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 ModelProportional Rates/Means Models for Recurrent EventsThe Frailty ModelProportional Subdistribution Hazards Model for Competing-Risks DataHazard RatiosNewton-Raphson MethodFirth’s Modification for Maximum Likelihood EstimationRobust Sandwich Variance EstimateTesting the Global Null HypothesisType 3 Tests and Joint TestsConfidence Limits for a Hazard RatioUsing the TEST Statement to Test Linear HypothesesAnalysis of Multivariate Failure Time DataModel Fit StatisticsSchemper-Henderson Predictive MeasureResidualsDiagnostics Based on Weighted ResidualsInfluence of Observations on Overall Fit of the ModelSurvivor Function EstimatorsCaution about Using Survival Data with Left TruncationEffect 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 ModelAnalysis of Competing-Risks Data
- References
The LD statistic approximates the likelihood displacement, which is the amount by which minus twice the log likelihood (
), under a fitted model, changes when each subject in turn is left out. When the ith subject is omitted, the likelihood displacement is
![\[ 2 \log L(\hat{\bbeta }) - 2 \log L(\hat{\bbeta }_{(i)}) \]](images/statug_phreg0617.png){kind=small}
where 
is the vector of parameter estimates obtained by fitting the model without the ith subject. Instead of refitting the model without the ith subject, Pettitt and Bin Daud (1989) propose that the likelihood displacement for the ith subject be approximated by
![\[ \mr{LD}_ i = \hat{\bL }_ i’\mc{I}^{-1}(\hat{\bbeta }) \hat{\bL }_ i \]](images/statug_phreg0618.png){kind=small}
where 
is the score residual vector of the ith subject. This approximation is output to the LD= variable.
The LMAX statistic is another global influence statistic. This statistic is based on the symmetric matrix
![\[ \bB = \bL \mc{I}^{-1}(\hat{\bbeta }) \bL ’ \]](images/statug_phreg0619.png){kind=small}
where 
is the matrix with rows that are the score residual vectors 
. The elements of the eigenvector associated with the largest eigenvalue of the matrix 
, standardized to unit length, give a measure of the sensitivity of the fit of the model to each observation in the data.
The influence of the ith subject on the global fit of the model is proportional to the magnitude of 
, where is the ith element of the vector 
that satisfies
![\[ \bB \bzeta =\lambda _{\max } \bzeta ~ ~ \mr{and}~ ~ \bzeta ’\bzeta = 1 \]](images/statug_phreg0624.png){kind=small}
with 
being the largest eigenvalue of . The sign of is irrelevant, and its absolute value is output to the LMAX= variable.
When the counting process MODEL specification is used, the LD= and LMAX= variables are set to missing, because these two global influence statistics can be calculated on a per-subject basis only.