第6章 生存分析與cox比例風險模型

1、q = 某年內(nèi)某年年初人口數(shù)p = 某年活滿一年人數(shù)某年年初人口數(shù)p = 1- q) = tk時刻仍存活的例數(shù)S (t ) = P(T tkk觀察總例數(shù)0 S(t) 1S(tk ) = P(T tk ) = p1.p2.pk圖 2. 生存曲線圖 3. 隨訪資料常見形式示意圖圖 4. 隨訪資料常見形式示意圖表 2. 膀胱腫瘤3.0cm組生存率及標準誤的計算1- S (t)SES (t) = S (t)nt - dtS(t) ua / 2SES(t)0.7144 1.96 0.1207曲線高度下降坡度圖 5. 腫瘤3.0cm組生存曲線圖解法圖 7. 某惡性腫瘤生存曲線（壽命表法）中位生存時間(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圖 6. 腫瘤3.0cm組和腫瘤3.0cm生存曲線12345678910012345678910907651252074132000125993553742842081571209579666254序號確診后年數(shù)期內(nèi)死亡數(shù)期內(nèi)截尾數(shù)期初病例數(shù)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確診后年數(shù)期內(nèi)死亡數(shù)期內(nèi)截尾數(shù)期初病例數(shù)期初有效例數(shù)死亡概率生存概率生存率生存率標準誤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 =（組數(shù)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】數(shù)據(jù)，腫瘤3.0cm患者組和腫瘤3.0cm患者組2年生存率分別是0.8572和0.4375，標準誤分別為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模型的基本結構 IIIh(t, X ) = h (t)exp(b X+ b X+ . + bX)01122mmCox模型的基本結構 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