Beginning in SAS 9.1, k-sample stratified tests are available with the GROUP= option in the STRATA statement. Stratified tests are discussed in "Comparison of Two or More Groups of Survival Data: Stratified Tests" in the Details: Computational Formulas section of the LIFETEST documentation. However, the null hypothesis for stratified tests is not adequately stated. It is clarified below.

The following statements produce a stratified, k-sample, log-rank test of a GROUP= variable in which the STRATA variable has m levels. The NOTABLE option prevents estimating a survival curve for each level of the STRATA variable which would not be indicative of the curves to be tested here.

   proc lifetest data=<data-set-name> notable;
      time duration*censor(1);
      strata <m-level-variable> / group=<k-level-variable>  test=(logrank);
      run;

The statements above provide a joint test of a null hypothesis which states that the k survival curves in stratum 1 are the same, and that the k survival curves in stratum 2 are the same, ... , and that the k survival curves in stratum m are the same. That is, the k survival curves may differ across the strata but not within strata under this hypothesis. The hypothesis can be equivalently stated in terms of hazard functions. The null hypothesis is not satisfied if at least one pair of hazard (or survival) functions differs within some stratum. As shown in Klein & Moeschberger (1997, Section 7.5), the null and alternative hypotheses in terms of the hazard functions h(t) or the survival functions S(t) are:

H₀: h_1s(t) = h_2s(t) = ... = h_k s(t) , or equivalently

H₀: S_1s(t) = S_2s(t) = ... = S_k s(t) , for strata s=1, 2, ... , m  and groups i=1, 2, ... , k

versus

H₁: h_is(t) ≠ h_js(t) , or equivalently

H₁: S_is(t) ≠ S_js(t) , for some groups i and j in some stratum s

See the References section of the LIFETEST documentation for citation of the Klein & Moeschberger (1977) reference.

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