The following statistics can be used to test the global null hypothesis . Let d be the number of clusters (or observations) minus the number of strata (or one) and p be the number of estimable parameters in the analysis model.
The likelihood ratio test is expressed as
where L() denotes the partial pseudo-likelihood described in Partial Likelihood Function for the Cox Model. The p-value is computed by using a chi-square distribution with p degrees of freedom. The usual assumptions required for a likelihood ratio test do not hold for the pseudo-likelihood that is used by PROC SURVEYPHREG, leading to other methods for testing the global null hypothesis, such as the Wald test discussed below.
Wald’s test is expressed as
The p-value is computed by using an F distribution with (p, d) degrees of freedom. For the Taylor series linearization method, the DF=PARMADJ option in the MODEL statement computes the p-value by using an F distribution with (p, d – p + 1) degrees of freedom. The DF= q option in the MODEL statement replaces the (d – p + 1) factor in the numerator of the Wald’s statistics by q and computes the p-value by using an F distribution with (p, q) degrees of freedom.
If you specify the DF=NONE option in the MODEL statement, then the procedure computes
and the p-value is computed by using a chi-square distribution with p degrees of freedom.