Schoenfeld and Delta Beta from Cox Regression 1 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 1080.825 AIC 1279.960 1090.825 SBC 1279.960 1104.966 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 199.1349 5 <.0001 Score 269.3073 5 <.0001 Wald 198.2020 5 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.87921 0.09873 79.2980 <.0001 2.409 logalb 1 -3.05332 0.72408 17.7818 <.0001 0.047 age 1 0.03327 0.00866 14.7565 0.0001 1.034 logproth 1 3.01567 1.02380 8.6764 0.0032 20.403 edema 1 0.78470 0.29913 6.8814 0.0087 2.192 Schoenfeld and Delta Beta from Cox Regression 2 EST COVB 0.8792059 -3.05332 0.033266 3.0156652 0.7846988 0.0097481 0.0079913 0.000068 -0.016412 -0.004336 0.0079913 0.5242864 0.0005448 0.0002638 0.0588491 0.000068 0.0005448 0.000075 -0.000947 0.0000946 -0.016412 0.0002638 -0.000947 1.0481622 -0.072875 -0.004336 0.0588491 0.0000946 -0.072875 0.08948 STDERR 0.0987323 0.7240762 0.0086598 1.0237979 0.2991321 Standardized Delta-Beta from Mayo Model 3 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 Stratum bili Total Event Censored Censored 1 0.725 163 32 131 80.37 2 2.35 63 31 32 50.79 3 5 50 31 19 38.00 4 53.375 36 31 5 13.89 ------------------------------------------------------------------- Total 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 850.353 777.110 AIC 850.353 785.110 SBC 850.353 796.423 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 73.2435 4 <.0001 Score 84.4283 4 <.0001 Wald 77.6349 4 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logalb 1 -2.97555 0.71881 17.1356 <.0001 0.051 age 1 0.03086 0.00895 11.8994 0.0006 1.031 logproth 1 3.46790 1.02647 11.4141 0.0007 32.069 edema 1 0.96011 0.31472 9.3065 0.0023 2.612 Standardized Delta-Beta from Mayo Model 4 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 Stratum albumin Total Event Censored Censored 1 1.55 45 30 15 33.33 2 3.25 62 30 32 51.61 3 3.535 89 32 57 64.04 4 51.835 116 33 83 71.55 ------------------------------------------------------------------- Total 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 908.064 771.247 AIC 908.064 779.247 SBC 908.064 790.560 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 136.8173 4 <.0001 Score 152.5997 4 <.0001 Wald 132.1626 4 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.91251 0.10230 79.5580 <.0001 2.491 age 1 0.03341 0.00899 13.8009 0.0002 1.034 logproth 1 3.01324 1.06362 8.0260 0.0046 20.353 edema 1 0.74468 0.31881 5.4560 0.0195 2.106 Standardized Delta-Beta from Mayo Model 5 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 Stratum age Total Event Censored Censored 1 23 115 31 84 73.04 2 49.5 77 32 45 58.44 3 57 67 30 37 55.22 4 80.5 53 32 21 39.62 ------------------------------------------------------------------- Total 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 920.774 740.574 AIC 920.774 748.574 SBC 920.774 759.888 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 180.1999 4 <.0001 Score 233.6904 4 <.0001 Wald 170.3305 4 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.88641 0.10623 69.6220 <.0001 2.426 logalb 1 -3.41811 0.78891 18.7723 <.0001 0.033 logproth 1 3.31371 1.05926 9.7865 0.0018 27.487 edema 1 0.73547 0.31288 5.5257 0.0187 2.086 Standardized Delta-Beta from Mayo Model 6 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 Stratum proth Total Event Censored Censored 1 5.25 138 28 110 79.71 2 10.75 63 19 44 69.84 3 11.4 72 45 27 37.50 4 55.9 39 33 6 15.38 ------------------------------------------------------------------- Total 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 893.991 768.179 AIC 893.991 776.179 SBC 893.991 787.493 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 125.8118 4 <.0001 Score 137.5150 4 <.0001 Wald 120.2809 4 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.83311 0.10532 62.5759 <.0001 2.300 logalb 1 -3.24369 0.76856 17.8123 <.0001 0.039 age 1 0.03264 0.00875 13.9248 0.0002 1.033 edema 1 0.47383 0.31935 2.2014 0.1379 1.606 Standardized Delta-Beta from Mayo Model 7 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 Stratum edema Total Event Censored Censored 1 0 263 89 174 66.16 2 0.5 29 17 12 41.38 3 1 20 19 1 5.00 ------------------------------------------------------------------- Total 312 125 187 59.94 Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 1049.421 918.721 AIC 1049.421 926.721 SBC 1049.421 938.034 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 130.7008 4 <.0001 Score 143.4578 4 <.0001 Wald 132.7211 4 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.84654 0.09950 72.3784 <.0001 2.332 logalb 1 -2.84523 0.73257 15.0846 0.0001 0.058 age 1 0.03429 0.00892 14.7690 0.0001 1.035 logproth 1 3.14352 1.02734 9.3628 0.0022 23.185 Calculate Harrel's Z 8 Harrell's Z test for a linear trend in the residuals VARNAME CORR HARRELZ PVAL log bilirubin 0.0858969 0.9511064 0.3415504 log albumin 0.0177489 0.1960635 0.8445605 age -0.091108 -1.009123 0.3129157 log proth -0.269762 -3.05522 0.002249 edema -0.201154 -2.252537 0.0242883 Schoenfeld Resid Plots to Check Proportional Hazards Assump 9 The PHREG Procedure Model Information Data Set WORK.A Dependent Variable time time in days 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 1080.825 AIC 1279.960 1090.825 SBC 1279.960 1104.966 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 199.1349 5 <.0001 Score 269.3073 5 <.0001 Wald 198.2020 5 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio logbili 1 0.87921 0.09873 79.2980 <.0001 2.409 logalb 1 -3.05332 0.72408 17.7818 <.0001 0.047 age 1 0.03327 0.00866 14.7565 0.0001 1.034 logproth 1 3.01567 1.02380 8.6764 0.0032 20.403 edema 1 0.78470 0.29913 6.8814 0.0087 2.192 Schoenfeld Resid Plots to Check Proportional Hazards Assump 10 The PHREG Procedure Supremum Test for Proportionals Hazards Assumption Maximum Absolute Pr > Variable Value Replications Seed MaxAbsVal logbili 1.1589 1000 19 0.0980 logalb 0.6513 1000 19 0.7230 age 0.9152 1000 19 0.2230 logproth 1.7340 1000 19 0.0020 edema 1.4844 1000 19 0.0230