The PHREG Procedure
- Overview
-
Getting Started
-
Syntax
PROC PHREG Statement ASSESS Statement BASELINE Statement BAYES Statement BY Statement CLASS Statement CONTRAST Statement EFFECT Statement ESTIMATE Statement FREQ Statement HAZARDRATIO Statement ID Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement OUTPUT Statement Programming Statements RANDOM Statement STRATA Statement SLICE Statement STORE Statement TEST Statement WEIGHT Statement
-
Details
Failure Time Distribution Time and CLASS Variables Usage Partial Likelihood Function for the Cox Model Counting Process Style of Input Left-Truncation of Failure Times The Multiplicative Hazards Model The Frailty Model Hazard Ratios Specifics for Classical Analysis Specifics for Bayesian Analysis Computational Resources Input and Output Data Sets Displayed Output ODS Table Names ODS Graphics
-
Examples
Stepwise Regression Best Subset Selection Modeling with Categorical Predictors Firth’s Correction for Monotone Likelihood Conditional Logistic Regression for m:n Matching Model Using Time-Dependent Explanatory Variables Time-Dependent Repeated Measurements of a Covariate Survivor Function Estimates for Specific Covariate Values Analysis of Residuals Analysis of Recurrent Events Data Analysis of Clustered Data Model Assessment Using Cumulative Sums of Martingale Residuals Bayesian Analysis of the Cox Model Bayesian Analysis of Piecewise Exponential Model
- References
| Displayed Output |
If you use the NOPRINT option in the PROC PHREG statement, the procedure does not display any output. Otherwise, PROC PHREG displays results of the analysis in a collection of tables. The tables are listed separately for the maximum likelihood analysis and for the Bayesian analysis.
Maximum Likelihood Analysis Displayed Output
Model Information
The "Model Information" table displays the two-level name of the input data set, the name and label of the failure time variable, the name and label of the censoring variable and the values indicating censored times, the model (either the Cox model or the piecewise constant baseline hazard model), the name and label of the OFFSET variable, the name and label of the FREQ variable, the name and label of the WEIGHT variable, and the method of handling ties in the failure time for the Cox model. For ODS purposes, the name of the "Model Information" table is "ModelInfo."
Number of Observations
The "Number of Observations" table displays the number of observations read and used in the analysis. For ODS purposes, the name of the "Number of Observations" is "NObs."
Class Level Information
The "Class Level Information" table is displayed when there are CLASS variables in the model. The table lists the categories of every CLASS variable that is used in the model and the corresponding design variable values. For ODS purposes, the name of the "Class Level Information" table is "ClassLevelInfo."
Class Level Information for Random Effects
The "Class Level Information for Random Effects" table is displayed when the RANDOM statement is specified. The table lists the categories of the classification variable specified in the RANDOM statement. For ODS purposes, the name of the "Class Level Information for Random Effects" table is "ClassLevelInfoR."
Summary of the Number of Event and Censored Values
The "Summary of the Number of Event and Censored Values" table displays, for each stratum, the breakdown of the number of events and censored values. For ODS purposes, the name of the "Summary of the Number of Event and Censored Values" table is "CensoredSummary."
Risk Sets Information
The "Risk Sets Information" table is displayed if you specify the ATRISK option in the PROC PHREG statement. The table displays, for each event time, the number of units at-risk and the number of units that experience the event. For ODS purposes, the name of the "Risk Sets Information" table is "RiskSetInfo."
Descriptive Statistics for Continuous Explanatory Variables
The "Simple Statistics for Continuous Explanatory Variables" table is displayed when you specify the SIMPLE option in the PROC PHREG statement. The table contains, for each stratum, the mean, standard deviation, and minimum and maximum for each continuous explanatory variable in the MODEL statement. For ODS purposes, the name of the "Descriptive Statistics for Continuous Explanatory Variables" table is "SimpleStatistics."
Frequency Distribution of CLASS Variables
The "Frequency Distribution of CLASS Variables" table is displayed if you specify the SIMPLE option in the PROC PHREG statement and there are CLASS variables in the model. The table lists the frequency of the levels of the CLASS variables. For ODS purposes, the name of the "Frequency Distribution of CLASS Variables" table is "ClassLevelFreq."
