Εισαγωγή Στη Βιοστατιστική Και Την Επιδημιολογία
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Εισαγωγή Στη Βιοστατιστική Και Την Επιδημιολογία
Transcript of Εισαγωγή Στη Βιοστατιστική Και Την Επιδημιολογία
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pi
pi
pi -
pi
, pi 2009,4 (v.4.2 23/9/2009)
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pi pi . pi pi 2005 pi . pi 3 .
, 16 pi 2008
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1.1 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 pi 7
2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 . . . . . . . . . . . . . . . . . . 8
2.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 pi pi . . . . . . . 10
2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.1 . . . . . . . . . . . . . . . . 112.4.2 . . . . . . . . . . . . . 132.4.3 . . . . . . . . . . . . . . . . . . 14
2.5 . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.1 - . . . . . . . . . . . . . . . . . . . . 142.5.2 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.2.2 pi pi . . . . . . . 182.5.2.3 . . . . . . . . . . . . . . . . . 19
2.5.3 - . . . . . . . . . . . . 192.5.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.3.2 . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.3.3 . . . . . . . . . . . . . . . . . 22
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3 , 23
3.1 - . . . . . . . . . . . . . . . . . . . . 233.1.1 pipi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 pipi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 pipi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 - . . . . . . . . . . . . . . . . . 263.2.1 2 2 . . . . . . . . . . . . . . 26
3.2.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.1.2 . . . . . . . . . . . . . . . . . . . . . . 273.2.1.3 . . . . . . . . . . . . . 28
3.2.2 pi . . . . . . . . . . . . . . . . . . . 293.2.3 (Relative Risk, RR) . . . . . . . . . . . . . . . . . . . . 293.2.4 (Odds Ratio, OR) . . . . . . . . . . . . . . . 31
3.2.4.1 (odds) . . . . . . . . . . . . . . . . . . . . . 313.2.4.2 pi Odds Ratio. . . 33
3.2.5 SPSS. . . . . . 363.3 (Odds Ratio) . . . . . . . . . . . . . . . . . . 363.4 pi - . . . . . . 373.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 pi ( -). 383.5.1.1 SPSS. . . . . . . . . . . . . . . . . 393.5.1.2 pi . . . . . . . 393.5.1.3 . . . . . . . . . . . . . . 41
3.5.2 pi pi pi pi - pi (pi ) . . . . . . . . . . . . . . . . . . . . 42
3.5.3 3: pi. . . . . . . . . . . . . . . . . . . . . . 443.6 pi pi 2 2 . . . . . 45
3.6.1 . . . . . . . . . . . . . . . . . . . . . . 453.6.1.1 pi . . . . . . . . . . . . . . . . . . . . . . . 453.6.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.1.3 . . . . . . . . . . . . . . . . . . . . . 523.6.1.4 3.2 () . . . . . . . . . . . . . . . . . . . . . 56
3.6.2 2 Pearson. . . . . . . . . . . . . . . . . . 583.6.3 . . . . . . . . . . . . . . . . . . . . . . . 59
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3.6.4 Fisher. . . . . . . . . . . . . . . . . . 613.6.5 . . . . . . . . . . . . . . . . . . . . . . 63
3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 643.7.2 2 2 pi . . . . . . . . . . . . . . . . . 673.7.3 pi ROC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.7.4 pi pipi pi . . . . . . . . . . . . 69
4 (Clinical Trials) 71
4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1 I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.2 II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3.4 IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.5 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.6 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6.1 . . . . . . . . . . . . . . . . . . . . . . . . . 774.6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.6.3 pi . . . . . . . . . . . . . . . . . . . . . . . . 804.6.4 pi . . . . . . . . . . . . . . 814.6.5 . . . . . . . . . . . . . . . . . 81
4.7 pi . . . . . . . . . . . . . . . . . . . . . . . 824.7.1 - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.8.1 pi pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.8.2 pi pi . . . . . . . . . . . . . . . . . . . . . . 84
5 pi pi 85
5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.1.1 pi pi pi . . . 88
5.2 / 88
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5.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.2 pi (Kappa). . . . . . . . . . . . . . . . . . . . . . 935.3 pipi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.4 pi pi . . . . . . . . 96
5.4.1 pi pi (Effect Modification). . . . . . . . . . . . . . . 995.4.2 pi . . . . . . . . . . . 1005.4.3 pi SPSS. . . . . . 1015.4.4 . . . . . . . . . . . . . . . 103
6 pi 107
6.1 pi 2 . . . . . . . . . . . . 1076.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.1.3 : , -
pi . . . . . . . . . . . . . . 109
7 (Logistic Regression) 113
7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.2 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187.3.1 . . . . . . . . . . 1187.3.2 . . . . . . . . . . . . 1197.3.3 pi . . . . . . . . . . 120
7.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.4.1 pi . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.4.2 pi . . . . . . . . . . . . . . . . . . . . . . 1257.4.3 pi . . . 127
7.5 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1277.5.1 pi . . . . . . . . . . . . . . . . . . . . . . . . 1287.5.2 Wald . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.5.3 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
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7.6 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.7 pi pi . . . . . . . . . . . . . . . . . . . . 1357.8 pi . . . . . . . . . . . . . . . . . . . . . . . . . 1357.9 Ordinal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8 pi (Survival Analysis) 137
8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.2.1 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1408.2.3 pipi . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438.4 pi . . . . . . . . . . . . . . . . . . . . . . 147
8.4.1 pi . . . . . . . . . . . . . . . . . . . 1478.4.2 SPSS . . . . . . . . . . . . . . . . . 150
8.4.2.1 . . . . . . . . . . . . . . . . . . . . . . . 1528.5 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1548.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.6.1 pi . . . . . . . . . . . . . . . . . . . . . . . . . . 1588.6.2 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1598.6.3 pi 164
8.7 pi - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1658.7.1 pi . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.8 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
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1
1.1 pi
pi pi pi pi pi pi pi - pi. pi pi pi- . pi pi pi pi pi pi pi pi , ,, pi pi (pi pi). pipi pi pi pi pi pi- pi. pi pi pi , .
pi pi pi pi . , pi pi Poisson ( ) pipi , pi pi pi +3, pi pi pi pi.
pi :
1. pi pi.
2. .
3. pi pi pi (pi pi-).
1
-
2 . : pi
4. pi pi pi (monitoring) pi- pi pi.
5. ( pi -screening).
6. .
7. pi, pi .
1.2 .
pi pi pi(, , pi). pi pi pi pipi (460-357 pi..) , pi. pi pi , , , , . pi pi pi.
, Graunt (1620-1674) pi pi . Farr(1807-1883) pi - pi pi . pi, Snow (1813-1858) pi pi pi pi pi pi. pi pi pi (, , ): Lambeth ( ) Soutwork (pi pi pi). Lambeth 8 pi . pi pi pi.
20 pi. pi pi pi pi pi Doll pi. Doll and Peto (1976). 1922 pi Harvard pi pi pi . pi pi pi pi . pi pi pipipi pi (1982, .4-7) McMahon & Trichopoulos (1996).
-
1: 3
1.3 pi .
pi pi- pi pi .
pi - pi ( pi).
1.1 : pi . pi-
pi (blood pressure) pi
pi pi pi pi (
). pi pipipi
Rosner (1994, . 14). pi -
pi pi pi
.
: pipi pi - :
1. pi ;
2. pi ;
3. ;
4. pi pipi ;
5. pi ;
6. ;
pi ( Rosner, 1994):
1. pi 4 pi.
2. pi .
3. pi pi . pi pi pi pi pi . pi pi pi ( pi).
-
4 . : pi
4. pipi pipi pi pi pi pi , , body-mass index . pi (pi.. , pi ) (pi.. pi) pi pi pi pi pi pi .
5. pi pi , pi , pi (missing values). pi 2 pi pi.
6. pi pi , pi pi -.
.
1. pi. - pi pi pi :
pi pi.pi. pi.pi. pi.pi. 98 142.5 21.0 142.0 18.1 0.5 11.2 84 134.1 22.5 133.6 23.2 0.5 12.1 98 147.9 20.3 133.9 18.3 14.0 11.7 62 135.4 16.7 128.5 19.0 6.9 13.6
pi pi 100 pi, pi pi pi pi (missing values), . pi pipi pi .
2. pi . pi . pi pi ( pi ) t (paired t-test).
pi pipi pi pi pi , pi- pi pi pi.
-
1: 5
pi pi - pi pi. pi pi ( ) pi . , pi pi , pi pi pi pipi pi pi pi .
-
6 . : pi
-
2
pi
2.1 .
1. pi (experimental - intervention studies). pi (clinical trials).
2. pi pi (observational medicalsurveys).
() - (Descriptive surveys, cross-sectionalstudies).
() pi pi (analytic/aetiologic studies). :
i. pi (prospective or cohort studies). - - (logitudinal studies) pi (follow-up studies).
ii. - (retrospective or case-control studies).
pi pipi pi .
7
-
8 . : pi
2.2
pi pi . , pi pi pi ( pi pi ). , pi pi, pi pi . pipi pi pi pi -pi.
2.2.1
pi , -pi, pi (pi.. ). pi :
1. pi pi pi. . pi pi pi. pi pi, , , .
2. pi pi. pi pi pipi. pi pipi , pi pi pi pi pi pi .
3. . pi pi -.
4. pipi pi pi.
2.2.2
, pi pi pi . : - pi pi pi pi , pipi pi pi pi (
-
2: pi 9
pi ) pi pi pi pi pi pi. pi 2.5.1, 2.5.2 2.5.3.
2.3
pi pi pi pi pi pi pi , . pi pi - . pi pi pi pi pi pi - pi . pipi, pipi pi. pi pi pi.
2.3.1
pi pi pipi pi pi pi pi pi pi . pi - pi pi pi pi pi ( ). (cross-sectional). pi pi pipi ( pi) - pipi (prevalence). pi pi pipi, pi pi pi pi .
pi pi pi (field surveys). pipi pipi pi . pi - pi pi pi .
pi : pi , pi pi . pi - : pi pi ( pi ), pi -
-
10 . : pi
pi pi pi pi ( pipi pi pi ).
2.3.2 pi pi
pi pi. - pi pi pi pi pipi . pi pi ( pi t-test Wilcoxon test) pipi pi pi pi (hierarhical generalised linear models) pi (structural equation models) .
pi pi pi (pi pipi ) pi ( ).
pi pipi pi pi pi - pi ( pi pi-pi) pi pi pi pi pi pi (pi).
2.4
pi pi - (association) pi pi pi . pipi- pi pi pi pi . pi (pi.. ) pi pi pi - pi -pi pi pi pi pi .
2.1 pi pi (confounder confounding variable)
pi, pipi pi,
( pi ). pi
pi pi
pi pi (pi.. pi). pi pi
-
2: pi 11
pi pi
pi pi pi
. pi (confounder)
pi. pi pi -
pi pi pi pi pi.
pi pi
.
pi , pi pi - pi pi pi . pi pi pi- pi . :
1. pi (consistency).
2. (strength).
3. (specificity).
4. (temporality).
5. (coherency).
pi pipi , ( pi) .
2.4.1
) pi : pi pi- pi pi. pipi pi pi , pi pi , pipi pi pi ( pi pi). pipi pi - pi pi pi .
-
12 . : pi
) : pi pi pi . pi pi . pipi, pi pi (dose-response effect) pi pi pi pi (pi.. ) pi .
: pi pi pi pi pi .
) : pi - pi pi pi pi pi pi . pi (, , pi pi ) pi pi . pi , pipi , pi. pi pi pi pi pi pi . pi pi pi pipi. , pi pi ( ).
