables in the input data set, the variable phat for the (cumulative) predicted probability, the variables lcl and ucl for the lower and upper confidence limits for the probability, and four other variables (IP_1, IP_0, XP_1, and XP_0) for the PREDPROBS= option. The data set also contains the variable _LEVEL_, indicating the response value to which phat, lcl, and ucl refer. For instance, for the first row of the OUTPUT data set, the values of _LEVEL_ and phat, lcl, and ucl are 1, 0.72265, 0.16892, and 0.97093, respectively; this means that the estimated probability that remiss=1 is 0.723 for the given explanatory variable values, and the corresponding 95% confidence interval is (0.16892, 0.97093). The variables IP_1 and IP_0 contain the predicted probabilities that remiss=1 and remiss=0, respectively. Note that values of phat and IP_1 are identical since they both contain the probabilities that remiss=1. The variables XP_1 and XP_0 contain the cross validated predicted probabilities that remiss=1 and remiss=0, respectively.

Output 53.1.8 Predicted Probabilities and Confidence Intervals
 Stepwise Regression on Cancer Remission Data Predicted Probabilities and 95% Confidence Limits

Obs remiss cell smear infil li blast temp _FROM_ _INTO_ IP_0 IP_1 XP_0 XP_1 _LEVEL_ phat lcl ucl
1 1 0.80 0.83 0.66 1.9 1.100 0.996 1 1 0.27735 0.72265 0.43873 0.56127 1 0.72265 0.16892 0.97093
2 1 0.90 0.36 0.32 1.4 0.740 0.992 1 1 0.42126 0.57874 0.47461 0.52539 1 0.57874 0.26788 0.83762
3 0 0.80 0.88 0.70 0.8 0.176 0.982 0 0 0.89540 0.10460 0.87060 0.12940 1 0.10460 0.00781 0.63419
4 0 1.00 0.87 0.87 0.7 1.053 0.986 0 0 0.71742 0.28258 0.67259 0.32741 1 0.28258 0.07498 0.65683
5 1 0.90 0.75 0.68 1.3 0.519 0.980 1 1 0.28582 0.71418 0.36901 0.63099 1 0.71418 0.25218 0.94876
6 0 1.00 0.65 0.65 0.6 0.519 0.982 0 0 0.72911 0.27089 0.67269 0.32731 1 0.27089 0.05852 0.68951
7 1 0.95 0.97 0.92 1.0 1.230 0.992 1 0 0.67844 0.32156 0.72923 0.27077 1 0.32156 0.13255 0.59516
8 0 0.95 0.87 0.83 1.9 1.354 1.020 0 1 0.39277 0.60723 0.09906 0.90094 1 0.60723 0.10572 0.95287
9 0 1.00 0.45 0.45 0.8 0.322 0.999 0 0 0.83368 0.16632 0.80864 0.19136 1 0.16632 0.03018 0.56123
10 0 0.95 0.36 0.34 0.5 0.000 1.038 0 0 0.99843 0.00157 0.99840 0.00160 1 0.00157 0.00000 0.68962
11 0 0.85 0.39 0.33 0.7 0.279 0.988 0 0 0.92715 0.07285 0.91723 0.08277 1 0.07285 0.00614 0.49982
12 0 0.70 0.76 0.53 1.2 0.146 0.982 0 0 0.82714 0.17286 0.63838 0.36162 1 0.17286 0.00637 0.87206
13 0 0.80 0.46 0.37 0.4 0.380 1.006 0 0 0.99654 0.00346 0.99644 0.00356 1 0.00346 0.00001 0.46530
14 0 0.20 0.39 0.08 0.8 0.114 0.990 0 0 0.99982 0.00018 0.99981 0.00019 1 0.00018 0.00000 0.96482
15 0 1.00 0.90 0.90 1.1 1.037 0.990 0 1 0.42878 0.57122 0.35354 0.64646 1 0.57122 0.25303 0.83973
16 1 1.00 0.84 0.84 1.9 2.064 1.020 1 1 0.28530 0.71470 0.47213 0.52787 1 0.71470 0.15362 0.97189
17 0 0.65 0.42 0.27 0.5 0.114 1.014 0 0 0.99938 0.00062 0.99937 0.00063 1 0.00062 0.00000 0.62665
18 0 1.00 0.75 0.75 1.0 1.322 1.004 0 0 0.77711 0.22289 0.73612 0.26388 1 0.22289 0.04483 0.63670
19 0 0.50 0.44 0.22 0.6 0.114 0.990 0 0 0.99846 0.00154 0.99842 0.00158 1 0.00154 0.00000 0.79644
20 1 1.00 0.63 0.63 1.1 1.072 0.986 1 1 0.35089 0.64911 0.42053 0.57947 1 0.64911 0.26305 0.90555
21 0 1.00 0.33 0.33 0.4 0.176 1.010 0 0 0.98307 0.01693 0.98170 0.01830 1 0.01693 0.00029 0.50475
22 0 0.90 0.93 0.84 0.6 1.591 1.020 0 0 0.99378 0.00622 0.99348 0.00652 1 0.00622 0.00003 0.56062
23 1 1.00 0.58 0.58 1.0 0.531 1.002 1 0 0.74739 0.25261 0.84423 0.15577 1 0.25261 0.06137 0.63597
24 0 0.95 0.32 0.30 1.6 0.886 0.988 0 1 0.12989 0.87011 0.03637 0.96363 1 0.87011 0.40910 0.98481
25 1 1.00 0.60 0.60 1.7 0.964 0.990 1 1 0.06868 0.93132 0.08017 0.91983 1 0.93132 0.44114 0.99573
26 1 1.00 0.69 0.69 0.9 0.398 0.986 1 0 0.53949 0.46051 0.62312 0.37688 1 0.46051 0.16612 0.78529
27 0 1.00 0.73 0.73 0.7 0.398 0.986 0 0 0.71742 0.28258 0.67259 0.32741 1 0.28258 0.07498 0.65683