Maximum Likelihood Iteration History
The "Maximum Likelihood Iteration History" table is displayed if you specify the ITPRINT option in the MODEL statement. The table contains the iteration number, ridge value or step size, log likelihood, and parameter estimates at each iteration. For ODS purposes, the name of the "Maximum Likelihood Iteration History" table is "IterHistory."
Gradient of Last Iteration
The "Gradient of Last Iteration" table is displayed if you specify the ITPRINT option in the MODEL statement. For ODS purposes, the name of the "Gradient of Last Iteration" table is "LastGradient."
Convergence Status
The "Convergence Status" table displays the convergence status of the Newton-Raphson maximization. For ODS purposes, the name of the "Convergence Status" table is "ConvergenceStatus."
Model Fit Statistics
The "Model Fit Statistics" table displays the values of 
2 log likelihood for the null model and the fitted model, the AIC, and SBC. For ODS purposes, the name of the "Model Fit Statistics" table is "FitStatistics."
Covariance Parameter Estimates
The "Covariance Parameter Estimates" table displays the estimate of the variance parameter of the random effect and the standard error estimate of the variance parameter estimator. For ODS purposes, the name of the "Covariance Parameter Estimates" table is "CovParms."
Testing Global Null Hypothesis: BETA=0
The "Testing Global Null Hypothesis: BETA=0" table displays results of the likelihood ratio test, the score test, and the Wald test for testing the hypothesis that all parameters are zero. For the frailty model, the score test is not displayed and an adjusted degrees of freedom is used (see the section Wald-Type Tests for Penalized Models for more information.) For ODS purpose, the name of the "Testing Global Null Hypothesis: BETA=0" table is "GlobalTests."
Likelihood Ratio Statistics for Type 1 Analysis
The "Likelihood Ratio Statistics for Type 1 Analysis" table is displayed if the TYPE1 option is specified in the MODEL statement. The table displays the degrees of freedom, the likelihood ratio chi-square statistic, and the p-value for each effect in the model. For ODS purposes, the name of "Likelihood Ratio Statistics for Type 1 Analysis" is "Type1."
Type 3 Tests
The "Type 3 Tests" table is displayed if the model contains a CLASS variable or if the TYPE3 option is specified in the MODEL statement. The table displays, for each specified statistic, the Type 3 chi-square, the degrees of freedom, and the p-value for each effect in the model. For the frailty model, the table also displays the adjusted Wald-type test results (see the section Wald-Type Tests for Penalized Models for details.) For ODS purposes, the name of "Type 3 Tests" is "Type3."
Analysis of Maximum Likelihood Estimates
The "Analysis of Maximum Likelihood Estimates" table displays the maximum likelihood estimate of the parameter; the estimated standard error, computed as the square root of the corresponding diagonal element of the estimated covariance matrix; the ratio of the robust standard error estimate to the model-based standard error estimate if you specify the COVS option in the PROC statement; the Wald Chi-Square statistic, computed as the square of the parameter estimate divided by its standard error estimate; the degrees of freedom of the Wald chi-square statistic, which has a value of 1 unless the corresponding parameter is redundant or infinite, in which case the value is 0; the p-value of the Wald chi-square statistic with respect to a chi-square distribution with one degree of freedom; the hazard ratio estimate; and the confidence limits for the hazard ratio if you specified the RISKLIMITS option in the MODEL statement. For ODS purposes, the name of the "Analysis of Maximum Likelihood Estimates" table is "ParameterEstimates."
Solution for Random Effects
The "Solution for Random Effects" table displays the BLUP estimates of the random effects, the estimated standard errors, the confidence intervals for the random effects, the exponentiated values of the BLUP estimates, and confidence intervals for the exponentiated random effects. For ODS purposes, the name of the "Solution for Random Effects" table is "SolutionR."
Regression Models Selected by Score Criterion
The "Regression Models Selected by Score Criterion" table is displayed if you specify SELECTION=SCORE in the MODEL statement. The table contains the number of explanatory variables in each model, the score chi-square statistic, and the names of the variables included in the model. For ODS purposes, the name of the "Regression Models Selected by Score Criterion" table is "BestSubsets."
