뇌졸중 뫵생 예측모형을 위한 cox와 weibull 모형의 뭥교 평가 · 2009-05-06 ·...
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41
서 론
2005 245,511
, 66,228
56, 576 ( , 13,410 ,
31,297 ) [1].
10 64.3
27.5 , 28.4 , 22.5 , 22.6
.
, , ,
[2,3].
.
(global
risk)
algorithm .
Kannel (1976)[3]
Cox (proportional
hazards model) [2,5,6] Weilbull [7]
.
Framingham
[8].
Cox
Weibull
.
Framingham
[3]
.
.
30 ,
Cox
Weilbull .
연구대상 및 방법
1. 연구자료
1992 1995
30
(Korean Cancer Prev-
ention Study, KCPS) 1,329,525 .
55
64 , , , ,
385,279 ( 223,584
, 161,695 ) .
1992 1995
뇌졸중 발생 예측모형을 위한 Cox와 Weibull 모형의 비교 평가
김윤남 조어린 남병호 박일수 지선하
연세대학교 보건대학원 연세대학교 보건대학원 국민건강증진연구소 국립암센터 국민건강보험공단
원 저
42
, , , ,
.
2. 분석에 사용된 변수
(exposure)
.
3-4
, .
, , ,
, , , , .
, ,
, ,
. , ,
,
.
,
.
, ,
,
. 140mm
Hg 90 mmHg
. National Cholesterol Education Program
(NCEP) Guideline <200 mg/dl,
200-239 mg/dl, 240 mg/dl [9]. National
Diabetes Data Group
126 mg/dl
[10].
.
(1993-2005 ) .
(1993 -2005
) . ICD
-10 I60-I69 .
(person-
year) ,
.
.
1993 1 1 2005 12 31
.
3. 분석방법
( 0.1% )
, . 30kg
, 130cm , 16kg/m2
.
385,279 .
70% ,
30% .
1992 , ,
, , , ,
, , (BMI) .
Cox
.
Cox Weibull
. Cox
X(x1 xi ; )
t
.
′ - 1
(baseline hazard) X
0 t
t . Cox
43
SAS 8.2 version Proc PHREG
Proc LIFETEST 10
Kaplan-Meier .
Weibull t
.
′ - 2
(scale parameter) . Weibull
Proc LIFEREG .
Cox
(partial likelihood) ,
t
. Weibull
Weibull
(maximum likelihood)
. Cox
.
. , Weibull -b[Weibull]/
Cox b[Cox]
[8]. z
. z=(-b[Weibull]/-b[Cox])/SE
b[Cox] Cox
, b[Weibull] Weibull , SE
. , 10
10- (decile)
. Cox
Weibull Kaplan-
Meier
. , 1-
Receiver Operating Characteristics (ROC)
curve (C- )
.
결 과
1
.
TotalMale Female Total
223,584 (100.0) 161,695 (100.0) 385,279 (100.0)
Age (yrs)
Mean ± S.D. 55.5 ± 3.9 56.3 ± 4.2 55.8 ± 4.1
50-54 101,129 (45.2) 63,550 (39.3) 164,679 (42.7)
55-59 82,262 (36.8) 56,547 (35.0) 138,809 (36.0)
60-64 40,193 (18.0) 41,598 (25.7) 81,791 (21.2)
Hypertension* No 115,943 (51.9) 96,274 (59.5) 212,217 (55.1)
Yes 107,641 (48.1) 65,421 (40.5) 173,062 (44.9)
SBP (mmHg) Mean ± S.D. 129.3 ± 18.3 126.5 ± 20.4 128.1 ± 19.2
DiabeticsNo 204,479 (91.5) 151,481 (93.7) 355,960 (92.4)
Yes 19,105 (8.5) 10,214 (6.3) 29,319 (7.6)
SmokingNo 101,558 (45.4) 153,645 (95.0) 255,203 (66.2)
Yes 122,026 (54.6) 8,050 (5.0) 130,076 (33.8)
Total Cholesterol**,
(mg/dl)
Mean ± S.D. 196.5 ± 39.1 205.8 ± 39.9 200.4 ± 39.7
< 200 126,352 (56.5) 75,261 (46.5) 201,613 (52.3)
200 ~ 240 68,584 (30.7) 56,412 (34.9) 124,996 (32.4)
> = 240 28,648 (12.8) 30,022 (18.6) 58,670 (15.2)
Stroke events***
14,941 (6.7) 8,858 (5.5) 23,799 (6.2)
* SBP 140 mmHg or DBP 90 mmHg, ** NCEP standard, *** 13-year follow-up results, Mean±S.D., ()=%
Table Table Table Table 1. 1. 1. 1. Baseline characteristics for subjects
44
. 33.8%
54.6%, 5.0% . 13
6.2%
23,799 .
