The PHREG Procedure

Model Fit Statistics

Suppose the model contains p regression parameters. The three statistics displayed by the PHREG procedure are calculated as follows:

–2 log likelihood:
where is a partial likelihood function for the corresponding TIES= option as described in the section Partial Likelihood Function for the Cox Model, and is the maximum likelihood estimate of the regression parameter vector.
Akaike’s information criterion (AIC):
Schwarz Bayesian criterion (SBC):
where d is the number of uncensored observations in the data (Volinsky and Raftery 2000). The SBC statistic is also known as the Bayesian information criterion (BIC).

The –2 log likelihood statistic has a chi-square distribution under the null hypothesis (that all the explanatory effects in the model are zero) and the procedure produces a p-value for this statistic. The AIC and SBC statistics offer two different ways of adjusting the –2 log likelihood statistic for the number of terms in the model and the number of observations used. It is recommended that you use these statistics when you compare different models for the same data (for example, when you use the METHOD=STEPWISE option in the MODEL statement); lower values of the statistic indicate a more desirable model.