Example 49.2: Best Subset Selection

The PHREG Procedure

Example 49.2: Best Subset Selection

An alternative to stepwise selection of variables is best subset selection. The procedure uses the branch and bound algorithm of Furnival and Wilson (1974) to find a specified number of best models containing one, two, three variables and so on, up to the single model containing all of the explanatory variables. The criterion used to determine "best" is based on the global score chi-squared statistic. For two models A and B, each having the same number of explanatory variables, model A is considered to be better than model B if the global score chi-squared statistic for A exceeds that for B.

Best subset selection analysis is requested by specifying the SELECTION=SCORE option in the MODEL statement. The BEST=3 option requests the procedure to identify only the three best models for each size. In other words, PROC PHREG will list the three models having the highest score statistics of all the models possible for a given number of covariates.

   proc phreg data=Myeloma;
      model Time*VStatus(0)=LogBUN HGB Platelet Age LogWBC
                            Frac LogPBM Protein SCalc
                            / selection=score best=3;
   run;

Output 49.2.1 displays the results of this analysis. The number of explanatory variables in the model is given in the first column, and the names of the variables are listed on the right. The models are listed in descending order of their score chi-squared values within each model size. For example, among all models containing two explanatory variables, the model that contains the variables LogBUN and HGB has the largest score value (12.7252), the model that contains the variables LogBUN and Platelet has the second largest score value (11.1842), and the model that contains the variables LogBUN and SCalc has the third largest score value (9.9962).

Output 49.2.1: Best Variable Combinations

The PHREG Procedure

Regression Models Selected by Score Criterion
Number of Variables	Score Chi-Square	Variables Included in Model
1	8.5164	LogBUN
1	5.0664	HGB
1	3.1816	Platelet
2	12.7252	LogBUN HGB
2	11.1842	LogBUN Platelet
2	9.9962	LogBUN SCalc
3	15.3053	LogBUN HGB SCalc
3	13.9911	LogBUN HGB Age
3	13.5788	LogBUN HGB Frac
4	16.9873	LogBUN HGB Age SCalc
4	16.0457	LogBUN HGB Frac SCalc
4	15.7619	LogBUN HGB LogPBM SCalc
5	17.6291	LogBUN HGB Age Frac SCalc
5	17.3519	LogBUN HGB Age LogPBM SCalc
5	17.1922	LogBUN HGB Age LogWBC SCalc
6	17.9120	LogBUN HGB Age Frac LogPBM SCalc
6	17.7947	LogBUN HGB Age LogWBC Frac SCalc
6	17.7744	LogBUN HGB Platelet Age Frac SCalc
7	18.1517	LogBUN HGB Platelet Age Frac LogPBM SCalc
7	18.0568	LogBUN HGB Age LogWBC Frac LogPBM SCalc
7	18.0223	LogBUN HGB Platelet Age LogWBC Frac SCalc
8	18.3925	LogBUN HGB Platelet Age LogWBC Frac LogPBM SCalc
8	18.1636	LogBUN HGB Platelet Age Frac LogPBM Protein SCalc
8	18.1309	LogBUN HGB Platelet Age LogWBC Frac Protein SCalc
9	18.4550	LogBUN HGB Platelet Age LogWBC Frac LogPBM Protein SCalc

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