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)