COX s Proportional Hazard Model Cox 2005117

Cox , . , , , , 1972Cox DR.

1 tth(t).

px1, x2,,xpTC n. :

X1 X2 . XP T C 1 x11 x21 x1p y1 1 2 x21 x22 x2p y2 0 n xn1 xn2 xnp yp .

2

3COX Logistic Logistic ln[P/(1-P)]=0+1X1+ 2X2 +pXp. Y^ 0 +1X1+2X2++pXp TYP

X1X2 Xpt h0(t), X1X2 Xp t th(t). COX h(t)/h0(t) P/1-P

4Cox

lnh(t)/ h0(t)=1x1+2x2++pxp

12p h0(t)COX

COXh(t)= h0(t)exp(1x1+2x2++pxp)

xjhr (hazard ratio) hr= ei 5 hrRR

6 Cox

CoxLogistic

7Cox Cox H0i 0 H1 i 0

HoH1 H0 2-2[ - ] p2

8Cox

H0 H1 H0 Z bkSE(bk) SE(bk)bk

9Cox

1. .

2. relative riskRR).

3. 1x1+2x2++pxp(

CHISS COX

12-3 50. , x1x2, x3, P83

+, X1/mm3 X2012, X31, 0COX

1 CHISS\dataa9_3cox.DBF a9_3cox.DBF

2 COX x1,x2,x3 time CENSOR 3

u p X1 0.001 0.002 0.591 0.5543 X2 0.456 0.206 2.211 0.0270 X3 -1.885 0.376 5.008 0.0000

RR 95%CI 1.00 0.997~1.005 1.58 1.053~2.364 0.15 0.073~0.317

CoxX2X3, X1 , , ,