# The PHREG Procedure

### Effect Selection Methods

Five effect selection methods are available. The simplest method (and the default) is SELECTION=NONE, for which PROC PHREG fits the complete model as specified in the MODEL statement. The other four methods are FORWARD for forward selection, BACKWARD for backward elimination, STEPWISE for stepwise selection, and SCORE for best subsets selection. These methods are specified with the SELECTION= option in the MODEL statement and are based on the score test or Wald test as described in the section Type 3 Tests and Joint Tests.

When SELECTION=FORWARD, PROC PHREG first estimates parameters for effects that are forced into the model. These are the first n effects in the MODEL statement, where n is the number specified by the START= or INCLUDE= option in the MODEL statement (n is zero by default). Next, the procedure computes the score statistic for each effect that is not in the model. Each score statistic is the chi-square statistic of the score test for testing the null hypothesis that the corresponding effect that is not in the model is null. If the largest of these statistics is significant at the SLSENTRY= level, the effect with the largest score statistic is added to the model. After an effect is entered in the model, it is never removed from the model. The process is repeated until none of the remaining effects meet the specified level for entry or until the STOP= value is reached.

When SELECTION=BACKWARD, parameters for the complete model as specified in the MODEL statement are estimated unless the START= option is specified. In that case, only the parameters for the first n effects in the MODEL statement are estimated, where n is the number specified by the START= option. Next, the procedure computes the Wald statistic of each effect in the model. Each Wald’s statistic is the chi-square statistic of the Wald test for testing the null hypothesis that the corresponding effect is null. If the smallest of these statistics is not significant at the SLSTAY= level, the effect with the smallest Wald statistic is removed. After an effect is removed from the model, it remains excluded. The process is repeated until no other variable in the model meets the specified level for removal or until the STOP= value is reached.

The SELECTION=STEPWISE option is similar to the SELECTION=FORWARD option except that effects already in the model do not necessarily remain. Effects are entered into and removed from the model in such a way that each forward selection step can be followed by one or more backward elimination steps. The stepwise selection process terminates if no further effect can be added to the model or if the effect just entered into the model is the only effect that is removed in the subsequent backward elimination.

For SELECTION=SCORE, PROC PHREG uses the branch-and-bound algorithm of Furnival and Wilson (1974) to find a specified number of models with the highest score (chi-square) statistic for all possible model sizes, from 1, 2, or 3 variables, and so on, up to the single model that contains all of the explanatory variables. The number of models displayed for each model size is controlled by the BEST= option. You can use the START= option to impose a minimum model size, and you can use the STOP= option to impose a maximum model size. For instance, with BEST=3, START=2, and STOP=5, the SCORE selection method displays the best three models (that is, the three models with the highest score chi-squares) that contain 2, 3, 4, and 5 variables. One of the limitations of the branch-and-bound algorithm is that it works only when each explanatory effect contains exactly one parameter—the SELECTION=SCORE option is not allowed when an explanatory effect in the MODEL statement contains a CLASS variable.

The SEQUENTIAL and STOPRES options can alter the default criteria for adding variables to or removing variables from the model when they are used with the FORWARD, BACKWARD, or STEPWISE selection method.