) : pi pipi pi pi pi pi . . pi pipi pi pi ( pi pi pi). pi pi pi pipi . pipi (pi.. pi pi). pipi pi pi pi pi pi pi ; pi pipi pi pi pi pi pi .
) : pipi - pi pi (pi.. , ,
-
2: pi 13
, ). pipi pi - , pipi pi pi pi pi pi .pipi pipi pi pi pi pi pi .
pipi pi pi -pi pi pi .
2.4.2
pi pi , pi pi pi . pi. pi pi pi pi .
pi pi. pi pi. pi pi pipi pi pi pi . pi pi pi ( pi pi pi) , pi pi ( pi pi, pi , ). pi -pi pi pi pi pipi pipi pi pi pi pi .
A (pi)
B ( ) ( )
pi pi , - pi . pi
-
14 . : pi
pi pi.
pi pi pi pi- pi (risk factor). pipi pi pi pi (protective factor). pi-pi pi pi , pi .
2.4.3
pi . pi pi pi pi :
.
pi pi - pi pi , pi pi pi. pi pi pi -pi pi ( ) pi . pi pi pi pi pi pi pi pi . , pi pi pi , pi .
2.5
2.5.1 -
pi (temporalrelationship). - . pi pi(snapshot). pi pi (-pi , pi, pi.) pi pipi pi pi. pi pi pi.
-
2: pi 15
- - ( pi ), pi . pi pipi ( pi pi ). , - pi pi pipi.
2.2 pipi (prevalence) pi/
pi pi
.
- pi pi pi- pi pi ( pi pi- pi pipi). pi pi pi pi , pi , pi pipi .
2.5.2 pi
2.5.2.1
pipi pi pi - (cohort studies), pi (follow-up) - (longitudinal). (cohort) - . pipi pipi . - (longitudinal) - (cross-sectional) pi pi ( ) . pi ( pi ). pi .
pipi pi pi - pi pi pipi pi pi . pi , pi pi pi. pi pi - ( pi pi
-
16 . : pi
). pi pi ( pi) pi - .
pi pi pi pipi pi pi pi pi pi pi ( pi).
pipi pi pi pi pi. - , pi - pi pi .
pipi pipi pi (historical records cohort studies). pi pi - pi pi . pi , pi pipi pi pi . pi pi pi pi pi pi Armitage (1994, . 184).
pi, pi pipi :
1. pi pi pi pi . pi (pi) (pi) ( pi pi) pi ( ).
2. pi pi ,, pi.
3. pi pi pi ( - pi ).
4. pi pi .
pi pi pipi . :
1. pi . pi pipi pi .
-
2: pi 17
2. ( 50-60 pipi pi 2-3 ).
3. pi pi (pi pi).
4. (pi , pipi ). pi pi pipi ( ).
pi , pipi . pi pi pi - pi -pi.
pi pi pi pipi ( pi ) . pipi pi pi pi pi pi pi pi pi. pipi pi pi pi ( ) pipi pi pi pi pi pi ( pi pi ). pipi pi (censoring) (censored) .
, pipi : - pi.
2.1 1951 pipi . -
59600
41000 pi. pi pi
pi pi pi. pipi pi pi
(pi ) pi-
pi pi
pi pi
pi.
pi pi -
: pi, pi pi -pi.
-
18 . : pi
, pi pi -
. 1976 pi pi pi :
pi pi pi pi. -
pi pi
pi . Doll & Peto (1976).
:
1. (41000).
pi ( pi) pi pipi
8/10000.
2. . pi pi .
pi pi pi .
2.5.2.2 pi pi
pi pipi pi - - pi pi . pi (/exposed -/non-exposed ).
pi pipi
1. pi pi pi pi pi pipi .
2. pipi pi pi pi pi. pi - . pi pi pi pi . pi - pi pi pi pi pi pi.
3. . pi pi pipi pi . pipi pipi pi. pipi pi. pi pi pi, pi , pi 8.
-
2: pi 19
4. pi pi ( pi, pipi pi.).
10000 pi pi pi .
pi pi pi (matching) pi pi pi. - . pi, pi pi -pi pi . pi pi . pi pi , pi pi pi . pi : pi , pipi-/pipi pi .
2.5.2.3
pi pi pi pi - pi. pi pi , pi, .
pi pi pi. pi pi pi pi . pi pi .pi pi pi (pi.. pi , pi, pi.).
, pi pi pi pi pi . pi pipi pi .
2.5.3 -
2.5.3.1
, pi pi, pi pi, pi . pi pi. pi (recallinformation) pi .
-
20 . : pi
pi - (case-controlstudies). pi pi : pipi (cases) ( pi ) (controls, pi ). pipi pi (disease group) pi (control group). pi pi pi pi ( pi) pi pi . pi pi pi pi. pi pi pi pi pi . pipi pi pi . pi pi - pi . pipi ( ). pi pi pi .
pi . pi pi pi pi pipi .
2.5.3.2
1. pi .
2. pi .
3. pi pi .
4. -pi .
) pi : pi pipi - pi pi . pi pi pi- pi. pi pipi pi . pi pi pipi, pi pi . pi pi .
-
2: pi 21
) pi : pi pi . pipi pipi pi. pipi pi pi pi . pi pi- ( pi pi ) pi pi pi pi pi . pipi pi . pi pi pi pi - pi.
pi pi pi , pi pi . (individual matching) pi pi pi (frequency matching).
pi pi pipi pi pi pi.
) : pi pi pi pi. pi- . pipi (pi.. pi pi ; /). pi, pi pipi /. pi pi pi . pi pi pi -pi . pi pipi, pi pi pi - pi (pi.. pi 5 pi pi).
pipi pi pi . pipi pipi pi . pi pipi pi pi .
) -pi : pi . pi .
-
22 . : pi
2.5.3.3
pi :
1. pi .
2. pi ( ).
3. .
4. pi pi .
5. pi pi pi .
pi :
1. pipi ( ).
2. pi pi pi .
3. pi pi pi (pi pi- ).
4. pi pi pipi.
5. pi pi pi pi (selectionbias).
6. pi pi .
pi pi pi- . pi pipi pi pi pipi pipi pipi - pi . pi pi pipi .
-
3
,
3.1 -
3.1.1 pipi
pipi (prevalence) pi ( ) pi- pi t ( pipi). pipi pi[t0, t1) pi ( ) pi pi pipi t [t0, t1) ( t0 t < t1). pi () pipi pi pi pi d t. pi pi
Prevalencedt =NdtNt,
pi Ndt pi d t N(x) pi t. pipi - (cross-sectional measure) pi pi pi pipi pi. pipi pi - n pi pi pi:
Prevalencedt = 1nni=1
Y di =nd
n,
pi Y di - pi pi (1) (0) i d nd
23
-
24 . : pi
pi d. pipi pi pipi pi
pi pi . pipi pi pipi pi Nt n pi pi . pi pipipi Daly et. al(1991, . 281-282) Pereira-Maxwell (1998, . 62).
3.1.2 pipi
pipi pi pi pi pi pi pi . pi pipi pipi pi pi .
pipi (case) pi pi (incident) pi pi pi .
pipi (cummulative incidence) [t0, t1) pi pi pi pi pi (Rosner, 1994, . 61).pi pi pi
Idt0,t1 = P(t0 < Dd < t1|Dd > t0) = NI
dt0,t1
NIdt0
pi Dd d, NIdt0,t1 pi d [t0, t1) NI(t0) pi d pi t0. pipi pipipi ( pipi) pi pi:
Idt0,t1 =
ni=1 Y
Id(t0,t1)in
i=1 YId(t0)i
=nidt0,t1nidt0
pi nid(t0, t1) nid(t0) pi NId(t0, t1) NI(t0).pipi Y Id(t0,t1)i Y Id(t0)i - (0 1) pi pi i pi [t0, t1) i pi t0 .
pi pi ( pi) t pi- pi t ( pi t) pi pi S(t) = P(Dd > t).
-
3: , 25
pi pi pi :
I(t0, t1) =S(t0) S(t1)
S(t0)= 1 S(t1)
S(t0).
3.1.3 pipi
pipi pi pi pi pi . pi pi pi pi pi. pi pi pi pipi pi pi pi pi pi.
pipi (incidence rate) pi [t0, t1) pi pi pi (Pereira-Maxwell, 1998, . 29). pi pi pi pi pi. , pi pipi pi pi pi. pi, pipi pi pi:
IRdt0,t1 =NIdt0,t1T(t0,t1)
=NIdt0,t1Nt0
i=1 Ti,(t0,t1)
pi Nt0 pi t0, T(t0,t1) pipi Ti,(t0,t1) pi [t0, t1) i. pi pi pi pi pi (t1 t0) pipi
IRdt0,t1 =NIdt0,t1
Nt0(t1 t0).
3.1.4
(duration) pi pi pi D ( Dd). pi pi D ( Dd). . pi pi pi pi
-
26 . : pi
pipi ( pi pi ) pipi .
3.2 - .
, pi ( pi ). pipi pi pi pi pi pi . pi . pipi pipi pi pi pi pi .
pi pi pi pi ( /), pi pi pi - pi. pi pi ( pi ) pi .
pi pi pipi (Bernoulli) pi X Ypi . pi - pi pi pi 2 2 pi .
3.2.1 2 2 .3.2.1.1
pi 2 pipi -pi (barchart) pi pi (two - waycontingency tables). pi pi pi pi - 2 pi pi. pi pi pi . X Y pipi I J I J . pi pi I J . pi pi pi (cell). (X, Y ) = (i, j)
-
3: , 27
(count) nij . n n = Ii=1Jj=1 nij . pi P(X = i, Y = j) piij pi pij = nij/n .
, I J pi pi pi I J . 2 2 pi pi :
Y: ..X:. 1 () 2 () X
1 () n11 n12 n1.2 (pi) n21 n22 n2... Y n.1 n.2 n.. = n
X Y pipi pi pi (marginal distributions). pi- i X ni. ( ni+) pi j Y n.j ( n+j) pi pi ni. = Jj=1 nij n.j = Ii=1 nij. . - pi + pi . n.. n++pi . pi pi pi pi pii. pi.j X Y pi. p.j. pipi pi pi pi (contingency tables) pi (counts). pi (cross-classified tables).
3.2.1.2
pi pi (pi.. Y ) pi - pi (response) (pi.. X ) pi (explanatory variable). pipi X pi pi pi pi . pi piij = P(X = i, Y = j) ( X ). Y (pipi) X . pi pi Y X . ,pi, pi- pi
pij|i = P(Y = j|X = i)
-
28 . : pi
Jj=1 pij|i = 1. pi (pi1|i , . . . , piJ |i) ( pi ) (conditional distribution) Y i pipi X .
pi 2 2 pi pi (pi 3.1). , pi, pi pi pi pi piP(| ) = pij=1|i=1 P(| pi) = pij=1|i=2 - pi pi.
3.2.1.3
piij = P(X = i, Y = j) = P(X = i)P(Y = j) = pii.pi.j . pi P(Y |X = i) i
pij|i = P(Y = j|X = i) = P(Y = j, X = i)P(X = i)=
P(Y = j)P(X = i)
P(X = i)= P(Y = j) = pi.j .
pi (Y ) pi - pi X . pi pi pi pii|j = P(X = i|Y = j).
pi
H0 : pij|i = pi.j i = 1, . . . , I j = 1, . . . , J .pi pi piJj=1 pij|i = 1, pipi j pi pi J1 pi pi J1 pipi pi pi J pipi. 2 2 pi pi pi pi
H0 : pij=1|i=1 = pij=1|i=2 H1 : pij=1|i=1 6= pij=1|i=2 , (3.1)
pi pipi pi pi
H0 : P(A|E) = P(A|E) H1 : P(A|E) 6= P(A|E),
pi A, E E pi ( ), pi .