Analysis of Effects Eligible for Entry
The "Analysis of Effects Eligible for Entry" table is displayed if you use the FORWARD or STEPWISE selection method and you specify the DETAILS option in the MODEL statement. The table contains the score chi-square statistic for testing the significance of each variable not in the model (after adjusting for the variables already in the model), and the p-value of the chi-square statistic with respect to a chi-square distribution with one degree of freedom. This table is produced before a variable is selected for entry in a forward selection step. For ODS purposes, the name of the "Analysis of Effects Eligible for Entry" table is "EffectsToEntry."
Analysis of Effects Eligible for Removal
The "Analysis of Effects Eligible for Removal" table is displayed if you use the BACKWARD or STEPWISE selection method and you specify the DETAILS option in the MODEL statement. The table contains the Wald chi-square statistic for testing the significance of each candidate effect for removal, the degrees of freedom of the Wald chi-square, and the corresponding p-value. This table is produced before an effect is selected for removal. For ODS purposes, the name of the "Analysis of Effects Eligible for Removal" table is "EffectsToRemoval."
Summary of Backward Elimination
The "Summary of Backward Elimination" table is displayed if you specify the SELECTION=BACKWARD option in the MODEL statement. The table contains the step number, the effects removed at each step, the corresponding chi-square statistic, the degrees of freedom, and the p-value. For ODS purpose, the name of the "Summary of Backward Elimination" table is "ModelBuildingSummary."
Summary of Forward Selection
The "Summary of Forward Selection" table is displayed if you specify the SELECTION=FORWARD option in the MODEL statement. The table contains the step number, the effects entered at each step, the corresponding chi-square statistic, the degrees of freedom, and the p-value. For ODS purpose, the name of the "Summary of Forward Selection" table is "ModelBuildingSummary."
Summary of Stepwise Selection
The "Summary of Stepwise Selection" table is displayed if you specify SELECTION=STEPWISE is specified in the MODEL statement. The table contains the step number, the effects entered or removed at each step, the corresponding chi-square statistic, the degrees of freedom, and the corresponding p-value. For ODS purpose, the name of the "Summary of Stepwise Selection" table is "ModelBuildingSummary."
Covariance Matrix
The "Covariance Matrix" table is displayed if you specify the COVB option in the MODEL statement. The table contains the estimated covariance matrix for the parameter estimates. For ODS purposes, the name of the "Covariance Matrix" table is "CovB."
Correlation Matrix
The "Correlation Matrix" table is displayed if you specify the COVB option in the MODEL statement. The table contains the estimated correlation matrix for the parameter estimates. For ODS purposes, the name of the "Correlation Matrix" table is "CorrB."
Hazard Ratios for label
The "Hazard Ratios for label" table is displayed if you specify the HAZARDRATIO statement. The table displays the estimate and confidence limits for each hazard ratio. For ODS purposes, the name of the "Hazard Ratios for label" table is "HazardRatios."
Coefficients of Contrast label
The "Coefficients of Contrast label" table is displayed if you specify the E option in the CONTRAST statement. The table displays the parameter names and the corresponding coefficents of each row of contrast label. For ODS purposes, the name of the "Coefficients of Contrast label" table is "ContrastCoeff."
Contrast Test Results
The "Contrast Test Results" table is displayed if you specify the CONTRAST statement. The table displays the degrees of freedom, test statistics, and the p-values for testing each contrast. For ODS purposes, the name of the "Contrast Test Results" table is "ContrastTest."
Contrast Estimation and Testing Results by Row
The "Contrast Estimation and Testing Results by Row" table is displayed if you specify the ESTIMATE option in the CONTRAST statement. The table displays, for each row, the estimate of the linear function of the coefficients, its standard error, and the confidence limits for the linear function. For ODS purposes, the name of the "Contrast Estimation and Testing Results by Row" table is "ContrastEstimate."
Linear Coefficients for label
The "Linear Coefficients label" table is displayed if you specify the E option in the TEST statement with label being the TEST statement label. The table contains the coefficients and constants of the linear hypothesis. For ODS purposes, the name of the "Linear Coefficients for label" table is "TestCoeff."
L[cov(b)]L’ and Lb-c
The "L[cov(b)]L’ and Lb-c" table is displayed if you specified the PRINT option in a TEST statement with label being the TEST statement label. The table displays the intermediate calculations of the Wald test. For ODS purposes, the name of the "L[cov(b)]L’ and Lb-c" table is "TestPrint1."