LLS(Log(-Log(survival))
. 1 5
.
.
.
.
, ,
, , , , ,
, Cox
,
, , ,
. 200~240 mg/dl
0
-1
-2
-3
-4
-5
-6
-7
-80.5 1 1.5 2 2.5 3
Log (time)
0
Log (-Log(survival))
(Male) (Female)
50-5455-5960-64
Age (yrs)
0
-1
-2
-3
-4
-5
-6
-7
-80.5 1 1.5 2 2.5 3
Log (time)
0
Log (-Log(survival))
Fig.Fig.Fig.Fig. 1. 1. 1. 1. Log-log survival vs. log time for ages 50-54, 55-59 and 60-64
Male Female
Cox Weibull*
Difference Cox Weibull*
Difference
Constant 4.0524 3.9109
Age, yrs 0.0618 0.0673 -0.0055 0.0759 0.0770 -0.0012
SBP, mmHg 0.2059 0.2049 0.0010 0.1713 0.1719 -0.0006
DiabeticsNo
Yes 0.4825 0.4822 0.0002 0.6267 0.6293 -0.0026
Smoking No
Yes 0.2239 0.2289 -0.0050 0.4680 0.4733 -0.0053
Total Cholesterol,
mg/dl
< 200
200 ~ 240 0.0066 0.0009 0.0057 0.0086 0.0061 0.0025
> = 240 0.1121 0.1050 0.0071 0.0624 0.0588 0.0036
=0.5427 =0.4764
* - [coefficient in Weibull model]/No significant differences at the 0.05 level
Table Table Table Table 2. 2. 2. 2. Estimated coefficients for Stroke, using Cox Proportional Hazard Model and Weibull model
45
.
2
. Cox
Weibull
. 0.01
.
z ,
0.05
.
Decile Cox Weibull
10
( 2).
Weibull Cox
. , =7.11(p-value
=0.626) =0.72(p-value=0.999)
. ROC C-
0.68 . C-
95% ±0.01 .
Cox Weibull
, Cox Weibull
<0.2 Kaplan-Meier
.
고 찰
Cox Weibull
. (Korean Cancer
Prevention Study, KCPS)
. 1993 2005
13 55 70
10 Cox
Weibull .
70% 30%
,
. , ,
, , ,
. ,
.
Cox .
Weibull , Weibull
.
Weibull
Weibull Cox
15
10
5
01
Decile
Stroke (%)(Male)
2 3 4 5 6 7 8 9 10
15
10
5
01
Decile
Stroke (%)(Female)
2 3 4 5 6 7 8 9 10
WeibullCox
Fig.Fig.Fig.Fig. 2. 2. 2. 2. Ten-year risk predictions for stroke events: Performance measures for Cox Proportional Hazard Model and Weibull model
46
. Weibull
[11]. Cox Weibull
. Weibull
LLS ,
Weibull .
,
.
. , 2
10-
. Weibull
Cox
. ,
.
10-
. ,
ROC
.
ROC 0.68
. Kaplan-Meier
,
.
1992 1995
.
. 1)
, ,
, ,
11% [13], 3)
[2,13]
.
, (toward
null) .
,
. ,
.
.
.
55 64
Cox Weibull
,
.
