The PHREG Procedure
- Overview
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Getting Started
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SyntaxPROC PHREG StatementASSESS StatementBASELINE StatementBAYES StatementBY StatementCLASS StatementCONTRAST StatementEFFECT StatementESTIMATE StatementFREQ StatementHAZARDRATIO StatementID StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementOUTPUT StatementProgramming StatementsRANDOM StatementSTRATA StatementSLICE StatementSTORE StatementTEST StatementWEIGHT Statement
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DetailsFailure Time DistributionTime and CLASS Variables UsagePartial Likelihood Function for the Cox ModelCounting Process Style of InputLeft-Truncation of Failure TimesThe Multiplicative Hazards ModelThe Frailty ModelHazard RatiosProportional Rates/Means Models for Recurrent EventsNewton-Raphson MethodFirth’s Modification for Maximum Likelihood EstimationRobust Sandwich Variance EstimateTesting the Global Null HypothesisType 3 TestsConfidence Limits for a Hazard RatioUsing the TEST Statement to Test Linear HypothesesAnalysis of Multivariate Failure Time DataModel Fit StatisticsResidualsDiagnostics Based on Weighted ResidualsInfluence of Observations on Overall Fit of the ModelSurvivor Function EstimatorsEffect Selection MethodsAssessment of the Proportional Hazards ModelThe Penalized Partial Likelihood Approach for Fitting Frailty ModelsSpecifics for Bayesian AnalysisComputational ResourcesInput and Output Data SetsDisplayed OutputODS Table NamesODS Graphics
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ExamplesStepwise RegressionBest Subset SelectionModeling with Categorical PredictorsFirth’s Correction for Monotone LikelihoodConditional Logistic Regression for m:n MatchingModel Using Time-Dependent Explanatory VariablesTime-Dependent Repeated Measurements of a CovariateSurvival CurvesAnalysis of ResidualsAnalysis of Recurrent Events DataAnalysis of Clustered DataModel Assessment Using Cumulative Sums of Martingale ResidualsBayesian Analysis of the Cox ModelBayesian Analysis of Piecewise Exponential Model
- References
The vector of weighted Schoenfeld residuals, 
, is computed as
![\[ \mb {r}_ i = n_ e \mc {I}^{-1}(\hat{\bbeta }) \hat{\mb {U}}_ i(t_ i) \]](images/statug_phreg0565.png){kind=small}
where 
is the total number of events and 
is the vector of Schoenfeld residuals at the event time 
. The components of are output to the WTRESSCH= variables.
The weighted Schoenfeld residuals are useful in assessing the proportional hazards assumption. The idea is that most of the common alternatives to the proportional hazards can be cast in terms of a time-varying coefficient model
![\[ \lambda (t,\bZ ) = \lambda _0(t)\exp (\beta _1(t)Z_1+\beta _2(t)Z_2 +\ldots ) \]](images/statug_phreg0568.png){kind=small}
where 
and 
are hazard rates. Let 
and 
be the jth component of 
and , respectively. Grambsch and Therneau (1994) suggest using a smoothed plot of (
) versus to discover the functional form of the time-varying coefficient 
. A zero slope indicates that the coefficient is not varying with time.
The weighted score residuals are used more often than their unscaled counterparts in assessing local influence. Let 
be the estimate of 
when the ith subject is left out, and let 
. The jth component of 
can be used to assess any untoward effect of the ith subject on . The exact computation of involves refitting the model each time a subject is omitted. Cain and Lange (1984) derived the following approximation of 
as weighted score residuals:
![\[ \delta \hat{\bbeta }_ i = \mc {I}^{-1}(\hat{\bbeta }) \hat{\bL }_ i \]](images/statug_phreg0578.png){kind=small}
Here, 
is the vector of the score residuals for the ith subject. Values of are output to the DFBETA= variables. Again, when the counting process MODEL specification is used, the DFBETA= variables
contain the component 
, where the score process 
is defined in the section Residuals. The vector for the ith subject can be obtained by summing these components within the subject.
Note that these DFBETA statistics are a transform of the score residuals. In computing the robust sandwich variance estimators of Lin and Wei (1989) and Wei, Lin, and Weissfeld (1989), it is more convenient to use the DFBETA statistics than the score residuals (see Example 67.10).