生存分析及cox比例风险模型课件.ppt

生存分析的主要内容•生存过程的描述•生存时间的分布特点•估计生存率•估计平均生存时间•绘制生存率曲线•生存过程的统计推断•生存时间的影响因素研究生存分析需具备的资料•生存时间或称时间变量•观察结果或称截尾变量•暴露变量及混杂因素肾移植例一般手术(A组): 3 9 15 20 20 26 30 41 46 3 9 15 20 20 26 30 41 46 64+ 64 135 64+ 64 135 223 365 450 596+ 680+ 900+ 223 365 450 596+ 680+ 900+ 900+900+改进手术(B组): 10 70+ 70+ 120 225 366 390+ 10 70+ 70+ 120 225 366 390+ 475+ 475+ 518+ 647+ 801+ 1001+ 1045+ 518+ 647+ 801+ 1001+ 1045+ 1045+1045+手术方式手术方式生存时间生存时间观察结果观察结果treattreattimetimeoutcomeoutcome1 13 31 11 19 91 11 141411 11 146461 11 164641 11 164640 0………………………………1 19009000 02 210101 1………………………………2 28018010 02 2100110010 02 2104510450 02 2104510450 0生存资料的定义(1)将数据定义为生存资料格式•stset 时间变量 [，failure(截尾变量)]•failure (截尾变量) stata以所有不等于0的非缺失值为预期的出现结果；•若failure选择项缺省，则stata默认所有纪录均出现结果生存资料的定义(2)四个变量---定义数据库后，stata系统自动产生的•_st /* 数据库中该条记录是否被定义为生存资料•_d/* 该条记录是否出现预期结果•_t/* 观察对象被随访的时间•_t0 /* 观察对象第一次被观察到的时间(开始过程的时间为0)stset￿time,failure(outcome)￿￿￿￿￿￿￿￿￿￿failure event: outcome != 0 & outcome < .failure event: outcome != 0 & outcome < .obs. time interval: (0, time]obs. time interval: (0, time] exit on or before: failure exit on or before: failure------------------------------------------------------------------------------------------------------------------------------------ 33 total obs. 33 total obs. 0 exclusions 0 exclusions------------------------------------------------------------------------------------------------------------------------------------ 33 obs. remaining, representing 33 obs. remaining, representing 18 failures in single record/single failure data 18 failures in single record/single failure data 11370 total analysis time at risk, at risk from t = 0 11370 total analysis time at risk, at risk from t = 0 earliest observed entry t = 0 earliest observed entry t = 0 last observed exit t = 1045 last observed exit t = 1045生存资料的描述•stci ,[by(分组变量)选择项]•p(#) /* 生存时间的百分位数•level(#) /* 可信区间的可信度•media /* 计算中位生存时间，为默认选项•rmean /* 计算平均生存时间. stci,by(treat)stci,by(treat) failure _d: outcome failure _d: outcome analysis time _t: time analysis time _t: time | no. of | no. of treat | subjects 50% Std. Err. [95% Conf. Interval] treat | subjects 50% Std. Err. [95% Conf. Interval]-------+--------------------------------------------------------------------+------------------------------------------------------------- 1 | 19 64 46.8995 20 450 1 | 19 64 46.8995 20 450 2 | 14 . . 225 . 2 | 14 . . 225 .-------+--------------------------------------------------------------------+------------------------------------------------------------- total | 33 365 143.4001 64 . total | 33 365 143.4001 64 .. . stci,rmean by(treat)stci,rmean by(treat) failure _d: outcome failure _d: outcome analysis time _t: time analysis time _t: time | no. of restricted | no. of restrictedtreat | subjects mean Std. Err. [95% Conf. Interval]treat | subjects mean Std. Err. [95% Conf. Interval]-------+--------------------------------------------------------------------+------------------------------------------------------------- 1 | 19 297.0329(*) 83.96867 132.457 461.60 1 | 19 297.0329(*) 83.96867 132.457 461.60 2 | 14 766.4481(*) 116.2397 538.622 994.274 2 | 14 766.4481(*) 116.2397 538.622 994.274-------+--------------------------------------------------------------------+------------------------------------------------------------- total | 33 512.9716(*) 83.84662 348.635 677.308 total | 33 512.9716(*) 83.84662 348.635 677.308(*)largest observed analysis time is censored, mean is underestimated(*)largest observed analysis time is censored, mean is underestimated.生存率的估计输出生存率、生存概率的标准误等统计量•sts list [,by(分组变量) 选择项]•failure /* 输出死亡函数 (1-S(t))•level /* 规定所输出可信区间的可信度. . sts list,by(treat)sts list,by(treat) failure _d: outcome failure _d: outcome analysis time _t: time analysis time _t: time Beg. Net Survivor Std. Beg. Net Survivor Std. Time Total Fail Lost Function Error [95% Conf. Int.] Time Total Fail Lost Function Error [95% Conf. Int.]--------------------------------------------------------------------------------------------------------------------------------------------------------------treat=1 treat=1 3 19 1 0 0.9474 0.0512 0.6812 0.9924 3 19 1 0 0.9474 0.0512 0.6812 0.9924 …... …... 680 3 0 1 0.2368 0.1015 0.0758 0.4475 680 3 0 1 0.2368 0.1015 0.0758 0.4475 900 2 0 2 0.2368 0.1015 0.0758 0.4475 900 2 0 2 0.2368 0.1015 0.0758 0.4475treat=2 treat=2 10 14 1 0 0.9286 0.0688 0.5908 0.9896 10 14 1 0 0.9286 0.0688 0.5908 0.9896 70 13 0 2 0.9286 0.0688 0.5908 0.9896 70 13 0 2 0.9286 0.0688 0.5908 0.9896 …... …... 1001 3 0 1 0.6753 0.1344 0.3464 0.8647 1001 3 0 1 0.6753 0.1344 0.3464 0.8647 1045 2 0 2 0.6753 0.1344 0.3464 0.8647 1045 2 0 2 0.6753 0.1344 0.3464 0.8647--------------------------------------------------------------------------------------------------------------------------------------------------------------绘制生存（死亡）曲线(1)绘制Kaplan-Meier生存(死亡)曲线•sts graph [,by(分组变量) separate 选择项] •failure /* 指定绘制“死亡”曲线，缺省时绘制生存曲线•Gwood /* 绘 制 生 存 (或 死 亡 )曲 线 及 其Greenwood可信区间•lost /* 在曲线上标出该时间点截尾值例数绘制生存（死亡）曲线(2)•绘制Kaplan-Meier生存曲线与Cox预测曲线•stcoxkm [,by(分组变量) separate 绘图命令选择项] 生存率的比较•sts test 分组变量 [,选择项]• logrank /* 进行log-rank检验，为缺省值. sts test treat. sts test treat failure _d: outcome failure _d: outcome analysis time _t: time analysis time _t: timeLog-rank test for equality of survivor functionsLog-rank test for equality of survivor functions | Events Events | Events Eventstreat | observed expectedtreat | observed expected------+-------------------------------+-------------------------1 | 14 8.571 | 14 8.572 | 4 9.432 | 4 9.43------+-------------------------------+-------------------------Total | 18 18.00Total | 18 18.00 chi2(1) = 6.71 chi2(1) = 6.71 Pr>chi2 = 0.0096 Pr>chi2 = 0.0096例8.8•某临床试验比较A，B两治疗方案对某病的治疗效果，A组(group=0)12人，B组(group=1)13人。