-
3: , 29
pi pi pi -, pi pi , pi . (pi ) pi pi .
3.2.2 pi
pi (, 1997 - attributable risk) (risk difference,Rosner, 1995, . 362-363) pipi ( ) pi -. pi (pi, 1982, .189). pi 22 pi pi pij=1|i=1 pij=1|i=2. pi
AR = piE piE = P(A|E) P(A|E) = pij=1|i=1 pij=1|i=2 = pij=2|i=2 pij=2|i=1
pi piE = P(A|E) piE = P(A|E) pi pi (E) (E). pi pi
AR = pE pE = pj=1|i=1 pj=1|i=2 =n11n1.
n21n2. =
n11n11 + n12
n21n21 + n22
,
pi pE pE pi . (3.1) pi pi H0 : AR = 0 H1 : AR 6= 0.
pi pipi pi . pi- 0.10 0.20 AR pi 0.6 0.7 pi pipi pi pi pi . pi pi pi (pi, 1982, . 190)pi pi pi
pAR =piE piEpiE
=P(A|E) P(A|E)
P(A|E) =pij=1|i=1 pij=1|i=2
pij=1|i=1=AR
piE.
3.2.3 (Relative Risk, RR)
pi pi pi pi (relative risk) pi pipi
-
30 . : pi
pi . pi 2 2 pi pi pij=1|i=1 pi pij=1|i=2,
RR =piEpiE
=P(A|E)P(A|E) =
pij=1|i=1pij=1|i=2
=1 pij=2|i=11 pij=2|i=2 .
pi pi
RR =pEpE
=pj=1|i=1pj=1|i=2
=n11/n1.n21/n2. .
pi , (3.1) pi pi H0 : RR = 1 H1 : RR 6= 1. pi, pi . , pi Y X pi , , pi pi pi pi pi pi X( X ).
RR = a, pi pipi pi pi pi :
1. pi (Y = 1) pi- (X = 1) a pi pi (X = 2).
2. a > 1 : pi (Y = 1) pi (X = 1) a 1 ( (a 1)100% ) pi pi (X = 2).
3. a < 1 : pi (Y = 1) pi (X = 1) 1 a ( (1 a)100% ) pi pi (X = 2) ( pi pi).
4. a = 1 : pi (Y = 1) pi (X = 1) pi (X = 2) ( X pi pi pi pi ).
-
3: , 31
3.2.4 (Odds Ratio, OR)
pi pi pi.
3.2.4.1 (odds)
odds pi pi pi pro-bability (pi) pi pi . odds A pi pi
Odds(A) =P(A)
1 P(A) pi pi pi pi ( pi pi, pi , ).
pi odds pi. Longman (1987) ( pi):
1. pi
2. .
odds pi . pi pi pi pi pi pi 2004 , -, pi ( pi pi ) pi 80pi 1 (80 : 1) odds =1/80. pi pi, odds pi pi ( pi pi) pi (Pereira-Maxwell, 1998, . 49).
- , odds pi pi pi pi . pi pipi pi pi pi pi -pi . pi pi pi . pi pi pi pi pi
-
32 . : pi
pi pi pi pi pi pi - odds : pi pi pi pi . pi pi pi (pi , 1997, . 30).
pi pi pi pi. - pi pi . pi pipi odds pi pipi pi pipi - pi- -pi (. odds12 = pi1/pi2 pi1+pi2 < 1). pi pi pi pi- . pi odds : ) pi ) pi .
pi 1 1 pi -
odds =pi
1 pi pi =odds
1 + odds.
pi pi pi. pi pi pi pi pi pi . pi pi pi 2004 80 : 1 pi pi 80 pi . pi pi (1/(80 + 1) =) 0.0123 .
pi pi pi . pi pi pi
1. odds =1 ( 1 : 1) pi pi ( 50%).
2. odds = a pi pi a pi .
3. odds = a
() a > 1 pi pi a 1 ((a 1)100%) pi pi .
-
3: , 33
() a < 1 pi pi 1 a ((1 a)100%) pi pi .
pi pi :
odds =1 pi pi .
odds > 1 pi pi pi pi pi .
odds < 1 pi pi pi pi .
pi 2 2 pi , pi pi- odds ( pipi X ) pi :
odds(X = 1) =pi1|i=1pi2|i=1
=pi1|i=1
1 pi1|i=1=pi11pi12
odds(X = 2) =pi1|i=2pi2|i=2
=pi1|i=2
1 pi1|i=2. =
pi21pi22
.
pipi pi pi
odds(X = 1) = p1|i=1p2|i=1
=n11/n1.n12/n1. =
n11n12
odds(X = 2) = p1|i=2p2|i=2
=n21/n2.n22/n2. =
n21n22
.
, pi- pi . pi pi
oddsE =P(A|E)
1 P(A|E) =piE
1 piE oddsE =P(A|E)
1 P(A|E) =piE
1 piE pi pi pi
oddsE = pE1 pE
oddsE = pE1 pE .3.2.4.2 pi Odds Ratio.
pipi pi pi pi pi- pi odds ratio .pi pi pi pi odds pipi X . pi pi- X = 1 X = 2 pi pi
OR =odds(X = 1)
odds(X = 2)=pi1|i=1/pi2|i=1pi1|i=2/pi2|i=2
=pi11/pi12pi21/pi22
=pi11pi22pi21pi12
. (3.2)
-
34 . : pi
pi pipi pi pi pi pi pi 2 2 pi . pi pipi (crossproduct ratio). pi : pi pi ( pi . pi, , 2000, .7075) pi pi pi odds ratio . pi pi pi pi pi.
2 2 pi pi () pi
OR =p11p22p21p12
=n11n22n21n12
.
pi pipi pi . - pi OR = piE
1piE 1piEpiE
OR = pE1pE
1pEpE
. pi .
, pi pi pipi , pi (odds) pipi pi pi pi pi pi.
(OR) pi 2 2
OR = 1.
(3.1) pi
H0 : OR = 1 H1 : OR 6= 1.
, OR > 1 pi pipi ( pi- pi ) pi pi pi pipi. pi OR =4 pi pipi X (pi pi, X = 1) pi pi pi pipi X( , . X = 2). OR =1/4 pi ( X = 2) pi pi pi pi - ( X = 1). pi pipi pi ( ) pipi pi . pi
-
3: , 35
. pi pi:
pi Y = 1 X = 1 OR pi pi X = 2
pi Y = 2 X = 2 OR pi pi X = 1.
pi ( pi) pi pi pi pi :
1. OR = a pi (Y = 1) (X = 1) a pi (X = 2). : pi (Y = 2) (X = 2) a pi (X = 1).
2. OR = a > 1 pi (Y = 1) (X = 1) a 1 ( {a 1}100%) pi (X = 2).
3. OR = a < 1 pi (Y = 1) (X = 1) 1 a ( {1 a}100%) pi (X = 2).
, pi pi-pi, pi pi -. OR > 1 pi pi X ( X pi pi pi ) OR < 1 pi X ( X pi pi ).
pi pi . pi pi . pipi pi pi pi pi. pipi pi (3.1) pi
H0 : logOR = 0 H1 : logOR 6= 0.
-
36 . : pi
pipi pi. -, pi pi , pi pi pi . pi pi pi (disease odds ratio,Rosner, 1994, . 365).
pi pi pi pi pi (exposure odds ratio, Rosner, 1994, . 366). 2 2 pi pipi pi pi pi . pi pipi pi 2 2 pi ( pi pi pi) pi .
3.2.5 SPSS.
SPSS pi pi pi pi 2 2 . pi
Analyze>Descriptive Statistics>Crosstabs. pi pi , pi pi pi Statistics pi Risk. ( pi) pi 2 2pi.
3.3 (Odds Ratio)
pi pi ( ) pi pi pi pi -pi pipi ( ) ( -) pi pi pi - pipi . pipi, pi pi pi . pi
-
3: , 37
pipi
OR =OddsEOddsE
=Odds(X = 1)
Odds(X = 2)=pij=1|1/pij=2|1pij=1|2/pij=2|2
=pij=1|1pij=1|2
pij=2|1pij=2|2
=RR(Y = 1)
RR(Y = 2).
pi pi pi ( pi pi ) pij=2|1 1 pij=2|2 1 RR(Y = 2) 1 pi OR RR(Y = 1). Rosner (1994, . 368) pi pi pi pi pipi pipi (. pi) 0.10 .
pi pipi pi pi pi pi . pi ( pi ) pi pij=1|1 pij=1|2. - pi pi pi . pipi , pi pipi pi pi, pi pi pi . pi , ,pi pi pi 3.2, pipi pi. (3.2) pi
OR =pi1|i=1/pi2|i=1pi1|i=2/pi2|i=2
=pi11pi22pi21pi12
. =pii=1|1pi1.pii=2|2pi2.pii=1|2pi2.pii=2|1pi1.
OR =pii=1|1pii=2|2pii=1|2pii=2|1
. (3.3)
pi pi pi pij=1|i i = 1, 2 pi pii|j=1 i = 1, 2 pi pi pi -. pipi pi pi pi- pi pi (X Y ) . pi pi pi pi pipi .
3.4 pi -
pi :
RR =P(A|E)P(A|E) =
piEpiE.
-
38 . : pi
- (A) A pi- pi pipi pi pi . pi Bayes pi pi X ( E E). -pi
RR =P(A|E)P(A|E) =
P(A, E)/P(E)
P(A, E)/P(E)
=P(E|A)P(A)/P(E)P(E|A)P(A)/P(E) =
P(E|A)P(E|A)
P(E)
P(E).
pipi , pi pi-. , , pi . pi pi
RR(A) =P(E|A)
1 P(E|A) P(E|A)P(A) + P(E|A)P(A)P(E|A)P(A) + P(E|A)P(A)
=P(E|A)
1 P(E|A) [1 P(E|A)]P(A) + [1 P(E|A)][1 P(A)]
P(E|A)P(A) + P(E|A)[1 P(A)] .
pipi pipi pi pi - pi - piP(E|A) P(E|A). pipi pipi pipi P(A) pi- pi pi - pi pipi pi pi.
3.5
3.5.1 pi ( -
).
3.1 2 2 3.1 pi pi Mann et. al (1975, Brit. J. Med.). 58 45
pi pi pi pi.
pi pi pi 19681972.
pi pi pipi pi pi pi
pi. pi . 1113 pi
Agresti (1990).
-
3: , 39
X: Y: pi ...pi 1: 2: X
1: 23 34 572: 35 132 167
.. Y 58 166 224
3.1: 3.1: pi pipi (Mann et. al , 1975).
3.5.1.1 SPSS.
pipi pi SPSS pi - 3 . X, Y . pi pi . pi 4 (2 2). pipi pi SPSS .
contrac myocard counts1 1 231 2 342 1 352 2 132
pipi counts Data>Weight Cases .
pi pi pi Analyze>Descriptive Stats>Crosstabs
pi row(s) column(s) contrac myocard . pi pi Splus Stat-exact pi pipi pi
pi 3.1.
