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
RANDOM Statement
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RANDOM variable </ options>;
The RANDOM statement enables you to fit a shared frailty model for clustered data. For more information about the frailty model, see the section The Frailty Model. The variable that represents the clusters must be a CLASS variable (declared in the CLASS statement).
The following options can be specified in the RANDOM statement:
- ABSPCONV=r
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specifies an absolute variance estimate convergence criterion for the doubly iterative estimation process. The PHREG procedure applies this criterion to the variance parameter estimate of the random effects. Suppose
denotes the estimate of the variance parameter at the jth optimization. By default, PROC PHREG examines the relative change in the variance estimate between optimizations (see the
PCONV=
option). The purpose of the ABSPCONV= criterion is to stop the doubly iterative process when the absolute change 
is less than the tolerance criterion r. This convergence criterion does not affect the convergence criteria applied within any individual optimization. In order
to change the convergence behavior within an individual optimization, you can use the ABSCONV=, ABSFCONV=, ABSGCONV=, ABSXCONV=,
FCONV=, or GCONV= option in the NLOPTIONS statement.
- ALPHA=value
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specifies the
level of the confidence limits for the random effects. The default is the value of the ALPHA=
option in the PROC PHREG statement, or 0.05 if that option is not specified. This option is ignored if the SOLUTION option
is not also specified.
- DIST=GAMMA | LOGNORMAL
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specifies the distribution of the shared frailty. DIST=GAMMA specifies a gamma frailty model. DIST=LOGNORMAL specifies a lognormal frailty model; that is, the log-frailty random variable has a normal distribution with mean zero. The default is DIST=LOGNORMAL.
- METHOD=REML | ML
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specifies the estimation method for the variance parameter of the normal random effects. METHOD=REML performs the residual maximum likelihood; METHOD=ML performs maximum likelihood. This option is ignored for the gamma frailty model. The default is METHOD=REML.
- NOCLPRINT
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suppresses the display of the "Class Level Information for Random Effects" table.
- PCONV=r
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specifies the variance estimate convergence criterion for the doubly iterative estimation process. The PHREG procedure applies this criterion to the variance estimate of the random effects. Suppose
denotes the estimate of variance at the jth optimization. The procedure terminates the doubly iterative process if the relative change
![\[ 2 \times \frac{ | \hat{\theta }^{(j)} - \hat{\theta }^{(j-1)} |}{ |\hat{\theta }^{(j)}| + |\hat{\theta }^{(j-1)}|} \]](images/statug_phreg0165.png)
is less than r. To check an absolute convergence criterion in addition, you can specify the ABSPCONV= option in the RANDOM statement. The default value for r is 1E–4. This convergence criterion does not affect the convergence criteria applied within any individual optimization. In order to change the convergence behavior within an individual optimization, you can use the ABSCONV=, ABSFCONV=, ABSGCONV=, ABSXCONV=, FCONV=, or GCONV= option in the NLOPTIONS statement.
- SOLUTION <(number-list)>
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displays statistical measures of the random-effect parameters. The behavior of this option depends on whether you also specify the BAYES statement:
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When you do not specify a BAYES statement, this option displays point estimates and confidence intervals for the random components and for the frailties.
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When you also specify a BAYES statement, this option displays the summary statistics and diagnostics of the random-effect parameters. Optionally, you can specify a number-list of indices of the random-effect parameters for which the summary statistics and diagnostics are to be displayed. For example, to display the summary statistics and diagnostics for the second to the fifth random-effect parameters, specify
SOLUTION(2 to 5)
If you specify SOLUTION without a list, summary statistics and diagnostics are displayed for each random-effect parameter.
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INITIALVARIANCE=value
INITIAL=value -
specifies an initial value of the dispersion parameter. For the lognormal frailty model, the dispersion parameter represents the variance of the normal random effect; for the gamma frailty model, it represents the variance of the gamma frailty. The default is INITIAL=1.