The SAS System 15:07 Friday, May 9, 2008 1 Measure the treatment effect(Z1) The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1279.858 AIC 1279.960 1281.858 SBC 1279.960 1284.686 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 0.1017 1 0.7498 Score 0.1017 1 0.7498 Wald 0.1015 1 0.7500 The SAS System 15:07 Friday, May 9, 2008 2 Measure the treatment effect(Z1) The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio trt 1 0.05709 0.17916 0.1015 0.7500 1.059 The SAS System 15:07 Friday, May 9, 2008 3 A two-group comparison of the gender groups(Z3) The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1276.187 AIC 1279.960 1278.187 SBC 1279.960 1281.015 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 3.7729 1 0.0521 Score 4.2683 1 0.0388 Wald 4.1882 1 0.0407 The SAS System 15:07 Friday, May 9, 2008 4 A two-group comparison of the gender groups(Z3) The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio sex 1 -0.48399 0.23650 4.1882 0.0407 0.616 The SAS System 15:07 Friday, May 9, 2008 5 Look at the presence of edema(Z7) The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1223.840 AIC 1279.960 1225.840 SBC 1279.960 1228.668 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 56.1202 1 <.0001 Score 97.8931 1 <.0001 Wald 78.5761 1 <.0001 The SAS System 15:07 Friday, May 9, 2008 6 Look at the presence of edema(Z7) The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio edema 1 2.27501 0.25665 78.5761 <.0001 9.728 The SAS System 15:07 Friday, May 9, 2008 7 Edema factored The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1222.391 AIC 1279.960 1226.391 SBC 1279.960 1232.047 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 57.5691 2 <.0001 Score 126.8590 2 <.0001 Wald 86.0639 2 <.0001 The SAS System 15:07 Friday, May 9, 2008 8 Edema factored The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio edema0_5 1 0.87135 0.26510 10.8035 0.0010 2.390 edema1 1 2.38554 0.26176 83.0583 <.0001 10.865 The SAS System 15:07 Friday, May 9, 2008 9 Likelihood Ratio test of edema linear vs. factored Obs LR pvalue 1 1.449 0.22869 The SAS System 15:07 Friday, May 9, 2008 10 Look at the continuous covariate age(Z2) The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1259.452 AIC 1279.960 1261.452 SBC 1279.960 1264.280 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 20.5079 1 <.0001 Score 20.8626 1 <.0001 Wald 20.6055 1 <.0001 The SAS System 15:07 Friday, May 9, 2008 11 Look at the continuous covariate age(Z2) The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio age 1 0.04000 0.00881 20.6055 <.0001 1.041 The SAS System 15:07 Friday, May 9, 2008 12 Estimating Survival Function and Cumulative Hazard Function The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1146.865 AIC 1279.960 1156.865 SBC 1279.960 1171.007 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 133.0944 5 <.0001 Score 259.7527 5 <.0001 Wald 168.3755 5 <.0001 The SAS System 15:07 Friday, May 9, 2008 13 Estimating Survival Function and Cumulative Hazard Function The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio sex 1 -0.53783 0.24510 4.8152 0.0282 0.584 age 1 0.03569 0.00919 15.1007 0.0001 1.036 edema 1 1.64180 0.29641 30.6804 <.0001 5.164 trt 1 0.04519 0.18840 0.0575 0.8104 1.046 bili 1 0.12862 0.01451 78.5316 <.0001 1.137 The SAS System 15:07 Friday, May 9, 2008 14 Estimating Survival Function and Cumulative Hazard Function The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time Censoring Variable delta Censoring Value(s) 0 Ties Handling BRESLOW Number of Observations Read 312 Number of Observations Used 312 Summary of the Number of Event and Censored Values Percent Total Event Censored Censored 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1279.960 1146.865 AIC 1279.960 1156.865 SBC 1279.960 1171.007 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 133.0944 5 <.0001 Score 259.7527 5 <.0001 Wald 168.3755 5 <.0001 The SAS System 15:07 Friday, May 9, 2008 15 Estimating Survival Function and Cumulative Hazard Function The PHREG Procedure Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio sex 1 -0.53783 0.24510 4.8152 0.0282 0.584 age 1 0.03569 0.00919 15.1007 0.0001 1.036 edema 1 1.64180 0.29641 30.6804 <.0001 5.164 trt 1 0.04519 0.18840 0.0575 0.8104 1.046 bili 1 0.12862 0.01451 78.5316 <.0001 1.137