3.5.1.2 pi .
pi pipi pi pi pi
-
40 . : pi
X: Y: pi ...pi 1: 2: X
1: p11 = 23224 = 0.103 p12 =34224
= 0.152 p1. = 23+34224 = 0.2552: p21 = 35224 = 0.156 p22 =
132224
= 0.589 p1. = 35+132224 = 0.745.. Y p.1 = 24+35224 = 0.259 p.2 = 34+132224 = 0.741
pi SPSS pi pi pipi pi pi cells Crosstabs pi Percentages:Total.
pi , pi pi, pipi pi pi . pi pi pi pi . pipi - P(Y |X = 1) P(Y |X = 2) ( pi pi pi pi ). pi - SPSS pi pi Cells Crosstabs pi pi (Percentages:Row). pi pi:
X: Y: pi.pi 1: 2:
1: p1|i=1 = 2357 = 0.404 p2|i=1 =3457= 0.596
2: p1|i=2 = 35167 = 0.210 p2|i=2 =132167
= 0.790
.. Y p.1 = 24+35224 = 0.259 p.2 = 34+132224 = 0.741, pipi pi pi ( pi)
0.404 0.210 (40.4% 21%). pi ( pi) ( 0.596 0.79).
pipi pi pi ( -pi) (pi) pi pi - . , pipi . pi pi , pi pi pi, P(X |Y ) X . pipi - ( pipi). pipi pi X ( pi -pi) SPSS pi Cells Crosstabs pi pi
-
3: , 41
(Percentages:Column). pi pi pi:
X: Y: pi ...pi 1: 2: X
1: p1|j=1 = 2358 = 0.397 p1|j=2 =34166
= 0.205 p1. = 23+34224 = 0.2552: p2|j=1 = 3558 = 0.603 p2|j=2 =
132166
= 0.795 p1. = 35+132224 = 0.745
pipi pipi pi. pi pi pi pi pi pi(39.7%) pi (20.5%). Bayespi pi P(Y |X) pi pi pi ( pipi).
3.5.1.3 .
pi pi . pi (pi pi SPSS)
pi pipi pi
1. OR = 2.551 :
() pi pi (Y = 1) pi pi pi pi (X = 1) 2.55
-
42 . : pi
pi pi pi pi pi(X = 2).
() . pipi pi : pi pi (Y = 2) pi pi pi pi (X = 2) 2.55 pi pi pi pi pi (X = 1).
() pi pi pi pi pi pi () pi ( ) pi.
() pipi pi: -pi pi pi pi pi.
2. RR(myocard = 1) = 23/5735/167 =
0.4040.210 = 1.936: pi pi-
pi pi pi pi 93% pi pi pi pi .
3. RR(myocard = 2) = 34/57132/167 =
0.5960.790 = 0.759: pi
pi pi pi pipi 24% pi pi pi .
4. : pi pipi - pi pipi . - Y pi pi - pi pi pi Bayes pi pi pi pi . pi pi pi pi pi .
3.5.2 pi pi pi pi-
pi (pi )
pi Daly et. al (1991, . 185) pi pipi .
-
3: , 43
3.2 pipi pi 368 pi
60 pi pi pi pi. pi 2
pi pi pi
. pi (X )
pi pi pi (Y ). 2 2 pi
X: Y: pi 2 .. pi ; 1: 2: X
1: 19 (12.3%) 135 (87.7%) 1542: 15 ( 7.0%) 199 (93.0%) 214
.. Y 34 ( 9.2%) 334 (90.8%) 368
3.2: 3.2: pi pi pi (Daly et. al , 1983).
pi pi 5.3%. pi pi pi pi pi pi, pi pi, 5.3 pi . pi pi. pi pi pi pi pi pi.
RR = 0.123/0.07 = 1.757. pi pi 1.76 (76% pi) pi pi.
pi pi 0.053/0.123 = 43.1%. 43% pi pi pi pi pi pi. pi, 43% (2 pi pi) pi pi pi pi pi pi pi ( pipi8 , 19 0.431 = 8.1).
OR = (19 199)/(15 135) = 1.867. pi pi pi 86% pi pi pi pi. pi , pi
-
44 . : pi
pi pi 10% , pi .
3.5.3 3: pi.
3.3 , pi pi -
pi . pi
pi
pi pi. , , pi
pi .
- pi pipi pi
. 1970 pi (MacKahon et. al
, 1970) , , , , , pi.
pi pi pi pi pipi .
pi pi
.
pi 30
(E : X 30 E : X 29). pi pi pi Rosner (1994 . 346). 2 2 pi
pi ..(1) 30 (2) 29 X
1: 683 2537 32202: 1498 8747 10245.. Y 2181 11284 13465
3.3: 3.3: pi (MacKahon et. al , 1970).
pi . ;
-
3: , 45
3.6 pi pi 22 -
3.6.1
3.6.1.1 pi
: pi E E pi Y pi : (A A). pipi pi pi . pi
H0 : P(A|E) = P(A|E) H1 : P(A|E) 6= P(A|E)
H0 : P(A|E) P(A|E) = 0
H1 : P(A|E) P(A|E) 6= 0
H0 : piE = piE H1 : piE 6= piE
H0 : piE piE = 0
H1 : piE piE 6= 0
H0 : AR = 0
H1 : AR 6= 0.
pi pi pi pi pi
Y |E Bin(piE, nE) Y |E Bin(piE, nE).pi pipi pi pi pi pi pi .
pipi pi pi z test. nEpiE, nE(1piE), nEpiE nE(1piE) pi pi pi
pE N(piE,
piE(1 piE)nE
) pE N
(piE,
piE(1 piE)nE
)pi pE pE pi . pi
AR = pE pE N(piE piE,
piE(1 piE)nE
+piE(1 piE)
nE
).
pi pi pipi :
z =AR AR
piE(1piE)nE
+piE(1piE)
nE
N(0, 1).
-
46 . : pi
H0 AR = piE piE = 0 piE = piE = pi pi
z =AR
pi(1 pi)(
1nE+ 1nE
) N(0, 1).
pi p = (nEpE + nEpE)/(nE + nE) pi
z =AR
p(1 p)(
1nE+ 1nE
) = pE pEp(1 p)
(1nE+ 1nE
) N(0, 1).
pi pi pipi , pi pipi pi. , pi-pi pi pi , pi
H0 : P(E|A) = P(E|A) H1 : P(E|A) 6= P(E|A).
pi pipi pi pipi pi 100(1 )% pi pi pi pi pi
AR z1/2pE(1 pE)
nE+pE(1 pE)
nE.
Rosner (1994, . 363) pipi pi pi nEpE(1 pE) 5 nEpE(1 pE) 5.
pi pi 22: pi 22 pi (E, E) (A, A) pi pi pi
AR = piE piE = pi1|1 pi1|2
AR = pE pE = p1|1 p1|2 =n11n1.
n21n2. =
n11n11 + n12
n21n21 + n22
=n11n21 + n11n22 n21n11 n21n12
(n11 + n12)(n21 + n22)=
n11n22 n21n12(n11 + n12)(n21 + n22)
=n11n22 n21n12
n1.n2. pi
p =n.1n
=n11 + n21
n11 + n12 + n21 + n22.
-
3: , 47
AR
H0 : piE = piE H1 : piE 6= piE H0 : AR = 0 H1 : AR 6= 0
zAR =pE pE
p(1 p)(
1nE+ 1nE
)p =
nEpE + nEpEnE + nE
pipi H0 |zAR| < Z/2.
pi pipi pi pipi pi 100(1 )% pi pi pi pi pi
AR z1/2pE(1 pE)
nE+pE(1 pE)
nE.
3.4: pi pi pi pi- .
-
48 . : pi
pipi pi pi , H0 ,
se(AR) =
p(1 p)
(1
n1. +1
n2.)=
n.1n.2n2
(1
n1. +1
n2.)
=
n.1n.2n2
(n1. + n2.n1.n2.
)=
n.1 n.2n n1. n2. .
pi pi pi
Z =n11
n11+n12 n21n21+n22
n.1 n.2n n1. n2. =
n11n22n21n12n1.n2.n.1 n.2n n1. n2.
=(n11n22 n21n12)
n
n.1n.2n1.n2. . pipi pi pi (pi - pi) X = (E, E) Y = (A, A).
-
3: , 49
3.6.1.2 .
: pi pi- RR = piE/piE. RR = pE/pE pi pi pi pi pi. pi - ( ).
log RR = log pE log pE
nEpE Bin(piE, nE)nEpE Bin(piE, nE),
pi Bin(p, n) pi pi p pi- n. pi pipi pi pi pE pE pi pi pi
E(pE) = piE Var(pE) =piE(1 piE)
nE
E(pE) = piE Var(pE) =piE(1 piE)
nE.
(pi nEpE 5 nE(1 pE) 5) pi pE pi pi pi pi pi pipi . pipi nEpE 5 nE(1 pE) 5.
pE N(piE,
piE(1 piE)nE
) pE N
(piE,
piE(1 piE)nE
).
pi Taylor pi h(x) pi
h(x) =k=0
h(k)(a)(x a)k
k!= h(a) + h (a)(x a) + h (a)(x a)
2
2+ h (a)
(x a)36
+ . . .
pi h(k)(x) pi k h(x). pi X a = E(X) = pi pi pipi
-
50 . : pi
pi pi X .pi pi pi pi pi
E(h(X)) =k=0
h(k)()E(X )k
k!
h() + h ()E(X ) + h ()E(X )2
2
h() + h ()V (X)2
. (3.4)
pi pi pi .
V (h(X)) = V
( k=0
h(k)()(X )k
k!
) V (h() + h ()(X )) {h ()}2V (X). (3.5)
pipi , X = pE, h(X) = log(pE),E(X) = piE V (X) = piE(1 piE)/nE pi (3.4)
E(log pE) log piE 1pi2E
piE(1 piE)2nE
= log piE 12nE
(1 piE)piE
pi nE log piE. pi log pE pi pi log piE. pi pi (3.5) pipi
V (log pE) 1pi2E
piE(1 piE)nE
=1
nE
(1 piE)piE
.
pi pi Taylor pi
log pE = log piE + (pE piE)(log piE) + O
pi
O =k=2
(log piE)(k) (pE piE)k
k!=
k=2
(1)k1k!pikE(pE piE)k
k!=
k=2
(1)k1(pE piEpiE
)k.
pi pi n(log pE log piE) = nE pE piE
piE+nEO
n pipi nE(log pE log piE) nE pE piE
piE
pi. N(0,1 piEpiE
)
-
3: , 51
pi
log pEpi. N
(log piE,
1
nE
(1 piE)piE
).
pi pi log pE pi
log pEpi. N
(log piE,
1
nE
(1 piE)piE
).
pi pipi pipi (-pi ) pi pi pi
log RR = log pe log pE pi. N(logRR,
1
nE
(1 piE)piE
+1
nE
(1 piE)piE
).
pi pi pi pE pE pi pi
V (log RR) =1
nE
(1 pE)pE
+1
nE
(1 pE)pE
=1
nE
nE rErE
+1
nE
(nE rE)rE
=1
rE 1nE
+1
rE 1nE.
pi rE rE pi . 100(1 )% pi pi log RR z1/2
V (log RR)
log RR z1/21
rE 1nE
+1
rE 1nE
pi zq 100q pi pipi . pi pipi pi
elog RRz1/2
1rE 1nE +
1rE 1n
E
pi e 2.71 . Rosner (1994, . 364) pipi pi pi nEpE(1 pE) 5 nEpE(1 pE) 5.
pi pi - pi :
H0 : RR = 1 H1 : RR 6= 1.