Next, a different variable selection method is used to select prognostic factors for cancer remission, and an efficient algorithm is employed to eliminate insignificant variables from a model. The following statements invoke PROC LOGISTIC to perform the backward elimination analysis:

```title 'Backward Elimination on Cancer Remission Data';
proc logistic data=Remission;
model remiss(event='1')=temp cell li smear blast
/ selection=backward fast slstay=0.2 ctable;
run;
```

The backward elimination analysis (SELECTION=BACKWARD) starts with a model that contains all explanatory variables given in the MODEL statement. By specifying the FAST option, PROC LOGISTIC eliminates insignificant variables without refitting the model repeatedly. This analysis uses a significance level of 0.2 to retain variables in the model (SLSTAY=0.2), which is different from the previous stepwise analysis where SLSTAY=.35. The CTABLE option is specified to produce classifications of input observations based on the final selected model.

Results of the fast elimination analysis are shown in Output 53.1.9 and Output 53.1.10. Initially, a full model containing all six risk factors is fit to the data (Output 53.1.9). In the next step (Output 53.1.10), PROC LOGISTIC removes blast, smear, cell, and temp from the model all at once. This leaves li and the intercept as the only variables in the final model. Note that in this analysis, only parameter estimates for the final model are displayed because the DETAILS option has not been specified.

Output 53.1.9 Initial Step in Backward Elimination
 Backward Elimination on Cancer Remission Data

The LOGISTIC Procedure

Model Information
Data Set WORK.REMISSION
Response Variable remiss Complete Remission
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

 Number of Observations Read 27 27

Response Profile
Ordered
Value
remiss Total
Frequency
1 0 18
2 1 9

Probability modeled is remiss=1.

Backward Elimination Procedure

Step 0. The following effects were entered:

Intercept temp cell li smear blast

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 36.372 33.857
SC 37.668 41.632
-2 Log L 34.372 21.857

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 12.5146 5 0.0284
Score 9.3295 5 0.0966
Wald 4.7284 5 0.4499

Output 53.1.10 Fast Elimination Step

Step 1. Fast Backward Elimination:

Analysis of Effects Removed by Fast Backward Elimination
Effect
Removed
Chi-Square DF Pr > ChiSq Residual
Chi-Square
DF Pr >
Residual
ChiSq
blast 0.0008 1 0.9768 0.0008 1 0.9768
smear 0.0951 1 0.7578 0.0959 2 0.9532
cell 1.5134 1 0.2186 1.6094 3 0.6573
temp 0.6535 1 0.4189 2.2628 4 0.6875

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 36.372 30.073
SC 37.668 32.665
-2 Log L 34.372 26.073

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 8.2988 1 0.0040
Score 7.9311 1 0.0049
Wald 5.9594 1 0.0146

