The SAS System                          1
                                   14:17 Wednesday, December 6, 2017

                 Obs    li    sex    aop     n    y

                  1      0     0      0      3    3
                  2      0     0      1      2    2
                  3      0     1      0      4    4
                  4      0     1      1      1    1
                  5      1     0      0      5    5
                  6      1     0      1      5    3
                  7      1     1      0      9    5
                  8      1     1      1     17    6
            Regular Logistic Regression for Sarcoma Data           2
                                   14:17 Wednesday, December 6, 2017

                       The LOGISTIC Procedure

                         Model Information

          Data Set                       WORK.GOORIN     
          Response Variable (Events)     y               
          Response Variable (Trials)     n               
          Model                          binary logit    
          Optimization Technique         Fisher's scoring


              Number of Observations Read           8
              Number of Observations Used           8
              Sum of Frequencies Read              46
              Sum of Frequencies Used              46


                          Response Profile
 
                 Ordered     Binary           Total
                   Value     Outcome      Frequency

                       1     Event               29
                       2     Nonevent            17


                      Model Convergence Status

         Quasi-complete separation of data points detected.       

WARNING: The maximum likelihood estimate may not exist.
WARNING: The LOGISTIC procedure continues in spite of the above 
         warning. Results shown are based on the last maximum 
         likelihood iteration. Validity of the model fit is 
         questionable.


                       Model Fit Statistics
 
                                    Intercept and Covariates
                     Intercept            Log       Full Log
       Criterion          Only     Likelihood     Likelihood

       AIC              62.603         50.798         17.673
       SC               64.431         58.112         24.987
       -2 Log L         60.603         42.798          9.673


              Testing Global Null Hypothesis: BETA=0
 
      Test                 Chi-Square       DF     Pr > ChiSq

      Likelihood Ratio        17.8049        3         0.0005
      Score                   13.1688        3         0.0043
      Wald                     5.5103        3         0.1380


             Analysis of Maximum Likelihood Estimates
 
                               Standard          Wald
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     14.7426       230.1        0.0041        0.9489
li            1    -12.6349       230.1        0.0030        0.9562
sex           1     -1.6362      0.9123        3.2167        0.0729
aop           1     -1.2204      0.7712        2.5042        0.1135


                        Odds Ratio Estimates
                                  
                          Point          95% Wald
             Effect    Estimate      Confidence Limits

             li          <0.001      <0.001    >999.999
             sex          0.195       0.033       1.164
             aop          0.295       0.065       1.338


   Association of Predicted Probabilities and Observed Responses

         Percent Concordant     72.0    Somers' D    0.627
         Percent Discordant      9.3    Gamma        0.771
         Percent Tied           18.7    Tau-a        0.299
         Pairs                   493    c            0.813
                     Exact Logistic Regression                     3
                                   14:17 Wednesday, December 6, 2017

                       The LOGISTIC Procedure

                         Model Information

          Data Set                       WORK.GOORIN     
          Response Variable (Events)     y               
          Response Variable (Trials)     n               
          Model                          binary logit    
          Optimization Technique         Fisher's scoring


              Number of Observations Read           8
              Number of Observations Used           8
              Sum of Frequencies Read              46
              Sum of Frequencies Used              46


                          Response Profile
 
                 Ordered     Binary           Total
                   Value     Outcome      Frequency

                       1     Event               29
                       2     Nonevent            17


                      Model Convergence Status

         Quasi-complete separation of data points detected.       

WARNING: The maximum likelihood estimate may not exist.
WARNING: The LOGISTIC procedure continues in spite of the above 
         warning. Results shown are based on the last maximum 
         likelihood iteration. Validity of the model fit is 
         questionable.