-
52 . : pi
pi
Z =log RR
1rE 1nE + 1rE
1nE
N(0, 1).
|Z | < Z1/2 pipi pi pipi - 100% pipi H0.
pipi pi pi pi pi-. pipi pi pi - : H1 : RR > 1 (pi pi) H1 : RR < 1 (pipi). (one sided tests) pi pipi- H0 pipi pi Z < Z pi pi(H1 : RR < 1) pipi pi Z > Z1 pi pi (H1 : RR > 1).
2 2 : 2 2 pi pi log RR
se(log RR) =1
n11 1n1.
+1
n21 1n2..
3.6.1.3 .
: pi ( Odds Ratio OR) pi pi
OR =OddsEOddsE
=piE/(1 piE)piE/(1 piE)
=piE(1 piE)piE(1 piE)
pi OR =
pE/(1 pE)pE/(1 pE)
=pE(1 pE)pE(1 pE)
.
pi pi pipi
log OR = logpE
1 pE logpE
1 pE.
E(pE) = piE V (pE) = piE(1 piE)/nE.
pi pi pi (3.4)
E
(log
pE1 pE
) log piE
1 piE +(pi2E + (1 piE)2
) piE(1 piE)ne
logOddsE + 1nE
(OddsE 1
OddsE
)
-
3: , 53
RR
100(1)% pi pi log RR z1/2
V (log RR)
log RR z1/21
rE 1nE
+1
rE 1nE
pi zq 100q pi pipi . pi pipipi
elog RRz1/2
1rE 1nE +
1rE 1n
E
pi e 2.71 . pipi pi pi nEpE(1 pE) 5 nEpE(1 pE) 5.
RR
pi pi pi :
H0 : logRR = 0 H1 : logRR 6= 0.
pi
Z =log RR
1rE 1nE + 1rE
1nE
N(0, 1).
|Z | < Z1/2 pipi pi pipi 100% pipi H0.
3.5: pi pi pi .
-
54 . : pi
h(x) = log x log(1 x), h (x) = x1 + (1 x)1 = 1/[x(1 x)] h (x) =x2 + (1 x)2. pipi nE E
(log pE
1pE) logOddsE .
V
(log
pE1 pE
) {h ()}2 V (pE)
(
1
piE(1 piE))2piE(1 piE)
nE
1nE
1
piE(1 piE)
(nErEnE
nE rEnE
)1=
(rE(nE rE)
nE
)1
(
nErE(nE rE)
)=
(nE rE + rErE(nE rE)
)
1nE
+1
nE rE .
E
(log
pE1 pE
) logOddsE nE ,
V
(log
pE1 pE
)=
1
rE+
1
nE rE.
pi
E(log OR) = logpiE
1 piE logpiE
1 piE= logOddsE logOddsE = logOR
V (log OR) =1
rE+
1
nE rE +1
rE+
1
nE rE.
(nE, nE) (pi pi pi )
log ORpi. N
(logOR,
1
rE+
1
nE rE +1
rE+
1
nE rE
).
pipi pi pi pi pi
log OR = logpiEpiE log 1 piE
1 piE= log RR log RR.
pi pi log RR log RR =log 1piE
1piEpipi pi pi
A ( RR A).
-
3: , 55
OR
100(1 )% pi pi log OR z1/2
V (log OR)
log OR z1/21
rE+
1
nE rE +1
rE+
1
nE rEpi zq 100q pi pipi . pi pipi pi
elog ORz1/2
1rE+ 1nErE +
1rE+ 1n
ErE
pi e 2.71 . pipi pi pi nEpE(1 pE) 5 nEpE(1 pE) 5.
OR
pi pi- pi :
H0 : logOR = 0 H1 : logOR 6= 0.
pi
Z =log OR
1rE+ 1nErE +
1rE+ 1nErE
N(0, 1).
|Z | < Z1/2 pipi pi pipi 100% pipi H0.
3.6: pi pi pi pi.
-
56 . : pi
2 2 : 2 2 pi pipi pi pipi
log ORpi. N
(logOR,
1
n11+
1
n12+
1
n21+
1
n22
).
pipi pi pi. pi pi pi pi pipi. pipi pi pi pi = 0.5 pi
ORcor =(n11 + )(n22 + )
(n21 + )(n12 + )
Var(log ORcor) =1
n11 + +
1
n12 + +
1
n21 + +
1
n22 + .
nij pipi .
3.6.1.4 3.2 ()
pi pi 3.2 pi 3.2 pi pi :
) pi : AR = pE pE = 0.123 0.070 = 0.053 . pi , pi pi
H0 : AR = 0 H1 : AR 6= 0. pi
V (AR|H0) = p(1 p)(1
nE+
1
nE
)
=34
368
334
368
(1
154+
1
214
)= 0.092 0.9080.1117 = 0.000936
se(AR|H0) =0.000936 = 0.0306 .
z = 0.0503/0.0306 = 1.7413 < z0.975 = 1.96 pipi H0 pi pi pi(pi = 0.10). : pipinEpE(1 pE) = 154 0.123(1 0.123) = 16.6 > 5 nEpE(1 pE) = 214 0.07(1 0.07) =23.96 > 5.
-
3: , 57
95% pi pi pi pi
se(AR) =
pE(1 pE)nE
+pE(1 pE)
nE
=
0.123(1 0.123)
154+0.07(1 0.07)
214=0.000700461 + 0.0003042056 = 0.0317
pi 95% pi pi 0.053 1.96 0.0317 = (0.009, 0.115) .
) :
RR =pEpE
= 0.123/0.070 = 1.76
log RR = log 1.76 = 0.5654
se(log RR) =
1
19 1154
+1
15 1214
=0.108132 = 0.3288 .
95% pi pi 0.56541.960.3288 =(0.0791, 1.2099) (e0.0791, e1.2099) = (0.924, 3.353).pi pi H0 : RR = 1 H1 : RR 6= 1 ZRR = 0.5654/0.3288 = 1.72 < z0.975 pipi H0 = 5% pi pi pi pi pi pi.
) pi:
OR =19 19915 135 = 1.867
log OR = log 1.867 = 0.6244
se(log OR) =
1
19+
1
135+
1
15+
1
199=0.1317 = 0.363 .
95% pi pi 0.6244 1.96 0.363 =(0.0867, 1.3358) (e0.0867, e1.3358) = (0.9167, 3.8030).pi pi H0 : OR = 1 H1 : OR 6= 1 ZOR = 0.6244/0.363 = 1.72 < z0.975 pipi H0 = 5% pi pi pi pi pi pi pi.
-
58 . : pi
3.6.2 2 Pearson.
pi pi . pi pi pi pipi pi Pearson.
pi pi X Y I J pipi.pi pi H0 : X Y - H1 : X Y . , pi 3.2.1.3 pi
piij = pii.pi.j. i, j pi pi
E(Nij|H0) = ij = npii.pi.j pi pi pi
eij = nni.n
n.jn
=ni.n.jn
.
pi pi Poisson
Nij Poisson(ij)
Nij ijij
. N(0, 1).
pi (Nij ij
ij
)2 . 21 2 (I 1)(J 1)
Ii=1
Jj=1
(Nij ij)2ij
. 2(I1)(J1).
pi pi- nij pi eij (i, j).pi pi
2obs =Ii=1
Jj=1
(Nij ij)2ij
. (3.6)
-
3: , 59
pipi pi 2obs > 2(I1)(J1),1. pipi pi- pi eij 5.
2 2 pi , pi pipi pi (. Armitage Berry, 1994, . 135)
2obs =n(n11n22 n12n21)2n1.n2.n.1n.2 = z2. (3.7)
Pearson 2 2 pi pi pi pi 3.6.1.1.
pi 2 2 pi pi 2 Yates pi pi pi:
2Yates =2i=1
2j=1
(|nij eij| 1/2)2eij
21 . (3.8)
3.2 ( ): pi
2obs =368(19 199 15 135)234 334 154 214 = 3.03(= 1.74
2) < 20.95 = 3.841
pipi pi . pi pi pi (3.6) pi
e11 = 34 154/368 = 14.23e12 = 139.77
e21 = 19.77
e22 = 194.2
2obs =(19 14.23)2
14.23+(135 139.77)2
139.77+(15 19.77)2
19.77+(199 194.23)2
194.23= 3.03 p value = 0.082 .
pi 2 Yates
2Yates =(|19 14.23| 1/2)2
14.23+(|135 139.77| 1/2)2
139.77+(|15 19.77| 1/2)2
19.77+(|199 194.23| 1/2)2
194.23= 2.43 p value = 0.119 .
pi pipi pi pipi 5%.
3.6.3 .
1935 Wilks piG2 = 2 log L0
L1 2d1d0
-
60 . : pi
pi Lk pi dk pi pipi pi Hk, k = 0, 1. I J pi pi
H0: X,Y H1: X,Y . H1 , pipi pi pi piij pi d1 =IJ 1 ( pi Ii=1Jj=1 piij = 1 pi pi pipi). H0 , pipi pi pii. pi.j pipi d0 =(I 1) + (J 1) = I + J 2 pi. pi d1 d0 = IJ 1 I J + 2 =IJ I J + 1 = I(J 1) (J 1) = (I 1)(J 1).
pipi, pi pi
L0 =Ii=1
Jj=1
(pii.pi.j)Nij log L0 = Ii=1
Jj=1
Nij log pii. + Ii=1
Jj=1
Nij log pi.jL1 =
Ii=1
Jj=1
piNijij log L1 =Ii=1
Jj=1
Nij log piij.
G2 = 2(log L0 log L1) = 2Ii=1
Jj=1
Nij logpii.pi.jpiij
= 2Ii=1
Jj=1
Nij logij/n
piij= 2
Ii=1
Jj=1
Nij logijnpiij
G2obs = 2Ii=1
Jj=1
nij logeijnij
.
pi Pearson pipi pi G2obs >2(I1)(J1),1. pi pi G2 2(I1)(J1) n/(IJ) 5 pi pipi Pearson.
pi pipi pi G2 pi pi- (nij) (eij) . pi pi Poisson . pi - 2 Pearson pi pi.
3.2 ( ): pi
G2obs = 2(19 log 14.2319 + 135 log 139.77135 + 15 log 19.7715 + 199 log 194.23199)= 2.982695 p value = 0.0842 .
pi pipi pi pipi 5%.
-
3: , 61
3.6.4 Fisher.
pipi pi pi pipi pipi pi pipi pipipi. (exact) pi pi pi pipi pipi . pi pi pi (pi pi- 2). pi p value pi pi pipi pi .
Fisher (Fishers exact test) pi pi pi pi- N11 pi . pi pi pi pi pi pi pi pi . pi pi pi p value pi pi pi pi pi pi.
3.4 pi pi
Y ..
X A A X
E 3 1 4
E 1 3 4
.. Y 4 4 8
pi H0 : OR = 1 H1 : OR > 1.
pi pi pipi pi pipi
pi Fisher. pi
pi n11 0, 1, 2, 3, 4. pi pi
-
62 . : pi
Y ..
X A A X
E 3 1 4 n11 = 3
E 1 3 4
.. Y 4 4 8 OR = 9
Y ..
X A A X
E 3+1=4 1-1=0 4 n11 = 4
E 1-1=0 3+1=4 4
.. Y 4 4 8 OR = ORcor = 81Y ..
X A A X
E 3-1=2 1+1=2 4 n11 = 2
E 1+1=2 3-1=2 4
.. Y 4 4 8 OR = 1
Y ..
X A A X
E 3-2=1 1+2=3 4 n11 = 1
E 1+2=3 3-2=1 4
.. Y 4 4 8 OR = 1/9 = 0.111
Y ..
