The SURVEYPHREG Procedure
- Overview
- Getting Started
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Syntax
PROC SURVEYPHREG StatementBY StatementCLASS StatementCLUSTER StatementDOMAIN StatementESTIMATE StatementFREQ StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementNLOPTIONS StatementOUTPUT StatementProgramming StatementsREPWEIGHTS StatementSLICE StatementSTORE StatementSTRATA StatementTEST StatementWEIGHT Statement -
DetailsNotation and EstimationFailure Time DistributionTime and CLASS Variables UsagePartial Likelihood Function for the Cox ModelSpecifying the Sample DesignMissing ValuesVariance EstimationDomain AnalysisHypothesis Tests, Confidence Intervals, and ResidualsOutput Data SetsDisplayed OutputODS Table NamesODS Graphics
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Examples
- References
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
![\[ \chi ^{2}_{\mr{LR}}=2 \left[ \log \left\{ \text {L} (\hat{\bbeta }) \right\} - \log \left\{ \text {L} (\mb{0}) \right\} \right] \]](images/statug_surveyphreg0126.png){kind=small}
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
![\[ W_{F}=\left( \frac{d-p+1}{dp} \right) \hat{\bbeta }’ \left[\widehat{\mb{V}}(\hat{\bbeta }) \right]^{-1} \hat{\bbeta } \]](images/statug_surveyphreg0128.png){kind=small}
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
![\[ W_{\chi ^{2}}=\hat{\bbeta }’ \left[ \widehat{\mb{V}}(\hat{\bbeta }) \right]^{-1} \hat{\bbeta } \]](images/statug_surveyphreg0129.png){kind=small}
and the p-value is computed by using a chi-square distribution with p degrees of freedom.