                       Model Fit Statistics
 
                                    Intercept and Covariates
                     Intercept            Log       Full Log
       Criterion          Only     Likelihood     Likelihood

       AIC              62.603         50.798         17.673
       SC               64.431         58.112         24.987
       -2 Log L         60.603         42.798          9.673


              Testing Global Null Hypothesis: BETA=0
 
      Test                 Chi-Square       DF     Pr > ChiSq

      Likelihood Ratio        17.8049        3         0.0005
      Score                   13.1688        3         0.0043
      Wald                     5.5103        3         0.1380


             Analysis of Maximum Likelihood Estimates
 
                               Standard          Wald
Parameter    DF    Estimate       Error    Chi-Square    Pr > ChiSq

Intercept     1     14.7426       230.1        0.0041        0.9489
li            1    -12.6349       230.1        0.0030        0.9562
sex           1     -1.6362      0.9123        3.2167        0.0729
aop           1     -1.2204      0.7712        2.5042        0.1135


                        Odds Ratio Estimates
                                  
                          Point          95% Wald
             Effect    Estimate      Confidence Limits

             li          <0.001      <0.001    >999.999
             sex          0.195       0.033       1.164
             aop          0.295       0.065       1.338


   Association of Predicted Probabilities and Observed Responses

         Percent Concordant     72.0    Somers' D    0.627
         Percent Discordant      9.3    Gamma        0.771
         Percent Tied           18.7    Tau-a        0.299
         Pairs                   493    c            0.813
                     Exact Logistic Regression                     4
                                   14:17 Wednesday, December 6, 2017

                       The LOGISTIC Procedure
 
                     Exact Conditional Analysis

                       Sufficient Statistics
 
                        Parameter     Value

                        Intercept        29
                        li               19
                        sex              16
                        aop              12


                      Exact Conditional Tests
 
                                            --- p-Value ---
         Effect   Test          Statistic    Exact      Mid

         li       Score            4.5416   0.0606   0.0421
                  Probability      0.0371   0.0606   0.0421
         sex      Score            3.3707   0.1169   0.0874
                  Probability      0.0591   0.1169   0.0874
         aop      Score            2.4797   0.1535   0.1111
                  Probability      0.0847   0.1535   0.1111


                     Exact Parameter Estimates
 
                         Standard      95% Confidence    Two-sided
 Parameter   Estimate       Error         Limits           p-Value

 li           -1.8860*          .  -Infinity    -0.1318     0.0742
 sex          -1.5479      0.8884    -4.0238     0.3627     0.1392
 aop          -1.1561      0.7506    -2.9972     0.5114     0.2182

           NOTE: * indicates a median unbiased estimate.


                         Exact Odds Ratios
 
                                 95% Confidence     Two-sided
      Parameter   Estimate           Limits           p-Value

      li             0.152*          0      0.876      0.0742
      sex            0.213       0.018      1.437      0.1392
      aop            0.315       0.050      1.668      0.2182

           NOTE: * indicates a median unbiased estimate.
                     Exact Logistic Regression                     5
                                   14:17 Wednesday, December 6, 2017

     Obs    li    sex    aop        Count     Score       Prob

       1    19      .      .     29445360     4.5416    0.03709
       2    20      .      .    147312480     1.4937    0.18556
       3    21      .      .    271271448     0.0981    0.34171
       4    22      .      .    231819344     0.3548    0.29201
       5    23      .      .     95325664     2.2638    0.12008
       6    24      .      .     17473144     5.8251    0.02201
       7    25      .      .      1204008    11.0387    0.00152
       8    26      .      .        19448    17.9046    0.00002
       9     .     14      .       299880    11.4024    0.00060
      10     .     15      .      4898040     6.7930    0.00984
      11     .     16      .     29445360     3.3707    0.05914
      12     .     17      .     87836280     1.1354    0.17641
      13     .     18      .    144347000     0.0871    0.28990
      14     .     19      .    135419960     0.2259    0.27197
      15     .     20      .     72090200     1.5516    0.14478
      16     .     21      .     20663500     4.0644    0.04150
      17     .     22      .      2795650     7.7642    0.00561
      18     .     23      .       121550    12.6510    0.00024
      19     .      .      8         1360    19.7833    0.00000
      20     .      .      9        64600    13.9096    0.00019
      21     .      .     10      1011160     9.0678    0.00291
      22     .      .     11      7401120     5.2578    0.02129
      23     .      .     12     29445360     2.4797    0.08469
      24     .      .     13     68686800     0.7335    0.19756
      25     .      .     14     97275360     0.0191    0.27979
      26     .      .     15     84307080     0.3366    0.24249
      27     .      .     16     44049720     1.6859    0.12670
      28     .      .     17     13251160     4.0672    0.03811
      29     .      .     18      2059720     7.4803    0.00592
      30     .      .     19       123760    11.9253    0.00036