第6章 生存分析与cox比例风险模型

1、q = 某年内某年年初人口数p = 某年活满一年人数某年年初人口数p = 1- q) = tk时刻仍存活的例数S (t ) = P(T tkk观察总例数0 S(t) 1S(tk ) = P(T tk ) = p1.p2.pk图 2. 生存曲线图 3. 随访资料常见形式示意图图 4. 随访资料常见形式示意图表 2. 膀胱肿瘤3.0cm组生存率及标准误的计算1- S (t)SES (t) = S (t)nt - dtS(t) ua / 2SES(t)0.7144 1.96 0.1207曲线高度下降坡度图 5. 肿瘤3.0cm组生存曲线图解法图 7. 某恶性肿瘤生存曲线（寿命表法）中位生存时间(2

2、- 3) : (2 - t) = (0.5562 - 0.4198) : (0.5562 - 0.5)t = 2 - (2 - 3)(0.5562 - 0.5) = 2.410.5562 - 0.4198图 6. 肿瘤3.0cm组和肿瘤3.0cm生存曲线12345678910012345678910907651252074132000125993553742842081571209579666254序号确诊后年数期内死亡数期内截尾数期初病例数012345678910907651252074132000125993553742842081571209579666254374.0284.0208.

3、0151.0117.590.574.564.559.551.590/374.0=0.240676/284.0=0.267651/208.0=0.45225/151.0=0.165620/117.5=0.17027/90.5=0.07734/74.5=0.05371/64.5=0.01553/59.5=0.05042/51.5=0.03880.75940.73240.75480.83440.82980.92270.94630.98450.94960.96120.75940.55620.41980.35030.29070.26820.25380.24990.23730.22810.02210.02

4、570.02550.02480.02390.02350.02330.02330.02320.0232确诊后年数期内死亡数期内截尾数期初病例数期初有效例数死亡概率生存概率生存率生存率标准误tdtctntntqtptS(t)SES(t)( A- Tngingin - d)2V= c 2(1-= gg)( ii )dgin -1Vninigi亦可用公式：= ( A - T )2c 2Tc 2c 2n =（组数1）ngidi=Tginic2= (11-17.5416)2n = 1c 2= 7.375.8064= (16 - 9.4584)2n = 1c 2= 7.375.8064RR = R1 =A1

5、 / T1= 11/17.5416 = 0.37R2A2 / T216 / 9.4584S1 (t) - S2 (t)u =SE2S (t) + SE2S(t)12 【案例】数据，肿瘤3.0cm患者组和肿瘤3.0cm患者组2年生存率分别是0.8572和0.4375，标准误分别为0.0935和0.1240，0.8572 - 0.4375u = 2.700.09352 + 0.12402aa = a / kh(t, X ) = h (t)exp(b X+ b X+ . + bX)01122mmCox模型的基本结构 IIIh(t, X ) = h (t)exp(b X+ b X+ . + bX)01122mmCox模型的基本结构 IVh(t, X ) / h (t) = exp(b X+ bX+ . + bX)01122mmlnh(t, X ) / h (t) = b X+ bX+ . + bX01122mmh(t, X ) = h (t)exp(b X+ b X+ . + bX)01122mmh(t, X ) = h (t)exp(b X )exp(b X ).exp(bX)01122mmbbbh(t, X ) = h (t)exp(b X+ b X+ . + bX)01122mmh(t, X ) / h (t) = exp(b X+ b X