Ginv(L[cov(b)]L’) and Ginv(L[cov(b)]L’)(Lb-c)
The "Ginv(L[cov(b)]L’) and Ginv(L[cov(b)]L’)(Lb-c)" table is displayed if you specified the PRINT option in a TEST statement with label being the TEST statement label. The table displays the intermediate calculations of the Wald test. For ODS purposes, the name of the "Ginv(L[cov(b)]L’) and Ginv(L[cov(b)]L’)(Lb-c)" table is "TestPrint2."
label Test Results
The "label Test Results" table is displayed if you specify a TEST statement with label being the TEST statement label. The table contains the Wald chi-square statistic, the degrees of freedom, and the 
-value. For ODS purposes, the name of "label Test Results" table is "TestStmts."
Average Effect for label
The "Average Effect for label" table is displayed if the AVERAGE option is specified in a TEST statement with label being the TEST statement label. The table contains the weighted average of the parameter estimates for the variables in the TEST statement, the estimated standard error, the z-score, and the p-value. For ODS purposes, the name of the "Average Effect for label" is "TestAverage."
Reference Set of Covariates for Plotting
The "Reference Set of Covariates for Plotting" table is displayed if the PLOTS= option is requested without specifying the COVARIATES= data set in the BASELINE statement. The tables contains the values of the covariates for the reference set, where the reference levels are used for the CLASS variables and the sample averages for the continuous variables.
Bayesian Analysis Displayed Output
Model Information
The "Model Information" table displays the two-level name of the input data set, the name and label of the failure time variable, the name and label of the censoring variable and the values indicating censored times, the model (either the Cox model or the piecewise constant baseline hazard model), the name and label of the OFFSET variable, the name and label of the FREQ variable, the name and label of the WEIGHT variable, the method of handling ties in the failure time, the number of burn-in iterations, the number of iterations after the burn-in, and the number of thinning iterations. For ODS purposes, the name of the "Model Information" table is "ModelInfo."
Number of Observations
The "Number of Observations" table displays the number of observations read and used in the analysis. For ODS purposes, the name of the "Number of Observations" is "NObs."
Summary of the Number of Event and Censored Values
The "Summary of the Number of Event and Censored Values" table displays, for each stratum, the breakdown of the number of events and censored values. This table is not produced if the NONSUMMARY option is specified in the PROC PHREG statement. For ODS purposes, the name of the "Summary of the Number of Event and Censored Values" table is "CensoredSummary."
Descriptive Statistics for Continuous Explanatory Variables
The "Simple Statistics for Continuous Explanatory Variables" table is displayed when you specify the SIMPLE option in the PROC PHREG statement. The table contains, for each stratum, the mean, standard deviation, and minimum and maximum for each continuous explanatory variable in the MODEL statement. For ODS purposes, the name of the "Descriptive Statistics for Continuous Explanatory Variables" table is "SimpleStatistics."
Class Level Information
The "Class Level Information" table is displayed if there are CLASS variables in the model. The table lists the categories of every CLASS variable in the model and the corresponding design variable values. For ODS purposes, the name of the "Class Level Information" table is "ClassLevelInfo."
Frequency Distribution of CLASS Variables
The "Frequency Distribution of CLASS Variables" table is displayed if you specify the SIMPLE option in the PROC PHREG statement and there are CLASS variables in the model. The table lists the frequency of the levels of the CLASS variables. For ODS purposes, the name of the "Frequency Distribution of CLASS Variables" table is "ClassLevelFreq."
Regression Parameter Information
The "Regression Parameter Information" table displays the names of the parameters and the corresponding level information of effects containing the CLASS variables. For ODS purposes, the name of the "Regression Parameter Information" table is "ParmInfo."
Constant Baseline Hazard Time Intervals
The "Constant Baseline Hazard Time Intervals" table displays the intervals of constant baseline hazard and the corresponding numbers of failure times and event times. This table is produced only if you specify the PIECEWISE option in the BAYES statement. For ODS purposes, the name of the "Constant Baseline Hazard Time Intervals" table is "Interval."
Maximum Likelihood Estimates
The "Maximum Likelihood Estimates" table displays, for each parameter, the maximum likelihood estimate, the estimated standard error, and the 95% confidence limits. For ODS purposes, the name of the "Maximum Likelihood Estimates" table is "ParameterEstimates."
Hazard Prior
The "Hazard Prior" table is displayed if you specify the PIECEWISE=HAZARD option in the BAYES statement. It describes the prior distribution of the hazard parameters. For ODS purposes, the name of the "Hazard Prior" table is "HazardPrior."