.
참고문헌
1. . , 2005.
2. Wolf PA, D’Agostino RB, Belanger AJ, Kannel
WB. Probability of stroke: a risk profile from the
Framingham study. Stroke 1991; 22;312-8.
3. Jee SH, Suh I, Kim IS, Appel LJ. Smoking and
atherosclerotic cardiovascular disease in men with
low levels of serum cholesterol. JAMA 1999;
282(22); 2149-55.
4. Kannel WB, Dawber TR, Sorlie P, Wolf PA.
Components of blood pressure and risk of atheroth-
rombotic brain infarction: he Framingham study.
Stroke 1976; 7;327-31.
5. D’Agostino RB, Wolf PA, Belanger AJ, Kannel
WB. Stroke risk profile: adjustment for antihypert-
47
ensive medication. The Framingham study. Stroke
1994; 25;40-3.
6. Wang TJ, Massaro JM, Levy D, et al. A risk score
for predicting stroke or death in individuals with
new-onset atrial fibrillation in the community. The
Framingham heart study. JAMA 2003; 290;1049
-56.
7. Carroll KJ. On the use and utility of the Weibull
model in the analysis of survival data. Control Clin
Trials. 2003 Dec; 24(6); 682-701.
8. Odell PM, Anderson KM, Kannel WB. New
models for predicting cardiovascular events. J Clin
Epidemiol. 1994 Jun; 47(6); 583-92.
9. National Cholesterol Education Program (NCEP)
Expert Panel on Detection Evaluation, and Educ-
ation Treatment of high blood cholesterol in Adults
(Adult Treatment Panel III). Third report of the
National Cholesterol Education Program (NCEP)
Expert Panel on Detection, Evaluation, Education,
and Treatment of high blood cholesterol in Adults
(Adults Treatment Panel III) Final report. Circul-
ation 2002; 106;3143-421.
10. National Diabetes Data Group. Report of the
Expert Committee on the Diagnostic Classification
of Diabetes. Diabetes Care 1997; 20;1183-97.
11. . - . , 2006 .
12. 2 . . , 1996 .
13. Jee SH, Suh I, Kim IS, Appel LJ. Smoking and
atheroclerotic cardiovascular disease in men with
lower levels of serum cholesterol: The Korean
Medical Insurance Corporation Study. JAMA 1999;
282(22)2149-2155
48
Objective: The objective was to compare Cox proportional hazards model and Weibull model for predicting
long-term probabilities for stroke risk in the Korean Cancer Prevention Study(KCPS).
Methods: The subjects comprised of 385,279 Korean aged 55 to 64 years who received health insurance from the
National Health Insurance Corporation and who had medical examinations in 1992 and 1995. 70% of the subjects were
used for model building and the rest for model evaluation. The final prediction model for stroke includes age, systolic
blood pressure, diabetes, total cholesterol and smoking. Subjects were follow-up for identification of incident stroke
cases between 1993 and 2005. Comparisons included predicted coefficients of stroke risk factors, incidence probabilities
over 10 years, and the area under a receiver operating characteristics (ROC) curve for both Cox’s proportional hazard
model and Weibull model.
Results: The average age of study population was 55.5 years in men and 56.3 years in women, respectively.
Percentage of men and women in study population were 58.0% and 42.0%, respectively. The study findings satisfied
proportionality according to the two models. There was no significant difference in coefficients between the two models
of prediction models in men and in women. Moreover, there was no difference in incidence probabilities of stroke and
c-statistics. C-statistics were 0.68 for men as same as for women.
Conclusion: There was no difference for the prediction of the stroke risk in the Korean population using Cox’s
proportional hazard model and Weibull model, thus the two models were found to be efficient for this purpose.
: Prediction model, proportional hazard model, Weibull model, Stroke
Evaluation of risk prediction model for stroke risk based on
Cox’s and Weibull model in Korea
Youn Nam Kim1), Ur Rin Cho
2), Byung-Ho Nam
3), Il Soo Park
4), Sun Ha Jee
1,2)