病人分组后检验其肾功能(kidney)，功能正常者记为0，不正常者记为1；治疗后生存时间为stime(天) ；问不同治疗方案及肾功能对病人的生存时间是否有影响?编号编号NO.NO.治疗治疗生存生存观察观察肾功能肾功能kidneykidney编号编号NO.NO.治疗治疗生存生存观察观察肾功能肾功能kidneykidney方案方案时间时间结果结果方案方案时间时间结果结果GroupGroupstimestimecensorcensorgroupgroupstimestimecensorcensor1 10 08 81 11 113131 11801801 10 02 20 08528520 00 014141 16326321 10 03 30 052521 11 115151 1224022400 00 04 40 02202201 10 016161 11951951 10 05 50 063631 11 117171 176761 10 06 60 08 81 10 018181 170701 10 07 70 0197619760 00 019191 113131 11 18 80 0129612960 00 020201 123231 11 19 90 0146014600 00 021211 1129612961 10 010100 063631 11 122221 12102101 10 011110 0132813280 00 023231 17007001 10 012120 03653650 00 024241 118181 11 125251 1199019900 00 0例8.8Cox比例风险模型 (1)估计Cox比例风险模型的命令格式为•stcox [协变量] [,nohr 选择项]•nohr /* 指定输出回归系数b而不是危险 比exp(b)•level(#) /* 可信区间的可信度例8.8Stset stime,failure(censor)Stset stime,failure(censor)Stcox group kidney,nolog nohrStcox group kidney,nolog nohrfailure _d: censorfailure _d: censor analysis time _t: stime analysis time _t: stimeCox regression -- Breslow method for tiesCox regression -- Breslow method for ties  No. of subjects = 25 Number of obs = 25No. of subjects = 25 Number of obs = 25No. of failures = 17No. of failures = 17Time at risk = 15334Time at risk = 15334 LR chi2(2) = 22.67 LR chi2(2) = 22.67Log likelihood = -35.707534 Prob > chi2 = 0.0000Log likelihood = -35.707534 Prob > chi2 = 0.0000------------------------------------------------------------------------------------------------------------------------------------------------------------ _t | _t | _d | Coef. Std. Err. z P>|z| [95% Conf. Interval] _d | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+-----------------------------------------------------------------------------+---------------------------------------------------------------- group | 1.243078 .5993177 2.07 0.038 .0684365 2.417719 group | 1.243078 .5993177 2.07 0.038 .0684365 2.417719 kidney | 4.105455 1.164533 3.53 0.000 1.823012 6.387898 kidney | 4.105455 1.164533 3.53 0.000 1.823012 6.387898------------------------------------------------------------------------------------------------------------------------------------------------------------•Cox比例风险函数:•(t)= 0(t)exp(1.243group+4.105kidney)•肾功能正常者接受B治疗方案比接受A治疗方案在某时刻的相对危险度为：RR=(t|group=1,kidney=0)/ (t|group=0,kidney=0) = 0(t)exp(1.243*1+4.105*0)/ 0(t)exp(1.243*0+4.105*1)=3.466•肾功能不正常者接受B治疗方案比接受A治疗方案在某时刻的相对危险度为3.466•肾功能不正常者接受B治疗方案比肾功能正常者接受A治疗方案在某时刻的相对危险度为210.300Weibull回归和指数回归•streg [协变量]， [选项]•dist（分布类型）/*拟合模型的分布类型。

exponential（指数分布）weibull（weibull分布）•nohr /* 指定输出回归系数b而不是危险 比exp(b)•level(#) /* 可信区间的可信度此课件下载可自行编辑修改，供参考！感谢您的支持，我们努力做得更好！。