Beginning in SAS 9.2 TS2M3, you can request a likelihood ratio (LR) test for each effect in the model using the TYPE3(LR) option in the MODEL statement. However, PROC PHREG does not perform model selection based on LR tests.

Prior to SAS 9.2 TS2M3, there is no option to perform LR tests automatically in PROC PHREG. These tests are relatively expensive to compute as one must fit, in addition to the full model, a reduced model for each variable or sub-model of interest.

It is possible to manually construct LR tests using PROC PHREG when comparing *nested* models using the same data. The general method of computing LR tests to compare models is discussed and illustrated in Example 4 of this Note. The logic follows the general linear test idea from linear models theory in which one compares full and reduced models. The reduced model is derived from (nested within) the full model by imposing a set of restrictions that serve as the null hypothesis for the test.

You can construct an LR test statistic by making separate runs of PROC PHREG to fit the appropriate models and then taking the positive difference in the –2logL "with covariates" statistics given by PROC PHREG in the Fit Statistics table. The LR test statistic is easily computed as LRT = abs(L_{1}–L_{2}), where *abs* refers to absolute value, and L_{1} and L_{2} refer to the –2logL values from PROC PHREG for the two models being compared. By taking the absolute value of the difference, it doesn't matter which model corresponds to L_{1} and L_{2}. The LRT statistic has an approximate chi-square distribution with degrees of freedom equal to the difference in the number of parameters between the full and reduced models.
After producing the LRT statistic you can use the PROBCHI function in the DATA step to compute a *p*-value for the test. Here is an example:

data lrt_pval;
LRT = <numeric value of LRT as computed above>;
df = <degrees of freedom as computed above>;
p_value = 1 - probchi(LRT,df);
run;
proc print data=lrt_pval;
title1 "LR test statistic and p-value";
run;

The procedure that is outlined above is discussed at length in Allison (2010) in regards to PROC LIFEREG and goodness-of-fit considerations in choosing an appropriate distribution for a parametric model. Also, Kleinbaum (2005) gives an example of a LR test in a Cox model.

**References:**

Allison, P. D. 2010. *Survival Analysis Using the SAS System: A Practical Guide, Second Edition*. Cary, NC: SAS Institute Inc.

Kleinbaum, D. G. and Klein, M. 2005. *Survival Analysis: A Self-Learning Text, Second Edition*. New York: Springer-Verlag.

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