Log-Hazard Prior
The "Log-Hazard Prior" table is displayed if you specify the PIECEWISE=LOGHAZARD option in the BAYES statement. It describes the prior distribution of the log-hazard parameters. For ODS purposes, the name of the "Log-Hazard Prior" table is "HazardPrior."
Coefficient Prior
The "Coefficient Prior" table displays the prior distribution of the regression coefficients. For ODS purposes, the name of the "Coefficient Prior" table is "CoeffPrior."
Initial Values
The "Initial Values" table is displayed if you specify the INITIAL option in the BAYES statement. The table contains the initial values of the parameters for the Gibbs sampling. For ODS purposes, the name of the "Initial Values" table is "InitialValues."
Fit Statistics
The "Fit Statistics" table displays the DIC and pD statistics for each parameter. For ODS purposes, the name of the "Fit Statistics" table is "FitStatistics."
Posterior Summaries
The "Posterior Summaries" table displays the size of the posterior sample, the mean, the standard error, and the percentiles for each model parameter. For ODS purposes, the name of the "Posterior Summaries" table is "PostSummaries."
Posterior Intervals
The "Posterior Intervals" table displays the equal-tail interval and the HPD interval for each model parameter. For ODS purposes, the name of the "Posterior Intervals" table is "PostIntervals."
Posterior Covariance Matrix
The "Posterior Covariance Matrix" table is produced if you include COV in the SUMMARY= option in the BAYES statement. This tables displays the sample covariance of the posterior samples. For ODS purposes, the name of the "Posterior Covariance Matrix" table is "Cov."
Posterior Correlation Matrix
The "Posterior Correlation Matrix" table is displayed if you include CORR in the SUMMARY= option in the BAYES statement. The table contains the sample correlation of the posterior samples. For ODS purposes, the name of the "Posterior Correlation Matrix" table is "Corr."
Posterior Autocorrelations
The "Posterior Autocorrelations" table displays the lag 1, lag 5, lag 10, and lag 50 autocorrelations for each parameter. For ODS purposes, the name of the "Posterior Autocorrelations" table is "AutoCorr."
Gelman-Rubin Diagnostics
The "Gelman-Rubin Diagnostics" table is produced if you include GELMAN in the DIAGNOSTIC= option in the BAYES statement. This table displays the estimate of the potential scale reduction factor and its 97.5% upper confidence limit for each parameter. For ODS purposes, the name of the "Gelman-Rubin Diagnostics" table is "Gelman."
Geweke Diagnostics
The "Geweke Diagnostics" table displays the Geweke statistic and its -value for each parameter. For ODS purposes, the name of the "Geweke Diagnostics" table is "Geweke."
Raftery-Lewis Diagnostics
The "Raftery-Lewis Diagnostics" tables is produced if you include RAFTERY in the DIAGNOSTIC= option in the BAYES statement. This table displays the Raftery and Lewis diagnostics for each variable. For ODS purposes, the name of the "Raftery-Diagnostics" table is "Raftery."
Heidelberger-Welch Diagnostics
The "Heidelberger-Welch Diagnostics" table is displayed if you include HEIDELBERGER in the DIAGNOSTIC= option in the BAYES statement. This table describes the results of a stationary test and a halfwidth test for each parameter. For ODS purposes, the name of the "Heidelberger-Welch Diagnostics" table is "Heidelberger."
Effective Sample Sizes
The "Effective Sample Sizes" table displays, for each parameter, the effective sample size, the correlation time, and the efficiency. For ODS purposes, the name of the "Effective Sample Sizes" table is "ESS."
Hazard Ratios for label
The "Hazard Ratios for label" table is displayed if you specify the HAZARDRATIO statement. The table displays the posterior summary for each hazard ratio. The summary includes the mean, standard error, quartiles, and equal-tailed and HPD intervals. For ODS purposes, the name of the "Hazard Ratios for label" table is "HazardRatios."
Reference Set of Covariates for Plotting
The "Reference Set of Covariates for Plotting" table is displayed if the PLOTS= option is requested without specifying the COVARIATES= data set in the BASELINE statement. The table contains the values of the covariates for the reference set, where the reference levels are used for the CLASS variables and the sample averages for the continuous variables.