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Values of the predicted probability columns (variables with prefix P_) in the SCORE OUT= data set of PROC LOGISTIC will be missing if any of the following conditions occurs:

• Values of one or more of the model predictors are missing. All predictor variables in the model must be nonmissing in order to compute a predicted value. Various computed statistics in the OUTPUT OUT= data set will be missing for this same reason.
• The values of one or more CLASS predictors in the data set being scored (the SCORE DATA= data set) do not appear in the data set used to fit (train) the model. The PROC LOGISTIC DATA= data set is the data set that trains the model. The model only has parameters for the values of a CLASS predictor that appear in the data set that trains the model. A new CLASS predictor value has no model parameter corresponding to it, so no prediction can be computed.
• The FORMAT statement, if used, appears before the SCORE statement. Simply move the FORMAT statement after the SCORE statement to avoid this problem.

To illustrate, consider a study of the analgesic effects of treatments on elderly patients with neuralgia. Two test treatments and a placebo are compared. The response variable is whether the patient reported pain or not. Researchers recorded age and gender of the patients and the duration of complaint before the treatment began. The data, consisting of 60 patients, are contained in the data set Neuralgia. The variable Pain is the response variable. A specification of Pain=Yes indicates there was pain, and Pain=No indicates no pain. The variable Treatment is a categorical variable with three levels: A and B represent the two test treatments, and P represents the placebo treatment. The variable Age is the age of the patients, in years, when treatment began.

/* Training data set */
   Data Neuralgia;
      input Treatment $ Sex $ Age Duration Pain $ @@;
      datalines;
   P  F  68   1  No   B  M  74  16  No  P  F  67  30  No
   P  M  66  26  Yes  B  F  67  28  No  B  F  77  16  No
   A  F  71  12  No   B  F  72  50  No  B  F  76   9  Yes
   A  M  71  17  Yes  A  F  63  27  No  A  F  69  18  Yes
   B  F  66  12  No   A  M  62  42  No  P  F  64   1  Yes
   A  F  64  17  No   P  M  74   4  No  A  F  72  25  No
   P  M  70   1  Yes  B  M  66  19  No  B  M  59  29  No
   A  F  64  30  No   A  M  70  28  No  A  M  69   1  No
   B  F  78   1  No   P  M  83   1  Yes B  F  69  42  No
   B  M  75  30  Yes  P  M  77  29  Yes P  F  79  20  Yes
   A  M  70  12  No   A  F  69  12  No  B  F  65  14  No
   B  M  70   1  No   B  M  67  23  No  A  M  76  25  Yes
   P  M  78  12  Yes  B  M  77   1  Yes B  F  69  24  No
   P  M  66   4  Yes  P  F  65  29  No  P  M  60  26  Yes
   A  M  78  15  Yes  B  M  75  21  Yes A  F  67  11  No
   P  F  72  27  No   P  F  70  13  Yes A  M  75   6  Yes
   B  F  65   7  No   P  F  68  27  Yes P  M  68  11  Yes
   P  M  67  17  Yes  B  M  70  22  No  A  M  65  15  No
   P  F  67   1  Yes  A  M  67  10  No  P  F  72  11  Yes
   A  F  74   1  No   B  M  80  21  Yes A  F  69   3  No
   ;

The following validation data set will be used in the SCORE statement to obtain predicted probabilities for the specified combinations of Treatment and Age. Notice that the first three observations use Treatments A, B, and P all of which appeared in the training data set, Neuralgia, and nonmissing values of Age. However, observation 4 contains a missing value (.) for Age in Treatment A. In observation 5, a nonmissing value of Age is specified, but the specified treatment, Z, is not one that appeared in the training data set.

   /* Validation data set */
   Data Validate;
      input Treatment $ Age;
      datalines;
   A 65
   B 72
   P 80
   A .
   Z 68
   ;

   proc print data=Validate;
      run;

The following statements train the model using the training data set, Neuralgia, and then score the Validate data set. The EVENT="No" option specifies that the probability of Pain=No is to be modeled.

   proc logistic data=Neuralgia;
      class Treatment;
      model Pain (event="No") = Treatment Age;
      score data=Validate out=Preds;
      run;

Notice that predictions are given for the first three observations, but not for the fourth because of the missing value of Age, and not for the fifth because the Treatment value didn't appear in the training data set.

   proc print data=Preds;
      run;

To see why this occurs it helps to know what the fitted model is. Following is the table of parameter estimates from the trained model:

From this table, the model can written as follows:

Logit(p) = 18.5356 + 0.7033*T_A + 1.2759*T_B - 0.2581*Age ,

where Logit(p) is the log odds of Pain=No. T_A and T_B are design variables representing the CLASS predictor, Treatment, and are coded as shown in the "Class Level Information" table below. The first Design Variable column is T_A, the second column is T_B.

Using the model, the first observation in the Validate data set can be scored as follows. From the "Class Level Information" table, Treatment=A is represented in the model by T_A=1 and T_B=0.

Logit(p) = 18.5356 + 0.7033*1 + 1.2759*0 - 0.2581*65 = 2.4624 ,

The probability of Pain=No can be obtained from the logit by the following transformation:

Pr(Pain=No) = 1 / (1+exp(-logit))

For the first observation, the predicted probability of Pain=No is 1 / (1+exp(-2.4624)) = 0.9215 and therefore the predicted probability of Pain=Yes is 1-0.9215 = 0.0785. (The slight difference from the SAS results is due to using rounded values here. The results from PROC LOGISTIC are more precise.)

For observation 2:

Logit(p) = 18.5356 + 0.7033*0 + 1.2759*1 - 0.2581*72 = 1.2283,
Pr(Pain=No) = 0.7735 and Pr(Pain=Yes) = 0.2265 .

For observation 3:

Logit(p) = 18.5356 + 0.7033*-1 + 1.2759*-1 - 0.2581*80 = -4.0916,
Pr(Pain=No) = 0.0164 and Pr(Pain=Yes) = 0.9836.

For the fourth observation:

Logit(p) = 18.5356 + 0.7033*1 + 1.2759*0 - 0.2581*.

Because the value of Age is missing, the model equation is incomplete and the logit and predicted probabilities cannot be computed. Note that simply ignoring the Age term in the model and computing the logit as 18.5356 + 0.7033*1 + 1.2759*0 is not valid because this is equivalent to setting Age=0 which is almost certainly not intended.

For the fifth observation:

Logit(p) = 18.5356 + 0.7033*. + 1.2759*. - 0.2581*68

Because Treatment Z does not appear in the training data set, there are no corresponding values of the design variables, T_A and T_B, so again the model equation is incomplete and the logit and predicted probabilities cannot be computed. Simply ignoring the two treatment terms and computing the logit as 18.5356 - 0.2581*68 is not valid because this is equivalent to setting T_A=T_B=0 and this represents no known Treatment. The only valid treatments are coded as shown in the "Class Level Information" table.

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