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
2.8530 4 0.5827

Summary of Backward Elimination
Step Effect
Removed
DF Number
In
Wald
Chi-Square
Pr > ChiSq
1 blast 1 4 0.0008 0.9768
1 smear 1 3 0.0951 0.7578
1 cell 1 2 1.5134 0.2186
1 temp 1 1 0.6535 0.4189

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept 1 -3.7771 1.3786 7.5064 0.0061
li 1 2.8973 1.1868 5.9594 0.0146

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
li 18.124 1.770 185.563

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 84.0 Somers' D 0.710
Percent Discordant 13.0 Gamma 0.732
Percent Tied 3.1 Tau-a 0.328
Pairs 162 c 0.855

Note that you can also use the FAST option when SELECTION=STEPWISE. However, the FAST option operates only on backward elimination steps. In this example, the stepwise process only adds variables, so the FAST option would not be useful.

Results of the CTABLE option are shown in Output 53.1.11.

Output 53.1.11 Classifying Input Observations
Classification Table
Prob
Level
Correct Incorrect Percentages
Event Non-
Event
Event Non-
Event
Correct Sensi-
tivity
Speci-
ficity
False
POS
False
NEG
0.060 9 0 18 0 33.3 100.0 0.0 66.7 .
0.080 9 2 16 0 40.7 100.0 11.1 64.0 0.0
0.100 9 4 14 0 48.1 100.0 22.2 60.9 0.0
0.120 9 4 14 0 48.1 100.0 22.2 60.9 0.0
0.140 9 7 11 0 59.3 100.0 38.9 55.0 0.0
0.160 9 10 8 0 70.4 100.0 55.6 47.1 0.0
0.180 9 10 8 0 70.4 100.0 55.6 47.1 0.0
0.200 8 13 5 1 77.8 88.9 72.2 38.5 7.1
0.220 8 13 5 1 77.8 88.9 72.2 38.5 7.1
0.240 8 13 5 1 77.8 88.9 72.2 38.5 7.1
0.260 6 13 5 3 70.4 66.7 72.2 45.5 18.8
0.280 6 13 5 3 70.4 66.7 72.2 45.5 18.8
0.300 6 13 5 3 70.4 66.7 72.2 45.5 18.8
0.320 6 14 4 3 74.1 66.7 77.8 40.0 17.6
0.340 5 14 4 4 70.4 55.6 77.8 44.4 22.2
0.360 5 14 4 4 70.4 55.6 77.8 44.4 22.2
0.380 5 15 3 4 74.1 55.6 83.3 37.5 21.1
0.400 5 15 3 4 74.1 55.6 83.3 37.5 21.1
0.420 5 15 3 4 74.1 55.6 83.3 37.5 21.1
0.440 5 15 3 4 74.1 55.6 83.3 37.5 21.1
0.460 4 16 2 5 74.1 44.4 88.9 33.3 23.8
0.480 4 16 2 5 74.1 44.4 88.9 33.3 23.8
0.500 4 16 2 5 74.1 44.4 88.9 33.3 23.8
0.520 4 16 2 5 74.1 44.4 88.9 33.3 23.8
0.540 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.560 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.580 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.600 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.620 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.640 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.660 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.680 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.700 3 16 2 6 70.4 33.3 88.9 40.0 27.3
0.720 2 16 2 7 66.7 22.2 88.9 50.0 30.4
0.740 2 16 2 7 66.7 22.2 88.9 50.0 30.4
0.760 2 16 2 7 66.7 22.2 88.9 50.0 30.4
0.780 2 16 2 7 66.7 22.2 88.9 50.0 30.4
0.800 2 17 1 7 70.4 22.2 94.4 33.3 29.2
0.820 2 17 1 7 70.4 22.2 94.4 33.3 29.2
0.840 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.860 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.880 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.900 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.920 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.940 0 17 1 9 63.0 0.0 94.4 100.0 34.6
0.960 0 18 0 9 66.7 0.0 100.0 . 33.3

Each row of the "Classification Table" corresponds to a cutpoint applied to the predicted probabilities, which is given in the Prob Level column. The frequency tables of observed and predicted responses are given by the next four columns. For example, with a cutpoint of 0.5, 4 events and 16 nonevents were classified correctly. On the other hand, 2 nonevents were incorrectly classified as events and 5 events were incorrectly classified as nonevents. For this cutpoint, the correct classification rate is 20/27 (=74.1%), which is given in the sixth column. Accuracy of the classification is summarized by the sensitivity, specificity, and false positive and negative rates, which are displayed in the last four columns. You can control the number of cutpoints used, and their values, by using the PPROB= option.