X A A X
E 3-3=0 1+3=4 4 n11 = 0
E 1+3=4 3-3=0 4
.. Y 4 4 8 OR = 0 ORcor = 1/81 = 0.012
pi p value pi pi OR 9 pi pi . pi
p value = P(A) + P(B) =
43
41
8
4
+ 4
4
40
8
4
= P(A) + P(B) =
4 45 6 7 8/(2 3 4) +
1
5 6 7 8/(2 3 4)=
16
5 2 7 +1
5 2 7 =17
70= 0.24286 .
pi pipi H0.
p value = P( OR 9) + P( OR 1/9)
-
3: , 63
= P(A) + P(B) + P() + P(E) = 1 P() = 1
42
42
8
4
= 1 36
70= 1 0.514 = 0.486
pipi H0 .
2 2 pi pi pi pi pi
P(n11, n12, n21, n22|n.1, n.2, n1., n2.) = n.1!n.2!n1.!n2.!n!n11!n12!n21!n22!
,
pi pipipi Rosner (1994, . 371). Fisher pi pi pipi pi
:
1. pi pi pi pi - pi pi.
2. pi pi.
3. pi pi pi (pi pi-) pi pi pi .
4. pi p-value
() H1 : piE 6= piE H1 : OR 6= 1 p-value= 2min{P(N11 n11), P(N11 n11)}.() H1 : piE > piE H1 : OR > 1 p-value= P(N11 n11).() H1 : piE < piE H1 : OR < 1 p-value= P(N11 n11).
pi eij < 5 pi pi pi pi .
3.6.5 .
pipi, pi , pi- pi . pipi pi, pi
-
64 . : pi
pi, pi pi ( - ) pi p value. pi pi pi (pi.. 10000 pi) pi p value. pi pi pi ( 99%) p value. pi H0 pipi pi pi pi pi pi . pi p value pi pi H0 H0 pipi pi p value.
3.7
(diagnostic tests) pipi (screening tests) pi pi pi pi- . check up, , pi . pi pi pi pi pi pi pi (pi pi) pi pi. pi pi pi pi pi pi pipi (pi ) pi ( pi).
pipi pi Bayes pi pi pi
P(Bk|A) = P(A|Bk)P(Bk)j P(A|Bj)P(Bj)
j P(Bj) = 1 Ai Aj = i 6= j.3.7.1 .
pi A A pi pi T+ T pi pi .
3.1 pi (positive predictive value)
pi pi
-
3: , 65
PV+ = P(A | T+).
3.2 pi (negative predictive value)
pi pi
PV = P(A | T).
3.5 pi 10000
100 .
pi PV+ = 1/100 = 0.01 pi
PV = 1 1/10000 = 0.9999.
pipi pi . pi pipi pi pi (pi pi pipi). pipi pi pi pi pipi. pipi pi, pi (pi pipi). PV+ pi pipi pipi ( PV+).
, pi pi pi .
3.3 (sensitivity) ( pi) pi-
( pi) pi
pi
sensitivity = = P(T+ | A).
3.4 (specificity) ( pi) pi-
( pi) pi
pi
specificity = = P(T | A).
3.5 pipi (false negative case) pi
.
-
66 . : pi
3.6 pipi (false positive case) pi
.
pi pi.
pi pi- pi . pipi .
pi pi -. pi pi , - pi pi pipi pi pi pip1|1 p2|2. pi pi :
PV+ = P(A | T+) = P(A)P(T+|A)
P(A)P(T+|A) + P(A)P(T+|A)=
P(A) sensitivity
P(A) sensitivity + {1 P(A)}{1 P(T|A)}=
A sensitivity
A sensitivity + (1 A)(1 specificity) . (3.9)
pi A = P(A) pipi . pi pi
PV =(1 A) specificity
(1 A) specificity +A(1 sensitivity) . (3.10)
pi pi pi pi -pi pipi - pipi pi .
3.6 pi 100 pi 100
pi. pi pi 84 pi
pi 23 . pi
pi 1:4.
pi pipi
A = 0.2
sensitivity = P(T+|A) = 84/100 = 0.84specificity = P(T|A) = 1 P(T+|A) = 1 23/100 = 0.77 .
-
3: , 67
pi pipi pi (3.9) (3.10) pipi
PV+ =0.2 0.84
0.2 0.84 + 0.8 0.23 = 0.48,
PV =0.8 0.77
0.8 0.77 + 0.2 0.16 = 0.95 .pi pi pi pi
pi .
3.7.2 2 2 pi pipi
.. A A XT+ n11 n12 n1.T n21 n22 n2.
.. Y n.1 n.2 n) : , pi pi pi. pi
PV+
= P(A|T+) = n11/n1. = n11/(n11 + n12)PV
= P(A|T) = n22/n2. = n22/(n21 + n22)
A = P(A) = n.1/n = (n11 + n21)/n . pipi pi pi pi-
pi :
Sensitivity = P(T+|A) = n11/n.1 = n11/(n11 + n21)Specificity = P(T|A) = n22/n.2 = n22/(n12 + n22) .
) -: - pi pi pi pipi . pipi pipi pipi pi pi pi pi (3.9) (3.10) pi . :
PV+
=A n11/(n11 + n21)
A n11/(n11 + n21) + (1 A)n12/(n12 + n22)
PV
=(1 A) n22/(n12 + n22)
(1 A) n22/(n12 + n22) + An21/(n11 + n21).
-
68 . : pi
3.7.3 pi ROC
pipi pi pi pi ( ). pi - . pipi (cut-off point) pi pi pi ( pi pi pi pi pi ). , T , t pi T t pi( ) T > t pi ( ).
pi pi ROC(Receiver OperatingCharacteristic curves) pi pi pi - pipi (1 specificity) ( X Y ) pi pi . pi pi ( pipi ).
pi pi ROC pi pi pi - pi .
pi pi ROC AUC(area under curve) pi pi pi pi pi pi pi ROC X . AUC pi (TA) pi pi (TA)
AUC = P(TA > TA)
pi
w =1
nAnA
nAi=1
nAj=1
S(TAi , TAj )
pi nA nA , TAi i , TAj j S(TAi , TAj ) pi (1) TAi > TAj , 1/2 TAi = TAj (0) TAi < TAj .
( pi pi ) pi piw = 1 w pi (
-
3: , 69
pi pipi ). pi H0 : AUC = 0.5
H1 : AUC > 0.5. AUC = 0.5 pi (pi pi pi ) pi .
pi pi ( 05_ROC EXAMPLE 1.pdf pi eclass ).
3.7 WAIS
3.8 hivassay
3.7.4 pi pipi pi .
pi pi pi pipi-.
P(T+) = P(T+, A) + P(T+, A)
= P(T+|A)P(A) + P(T+|A)P(A)= A sensitivity + (1 A)(1 specificity)
A =P(T+) (1 specificity)sensitivity + specificity 1 .
, pipi pi ( pi ) pi pi .
3.9 pi -
..
A A X
T+ 90 180 270
T 10 720 730
.. Y 100 900 1000
pi pipi pi
Sensitivity = 90/100 = 0.9
Specificity = 720/900 = 0.8
P(T+) = 270/1000 = 0.27
A =0.27 (1 0.8)0.9 + 0.8 1 = 0.07/0.7 = 0.1 .
-
70 . : pi
pi 10% pi pi pipi .
-
4
(Clinical Trials)
4.1
pi , (clinical trials) pi pi pi pi pi (. Armitage & Berry, 1994, . 189).
, pi pi pi pi -pi pi pi (. Perreira-Maxwell, 1998, AZ of Medical Statistics, . 11).
pipi pi pi pi pipi pi, pi pi (drugs) pi (treatments).
pi (treatment) (intervention technique). pi pi pi , pi . pi pi .
-pi (control/placebo groups). pi (placebo), pi pi. ,
71
-
72 . : pi
pi, pi pi , . /pi - . , pi pi pi pipi pi pi pi. pipi pi - pi, pi pi, pi pi, (reference treatment group), pi pi pi pipi .
pi -/ (Single or double blind). / pi, pi pi (single blinded). pipi pi / - pipi pi pi pi (double blinded).
pi pipi - pi/ pi .
pi(Randomization/Random allocation). pi pi . pipi pi (Randomized Controlled Trial), pi pi III I IV.
4.2 .
pi 18 pi Lind pi pi , Lind 6 pi 12 pi Salisbury. pi 12 pi pi 6 . 1926 Fisher pi, Amberson 1931 (1931, Am. Rev. Tumberc.), pi pi , pi 24 , pi pi / pi,pi pi . 1938 placebo(Dielh et al. 1938 JAMA), 1948, pi
-
4: 73
.
4.3
4.3.1 I
pi pi pi pi pi . pi pi . pi pi pipi pi ( pi ). pi pi pi pi pi pi pi pi pi (toxicity level). pi - (maximumtolarated dose - MTD) , pi () .
(pi ):
1. ( 3) .
2. pi .
3. pi 3 .
4. pi pi pi pi pipi .
5. pi 2 pi pi - pi pipi .
pi pi 1/3 pi
pipi pi pi pi pipi .
-
74 . : pi
pi
pi :
1. pi pi.
2. pi pipi.
3. pi .
4. pi 12 pi- pi .
5. pi .
6. pi pi .
7. pi .
pipi pi , pi pi pi . pi pi pi pi.
pipi pi pi .
, pi 1/3 (toxic low dose, TLD) pi pi .
pi pi , pipi pi pi , pi 3-4.
2-12 : 2 3.3 5 7 9 12 16
pi pi pi pi pi pi .
pi pipi pi 3 pi .
-
4: 75
4.3.2 II
, pi pi pi pi. , pi /pi. pi pi pipi . , pi , , pi pi pi. , pi .
: 2 (2-stage trials). 2 pi pipi pi
pi pi, 20% pi, < 20% . , pi 14. 2 , 10-20 pipi 1 2 pi pi. pipi .
pi pi pi- . pi pi pi pi % pi pi . pi pi pi pipi pi . pi- pi , pi pi pi . pipi pi pi pipi pi .
pi :
H0 : > 0 ( pi )
H1 : 0 (pi ).
pi H0, pi . , pi pi , , pi . pi pi ( pi
-
76 . : pi
), pi pi ( pipi pi ).
4.3.3 .
pi pi /pi. pi- pi . . pi .
4.3.4 IV.
pi pi pi pi . IV pi (screening) -. pi pi pi pi pi pi pi , pi pi . pi pi .
4.4 pi
pi . pi pi -pi pi pi. pi pi , 20 100 .
pi pi (primary prevention studies)pi , pi pi pi pi .
pi pi (secondaryprevention studies). pi ( pi ), pi pi pi pi 2 pi . pi pi pi pi.
pipi , pi
-
4: 77
. pi pi 10000 pi 1000 .
4.5 pi
pi (Randomization - random allocation), - . pi pi(selection bias), pi- . pipi pi pi pipi . pi pi .
pi :
1. ,
( pipi) ( pipi)
2.
( pipi) ( pipi)( ) (pi )
4.6 pi
4.6.1
pi pi pi- . pi. pi pi pi(-pi ), pi , pi , ( pi ) .
pi . (1998), pipi :
pi pi (background).
(objectives).
(design).
-
78 . : pi
(organization).
.
pi , pi/pi (background) pi -pi- pi . , pi pipi , pi pi -pi.
(objectives) :
pi,
pi,
pi pi-,
pi (adverse effects)- pi (side effects).
