Cox Proportional Hazard Model Coxs Regression http statdtedm

第十九章 比例风险模型——Cox回归 Proportional Hazard Model —— Cox’s Regression 华中科技大学同济医学院流统系 宇传华 （http: //statdtedm. 6 to 23. com

（http: //statdtedm. 6 to 23. com

比例风险(假定违背)举例 治疗组与安慰剂病人的死亡风险不呈比例 Source: Kay. Pharmaceut. Statist. 2004; 3: 295– 297 （http: //statdtedm. 6 to 23. com

偏似然函数（partial likelihood function，Lp） （http: //statdtedm. 6 to 23. com

对数偏似然函数[ l(b)＝ln. Lp ] （http: //statdtedm. 6 to 23. com

（http: //statdtedm. 6 to 23. com

（http: //statdtedm. 6 to 23. com

SAS程序 data a; input num sex age stage blood xray chmthrp censor day; cards; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ; 1 0 0 0 1 1 1 0 0 1 1 0 45 36 57 45 42 39 38 45 30 45 45 57 57 49 33 51 2 2 2 2 2 3 2 2 2 2 0 0 1 1 2 0 1 1 1 2 2 1 2 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 578 1549 938 4717 4111 1245 4435 3750 3958 2581 3572 2938 1932 3205 3451 2363 PROC PHREG; Model day*censor(0)=sex age stage blood xray chmthrp/ risklimits; RUN; （http: //statdtedm. 6 to 23. com

SAS程序输出结果 The SAS System 16: 31 Saturday, December 4, 2005 6 The PHREG Procedure Analysis of Maximum Likelihood Estimates Hazard Parameter 95% Hazard Ratio Variable DF Estimate Confidence Limits sex 0. 225 1 Error Chi-Square Pr>Chi. Sq Ratio 0. 26175 0. 89551 0. 0854 0. 7701 1. 299 0. 05274 0. 05286 0. 9955 0. 3184 1. 054 7. 515 age 0. 950 1. 169 stage 0. 024 1 3. 313 blood 0. 900 Standard 1 1 10. 158 -1. 27386 1. 10626 1. 26111 0. 61835 1. 0203 0. 3124 3. 2007 0. 0736 （http: //statdtedm. 6 to 23. com 0. 280 3. 023

3. 回归模型及回归系数的假设检验 Model Fit Statistics Without With Criterion Covariates -2 LOG L 61. 344 45. 145 AIC 61. 344 57. 145 SBC 61. 344 61. 393 Testing Global Null Hypothesis: BETA=0 Test Pr > Chi. Sq Chi-Square （http: //statdtedm. 6 to 23. com DF

3. 回归模型及回归系数的假设检验（续） The SAS System 16: 31 Saturday, December 4, 2005 6 The PHREG Procedure Analysis of Maximum Likelihood Estimates Hazard Parameter 95% Hazard Ratio Variable DF Estimate Confidence Limits sex 0. 225 1 Error Chi-Square Pr>Chi. Sq Ratio 0. 26175 0. 89551 0. 0854 0. 7701 1. 299 0. 05274 0. 05286 0. 9955 0. 3184 1. 054 7. 515 age 0. 950 1. 169 stage 0. 024 1 3. 313 blood 0. 900 Standard 1 1 10. 158 -1. 27386 1. 10626 1. 26111 0. 61835 1. 0203 0. 3124 3. 2007 0. 0736 （http: //statdtedm. 6 to 23. com 0. 280 3. 023

4. 模型的筛选及有关问题（逐步回归分析） PROC PHREG data=a 2; Model day*censor(0)=sex age stage blood xray chmthrp /risklimits selection=stepwise sle=0. 05 sls=0. 05; RUN; Analysis of Maximum Likelihood Estimates（参见书P 253的表 19－3） Hazard Parameter Standard 95% Hazard Ratio Variable Limits DF Estimate Error blood 1. 304 1 6. 511 1. 06957 xray 0. 220 1 0. 891 -0. 81419 Chi-Square 0. 41019 0. 35633 Pr>Chi. Sq 6. 7992 5. 2209 Ratio Confidence 0. 0091 2. 914 0. 0223 （http: //statdtedm. 6 to 23. com 0. 443

第三节 生存函数的估计 （http: //statdtedm. 6 to 23. com

SAS求基线生存率的程序 PROC PHREG data=a; Model day*censor(0)=blood xray/risklimits; baseline out=phout survival=s_t stderr=stderr / method=ch ; symbol 1 i=join v=none l=1; symbol 2 i=join v=none l=3; strata xray; proc gplot data=phout; plot s_t*day=xray; run; proc print data=phout; RUN; （http: //statdtedm. 6 to 23. com

SAS求基线生存率的结果 The SAS System 22: 52 Saturday, December 4, 2005 10 Obs blood xray 2 day s_t stderr 1 1. 42857 0 0 0 1. 00000. 2 1. 42857 0 0 578 0. 88994 0. 10515 3 1. 42857 0 0 1245 0. 76275 0. 15017 4 1. 42857 0 0 1549 0. 64400 0. 17032 5 1. 42857 0 0 1932 0. 49557 0. 18608 6 1. 42857 0 0 2581 0. 27749 0. 19103 7 1. 42857 0 0 3451 0. 11627 0. 13221 8 1. 42857 0 0 3572 0. 02041 0. 04420 9 1. 11111 1 1 0 1. 00000. 10 1. 11111 1 1 938 0. 93576 0. 06618 11 1. 11111 1 1 2363 0. 86037 0. 10263 12 1. 11111 1 1 2938 0. 76749 0. 13678 13 1. 11111 1 1 3205 0. 67610 0. 16068 14 1. 11111 1 1 3750 0. 54734 0. 18550 15 1. 11111 1 1 3958 0. 29068 0. 20267 16 1. 11111 1 1 4111 0. 13799 0. 14366 17 1. 11111 1 1 4435 0. 05579 0. 07881 （http: //statdtedm. 6 to 23. com

SAS求基线生存率的结果 （http: //statdtedm. 6 to 23. com

风险指数（HI） （http: //statdtedm. 6 to 23. com

（http: //statdtedm. 6 to 23. com

SAS处理生存资料的过程步 LIFETEST - Produces life tables and Kaplan-Meier survival curves. Is primarily for univariate analysis of the timing of events. LIFEREG – Estimates regression models with censored, continuous-time data under several alternative distributional assumptions. Does not allow for time-dependent covariates. PHREG– Uses Cox’s partial likelihood method to estimate regression models with censored data. Handles both continuous -time and discrete-time data and allows for time-dependent covariables （http: //statdtedm. 6 to 23. com

谢谢！ （http: //statdtedm. 6 to 23. com