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
Model Fit Statistics
Suppose the model contains p regression parameters. Let 
and 
be the event indicator and the frequency, respectively, of the jth observation. The three criteria displayed by the PHREG procedure are calculated as follows:
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–2 Log Likelihood:
![\[ -2\mbox{ Log L}=-2 \log (L_ n(\hat{\bbeta })) \]](images/statug_phreg0519.png)
where
is a partial likelihood function for the corresponding TIES= option as described in the section Partial Likelihood Function for the Cox Model, and 
is the maximum likelihood estimate of the regression parameter vector.
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Akaike’s Information Criterion:
![\[ \mbox{AIC}=-2\mbox{ Log L}+2p \]](images/statug_phreg0521.png)
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Schwarz Bayesian (Information) Criterion:
![\[ \mbox{SBC}=-2\mbox{ Log L}+p\log (\sum _ jf_ j\Delta _ j) \]](images/statug_phreg0522.png)
The –2 Log Likelihood statistic has a chi-square distribution under the null hypothesis (that all the explanatory effects in the model are zero) and the procedure produces a p-value for this statistic. The AIC and SBC statistics give two different ways of adjusting the –2 Log Likelihood statistic for the number of terms in the model and the number of observations used. These statistics should be used when comparing different models for the same data (for example, when you use the METHOD=STEPWISE option in the MODEL statement); lower values of the statistic indicate a more desirable model.