(design) pi pi (studyor target population) pi pi pi (in-clusion criteria) pi pi pi (exclusion criteria). pi , pipi , - (enrolment of participants). pi (informed consent), pi (assessment of eligibility), (baseline examination) - (pi). pi - (Intervention) pi
) - (description and schedule)
) (measures of compliance)
pi, pi pi pi/ - (follow up description+schedule). pi (ascertainment of response variables),
) pi (training), pi pi : pi 3 ; pi 3 , ;.
-
4: 79
) (data collection)
) (quality monitoring/control).
** , pi pi -pi pi pi pi pi-, .
** , pi , pi pi -, pi. pipi pi . pi pi (data collectors).
** pi , pi , pi .
, pi
) (Interim analysis)
)
. (organization), pi (participating
investigators) pi
) / (statistical unit/data co-ordinating center)
) (labs and other special units)
)
pi pipi pi-pipi, pipi pi .
- pi.
-
80 . : pi
4.6.2
pi . - pipi pi. pi pi pi- pi pi - , pipi pi . inclusion exclusion pi- pi.
4.6.3 pi
pi pi , pi, placebo - / pi. pipi pi pi pi -/ pi pi pi (pi) , pi pi pi, pi , pi pi pi (pi- Placebo). pi Hawthorne pi pi pi, pi pi pi pi pi , . pi pi pi
pi
pi
pi pi pi
pi pi pi
pipi pi pi ( pi pipi pi-).
-
4: 81
4.6.4 pi
pi, - pi , pi:
pi pi pi
/pi pi pi
pi
pi pi pi pi pi pi pi.. pi . :
/ (single blinded): pipi
pi / - (double blinded): (/) pi pi
pipi pi , pi - pi pi pi pi pi .
4.6.5
pi pi pi , pi / (pi.. ID). pi. /pi pi pi pi (selection bias). pi :
pi pi
pi pi ( pi )
pi
-
82 . : pi
pi pi
pi pi pi pi/pi pi pi pi pi pi pi pi pi pi pi pi pi pi pi- pi pi .
pi pi pi pi pi pipi pi pi pi-, pi pipi pi pi pi (pi.. pi ) pipi pi pi pi (pi..pi ). pi pi pi pi pi /pi .
pi pi - pi pi pi - . :
pi,
pipi pi pi pi pi .
4.7 pi
4.7.1 -
- pi pi pi - pi. pi pi pi , pi, (publication bias).
pi pi ( pi pi pi pi pi). - .
pi pi . - pi
H0 : j = 0 ().
-
4: 83
pipi pipi L < 0 U > 0 pi / L < < U pi pi. pi - pi :
1 :
1. HA0 : > L HA1 : L2. HB0 : < U HB1 : U .3. pi HA0 HB0 -.
2 :
1. (1-2)% pipi pi (1, 2).
2. - L < (1, 2) < U pipipi - 1 pi.
4.8
4.8.1 pi pi
pi pi (unrestricted randomization), pi ( pi). pi pi-, pi pi pi pi .
pi pi (blocked/ restricted randomization), pi pi pipi /2. pi . pi . pi pi block ( ) pi .
, =2 2: , , =4 6: , , , , ,
t-test, ANOVA, 2 test
-
84 . : pi
4.8.2 pi pi
pi pi, pi. pi pi pi (pi pi pipi pi pi). pi - pi pi . pi pipi pi pipi pi
pi pi pi pi pi pi- pipi pi. pi pi pi pi pi .
pi pi pi pi pi .
pi pipi pi
pi
pi
: Multiway Analysis of Variance
-
5
pi pi
5.1
5.1 (Confounding factor) pi -
pi pi .
pi pipi pi pi pi
.
pi ( ) pi pi - pi (matching) pipi pipipi(standardization) pi pi pi . pi pi pi pi (controlling for a confounding factor) pi pi pi (confounder adjusted results).
5.2 - pi
( pipi pi pi) -
pi pi (stratification stratified analysis).
5.3 (Positive confounder) pi
( ) pi .
5.4 (Negative confounder) pi-
pi pi pi :
85
-
86 . : pi
1. pi .
2. pi .
5.5 pi (causal pathway)
pi pi pi .
5.1 pi
pi ( pi
). pi pipi 5.1.
X: Y: ... 1: 2: X1: 2 pi 33 1667 17002: < 2 pi 27 2273 2300.. Y 60 3940 4000
5.1: 5.1 (Rosner, 1994, . 399400).
pi pi pi pi
. 1.667 pipi
= 10% ( 2 p = 0.065).
pipi - pi pi pi pi pi pi pi . pi pi pi
: pi (1) : pi (2)X: Y: . . .. Y: . . ..
. 1: 2: X 1: 2: X1: 2 pi 24 776 800 9 891 9002: < 2 pi 6 194 200 21 2079 3000.. Y 30 970 1000 30 2970 3000
5.2: pi pi pi - 5.1 (Rosner, 1994, . 399400).
-
5: pi - 87
pi pi . pi pi 5.2. pi pi pi pi pi pi.
5.2 pi pi pi Sha-
piro et. al (1979) pi Lancet. -
pi pi pi pi pi pi :
. , pi pi / : 25-29, 30-34,
35-39, 40-44, 45-49. 5.3 pi .
pi . (cases) (controls) (OR) .(%)
25-29 4 62 7.2 23 2 2 224
30-34 9 33 8.9 9 5 12 390
35-39 4 26 1.5 8 9 33 330
40-44 6 9 3.7 3 16 65 362
45-49 6 5 3.9 3 25 93 301
29 135 1.7 8 12 205 1607
5.3: pi 5.2.
pi pi pi 5.3, pi pi =1.7 . , pi pi .
pi pipi pipi pi
pi pi pipi .
-
88 . : pi
pi pi .
5.1.1 pi pi pi -
pi pi pi pi pi.pi
1. pi (pi.. )
2. pi .
pi pi pi pi pi . pi pipi
1. pi pi
2. pipipi
3. pi Mantel-Haenszel
4. pi
5.2 / -
5.2.1 -
3.6 pi pi . pi - ( ). (matching) pi pi ( ).
-
5: pi - 89
5.3 pi pi pi
pi . pi pipi
pi pi . pi -
() ( 5 )
. pi
. pi 5
pi pi pi 5 (/).
pi pi pi :
X: pi 5 ..pi 1: 2: X
1: 526 95 6212: 515 106 621
.. Y 1041 201 1242
5.4: 5.3 (Rosner, 1994, . 377).
pi pipi pi ( pipi - 5%) pi pi (2 = 0.59 < x21,0.95 = 3.84, p-value=0.557 > 0.05). pipi pi . - pi pi pi . pi pipi pi 621. pi pi pi pi pi. pi : pi pi, pi, pi pi- pi pi . pi pipi pi :
pi pi pi /pi .pi
P(pi pi ) = P(pi pi ) pi1. = pi.1 n12 = n21.
pi pipi pi , 2 2 pi , 2 5.2.1 pi pi pi.
-
90 . : pi
X: .. pi 5 ..
pi 1: 2: X1: 510 16 5262: 5 90 95
.. Y 515 106 621
5.5: 5.3 (Rosner, 1994, .377).
5.6 (concordant pair)
pi pi pi ( pi)
.
5.7 (disconcordant pair)
pi pi pi ( pi)
.
pi pipi - .
pipi, pi H0
n21 Binomial(1
2, nD
).
pi E(n21) = nD/2 V (n21) = nD/4. pi pipi npq 5 nD 20pi pi pi pi
n21 nD/2nD/4
N(0, 1).
pipi McNemar pi pi -:
(n21 nD/2)2nD/4
21 . (5.1)pi nD nD = n12 + n21. pipi pi pi :
(|n21 nD/2| 1/2)2nD/4
21 . (5.2)
McNemar pi pi pi -:
-
5: pi - 91
1. 2 2 pi pi. pi ( pi) pi (pi pi ) pi (pi) (pi pi ).
2. pi pi 2obs pi pi 5.1 5.2.
3. pipi H0 : pi 2obs >
21,1. pi pi p value = P(X2 2obs)
pipi pi p value < .
: pipi pi nD 20. 5.3 (pi): nD = 21
20 pi pi pipi pi
2obs =(|n21 nD/2| 1/2)2
nD/4=
(|5 10.5| 1/2)210.5/4
=52
5.25= 4.76 > 21,0.95 = 3.84
pi pipi pi pi ( pi - pi). pi p value
p value = P(X2 2obs) = P(X2 4.76) = 1 P(X2 4.76) = 1 0.9708 = 0.029.
nD < 20 pipi pi pi . p value pi pi pi
p value =
1 n21 = nD/2
2n21k=0
nDk
2nD n21 < nD/22
nDk=n21
nDk
2nD n21 > nD/2.
-
92 . : pi
5.4 20 pi
pi pi :
C O C O C O C O1 - - 6 + - 11 + - 16 + -2 - - 7 - - 12 + - 17 + -3 + - 8 + + 13 - - 18 - -4 + + 9 + + 14 + - 19 - -5 - - 10 - - 15 - + 20 - -
5.6: 5.4 pi (+: , : , C: , O pi ).
pi pi . 20 40; 20 pi (pi pi ). pi pi pipi :
pi pi .. 1: 2: X1: 3 7 102: 1 9 10.. Y 4 9 20
5.7: 2 2 5.4.
pi pvalue pi nD = 1+7 = 8 < 20. n21 < nD/2 = 8/2 = 4, p value pi pi pi
p value = 2 8
0
28 + 8
1
28 = 9
(1
2
)7= 0.070 > 0.05
pipi H0 pipi 5%.
5.1 pipi SPSS.
SPSS: McNemar SPSS 12.0 pi :
-
5: pi - 93
1. Analyse>Descriptives>Crosstabs :
2. Statistics|McNemar : pi McNemar pi - pi
3. Exact|Exact : pi McNemar.
5.2.2 pi (Kappa).
pi ( ). pipi pi pi pi pipi -. pi (reliability studies) pipi pi pipi (reproducibility and reliability). pipi pi pi- . pipi pi pi pi pi (pi.. pi pi pi ) , .
pi pipi pi I I ( pipi pi) pi pio =
Ii=1 piii
pi pi pi pi po =Ii=1 nii/n. pi pi-
(pi pi pi) pi pie =
Ii=1 pii.pi.i pi pi
pi pe =Ii=1 ni.n.i/n2 . -
pi pi . - pio pie pi pi. pi pi pi pi pi. pi max(pio pie) = 1 pie pipi pio = 1 pi pipi pi Cohen (1960):
=
Ii=1 piii
Ii=1 pii.pi.i
1Ii=1 pii.pi.i =pio pie1 pie ,
-
94 . : pi
pi pi
=
Ii=1 nii/n
Ii=1 ni.n.i/n2
1Ii=1 ni.n.i/n2 =po pe1 pe .
(pi ). pi- pi pi pi ( ). pi pi pi . Agresti (1990, . 366-367) pi pi.
pipi pi pi
Var() =1
n(1 pe)2(pe + p
2e
Ii=1
pi.p.i(pi. + p.i)).
pi pi H0 : = 0 H1 : > 0 pi pi z =
Var() pi
pi N(0, 1) H0 . pi pipi.
5.5 pi pi, -
pi pi
pi .
(Food Frequency Questionaire) pi
. pi
pi pi
pi. pi pi 537
pi .
pi . pi
5.5 pi .
pi pipi :
po = (136 + 240)/537 = 376/537 = 0.70
pe = 205 228/5372 + 332 309/5372 = 0.382 0.618 + 0.425 0.575 = 0.518 =
0.70 0.5181 0.518 = 0.378
se() = 0.040.
-
5: pi - 95
X: .. 1: 1 2:< 1 ..
/ / X1: 1 / 136 92 2282: > 1 / 69 240 309
.. Y 205 332 537
5.8: 2 2 5.5.
pi z = 0.378/0.040 = 8.799 > 1.65 pipi pi pi - pi (H0 : = 0).
pipi pi pi pi pi pi pi pi . pi pipi ( pipi Pearson = 0). Landis Koch (1977) pi pi :
> 0.75 pi pipi ( ).
0.4 0.75 pi pipi ( -pi ).
0 < 0.4 pi pipi ( ).
Rosner (1994, . 426) pi pipi pi pi pi . pipi pi .
pipi McNemar pi. pi McNemar pi . 2 2 pi pi pipi pi pi pi, pi pi pi. pi pi pi pi pi - --pi
-
96 . : pi
. pi pipi pi ( ) pi pi pi pi ( Pearson t-test ). pi pi pi pi . McNemar - pi .
5.3 pipi
pipipi pi pi - pi pi pi pi pi pi . pipipi pi ( ) pi pi pi pi pi. pi i pipi pi Ipipi pipi pi pi pi
pst =Ii=1
ninpi =
Ii=1
wi pi
pi ni pipi pi pi i pipi pi, n pi-pi pi wi = ni /n pipi pi pi i pipi pi.
pipi pst pi pi pi pi pi pipipi ( pi ). pipi pi pi- pi pi pi- pi pi pi pi .
5.4 pi pi -
5.6 1985 pi 518 pipi
518 ( pi pi Sandler et. al , 1985,
-
5: pi - 97
Amer.J.Epidem.). pi pi pi
pi. pi pi
pi / pi pi 1 6
.
pi pi, pi pi
pi pi ( pi
pi pi ). 5.6 pi .
: pi (1) : pi (2)X: Y: .pi .. Y: .pi ..
1: 2: X 1: 2: X1: 120 111 231 161 117 2782: 80 155 235 130 124 254.. Y 200 266 466 291 241 532 (OR) 2.1 1.395% 1.72-2.47 0.95-1.64
5.9: pi pi pi pi 5.6 (Rosner, 1994, . 399400).
pipi pi, pi pi pi ( pi) - = 1.64 (95% =1.35-1.88). pi pi pi pi (pipi pi pi pi pi). pi pi-pi pi pi pi pi.
2 2 K pi, pi K pipi pi pi / pi (pipi pi ). pi pi X Y pipi pi Z
H0 : OR1 = OR2 = . . . = ORK = 1 .
pipi k pi
-
98 . : pi
Z=kX: Y ..
1: 2: X1 n11k n12k n1.k2 n21k n22k n2.k
.. Y n.1k n.2k n..kpi pi pi
n11k HyperGeometric(n1.k, n2.k, n.1k)pi HyperGeometric(m, n, N) pi pi
f (x) =
nx
mN x
n +m
N
,
E(X) = Np = N n(n+m) V (X) = Np(1 p)n+mNn+m1 = N nm(n+m)2 n+mNn+m1 .
pi pi H0
E(n11k) =n1.kn.1kn..k
V (n11k) =n1.kn2.kn.1kn.2kn2..k(n..k 1) .
H0, ( pi pi) 11
E =Kk=1
E(n11k) =Kk=1
n1.kn.1kn..k
pi pipi pi pi O = n11. =Kk=1 n11k . pi H0, E(O) = E V (O) =
Kk=1 V (n11k) = V .
Mantel-Haenszel :
2MH =(|O E| 1/2)2
V 21
5.6 (pi).
pipi pi
O = n111 + n112 = 120 + 161 = 281
-
5: pi - 99
E1 =231 200
466= 99.1, E2 =
278 291532
= 152.1 E = 99.1 + 152.1 = 251.2
V1 =231 235 200 266
4662 465 = 28.6
V2 =291 241 278 254
5322 531 = 32.95V = V1 + V2 = 28.6 + 32.95 = 61.55
pi 2MH =(|281251.2|1/2)2
61.55 = 13.94 > 3.84 = 21,0.95, p value = 0.0001887 -
pipi pi pi pi pi pi / pi ( pi pi pipi pi).
5.4.1 pi pi (Effect Modification).
pi , pi -pi pipi pi. pi pi- -pi pi pi pipi pi. pi pi pi . pi pi pi (effect modifier).
5.8 -pi -
pipi pi pi pi pi
pi pi pi pi
pi pipi pi (effect modification).
pi pi pi (effect modifier) pi-
.
pi 5.6 pi pi pi pi pi pi (1.3 pi 2.1 pi). pi pipi 10% pipi 5%.
pi pi H0 : OR1 = OR2 = . . . = ORK - H1 : ORi 6= ORj pi pipi i 6= j pi.
pi pi
2HOM =Kk=1
wk(log ORk logOR
)2 2K1
-
100 . : pi
wk =1
Var(log ORk)=(
1
n11k+
1
n12k+
1
n21k+
1
n22k
)1,
logOR =
Kk=1wk log ORkK
k=1wk ORk =
n11kn22kn12kn21k
.
pi
2HOM =Kk=1
wk(log ORk
)2 (K
k=1wk log ORk)2
Kk=1wk
.
5.6 (pi ).
pi
log OR1 = log120 15580 111 = log 2.0945 = 0.7394
log OR2 = log161 124130 117 = log 1.3126 = 0.2720
w1 =(
1
120+
1
111+
1
80+
1
155
)1= (0.0083 + 0.0090 + 0.0125 + 0.0065)1
= 1/0.0363 = 27.55
w2 =(
1
161+
1
117+
1
130+
1
124
)1= (0.0062 + 0.0085 + 0.0077 + 0.0081)1
= 1/0.0305 = 32.79
pi
2HOM = 27.55 (0.7394)2 + 32.79 (0.272)2 (27.55 0.7394 + 32.79 0.272)2
27.55 + 32.79
= 15.06 + 2.43 857.86660.34
= 3.27 p value = 0.070
2HOM = 3.27 < 21,0.95 = 3.84 pipi H0 pi pi - pi pi pipi 5%.
5.4.2 pi .
( ) pi pi pi. Mantel-Haenszel pi pi
ORMH =
Kk=1 n11kn22k/n..kKk=1 n12kn21k/n..k .
-
5: pi - 101
pipi pi pi
Var(log ORMH) =
Kk=1 PkRk
2(K
k=1 Rk)2 +
Kk=1(PkSk + QkRk)
2(K
k=1 Rk) (K
k=1 Sk) + Kk=1QkSk
2(K
k=1 Sk)2
Pk = n11k + n22k
Qk = n12k + n21k
Rk = n11kn22k/n..kSk = n12kn21k/n..k .
pi (1 )100% pi pi pi
log ORMH z1/2Var(log ORMH)
pi (elog ORMHz1/2
Var(log ORMH), elog ORMH+z1/2
Var(log ORMH)
).
5.6 (pi ).
pi
ORMH =120 155/466 + 161 124/53280 111/466 + 130 117/532 = 1.63.
pipi Var(log ORMH) = 0.01646 pi 95% pi pi
log 1.63 1.960.01646 (0.234, 0.737).
95% (e0.234, e0.737) = (1.26, 2.09).
5.4.3 pi SPSS.
pipi SPSS (version 13)
1. Analyze>Descriptives>Crosstabs: pi pi Analyze>Descriptives>Crosstabs.
2. Crosstabs
-
102 . : pi
() ROWS Cancer: pi pi pi ( pi 5.6 ).
() COLUMNS Passive Smoker: pi pi pi ( pi5.6 pi pi).
() LAYER Personal Smoking: pi pi ( pi 5.6 pi).
3. STATISTICS > Cohrans and Mantel-Haenszel Statistics
: pi- pi STATISTICS Crosstabs - pi pi : Cohrans and Mantel-HaenszelStatistics. pi pipi pi H0 : ORMH = ( ). pi pi pi -pi .
pi pi pi :
1 Tests of Homogeneity of the Odds Ratio: pi - ( Breslow-Day Tarone) - . pi- 5.6 2MH = 3.27 p-value=0.070 pi pipi pi pipi 5% ( pi pi ).
2 Tests of Conditional Independence: Coh-ran Mantel-Haenszel pi- -pi -. pi. Mantel-Haenszel 2MH = 13.94 p-value=0.000 ( pi -) pi pi pi pi pi pi.
3 Mantel-Haenszel Common Odds Ratio Estimate: . pi pipi - pipi pi 1. pi 3 :
1. Estimate: (ORMH )
2. ln(Estimate): (log ORMH )
-
5: pi - 103
3. Std. Error of ln(Estimate): pi (Var(log ORMH))
4. Asymp. Sig. (2-sided): p-value H0 : ORMH = ( pi Statistics Crosstabs).
5. Asymp. 95% Confidence Interval, Common Odds Ratio: 95% pi- .
6. Asymp. 95% Confidence Interval, ln(Common Odds Ratio): 95% pi .
pi 5.6 pi pi
1. Estimate: 1.625 .
2. ln(Estimate): 0.486 .
3. Std. Error of ln(Estimate): 0.128 .
4. Asymp. Sig. (2-sided): 0.000 = 1 0.903 = 1.6 .
5. Asymp. 95% Confidence Interval, Common Odds Ratio: 1.264 - 2.090 .
6. Asymp. 95% Confidence Interval, ln(Common Odds Ratio): 0.234 - 0.737 .
5.4.4 .
pi McNemar pi Mantel-Haenszel. pi. 2 2 pi pi k = 1, 2, . . . , n, pi n . pipi pi
ORMH =
nk=1 N11kN22k/N..knk=1 N12kN21k/N..k
pi Nijk pi i, j /pi - k (pi Nijk nij pi ).
pipi /pi : (1,1), (1,2), (2,1) pi (2,2). pi pi
-
104 . : pi
(A = i, B = j) (1) (2) N11kN22k/N..k N11kN22k/N..k nij
(1,1) (1) 1 0 1 0/2 = 0 1 0/2 = 0 n11 (2) 1 0
(1,2) (1) 1 0 1 1/2 = 1/2 0 0/2 = 0 n12 (2) 0 1
(2,1) (1) 0 1 0 0/2 = 0 1 1/2 = 0 n21 (2) 1 0
(2,2) (1) 0 1 0 1/2 = 0 0 1/2 = 0 n22 (2) 0 1
pi pi pipi
ORMH =0 n11 + 12n12 + 0 n21 + 0 n220 n11 + 0 n12 + 12n21 + 0 n22
= n12/n21
pi nij pi pi () i j . pi
OR =n12n21
pipi pi pi
Var(log OR) =1
n12+
1
n21.
pi pipi pi pi 100(1 )% pi- pi pi
logn12n21
z1/2
1
n12+
1
n21
pi pielog n12n21z1/2
1n12
+ 1n21 , elog
n12n21
+z1/2
1n12
+ 1n21
. 5.3 (pi).
pi 5.3, 5.2.1 OR = 16/5 =3.2 pi pi pi /pi (pipi) -pi pi .
pipi Var(log OR) = 1/5+1/16 = 0.2625 95% Var(logOR) pi pi
log 3.2 1.960.2625 (0.159, 2.170)
-
5: pi - 105
95% OR pi pi
(e0.159, e2.170) (1.17, 8.73) .
pi . pi OR1 = 5/16 =0.3125 pi pi pi /pi pipi 70% pi - pi /pi pipi 70% pi . pi pi
(0.3125 e1.960.2625, 0.3125 e1.96
0.2625) (0.11, 0.85) .
-
106 . : pi
-
6
pi
6.1 pi 2 -
pi pi pipi pi pipi ( 0.05) (1 ) pi pi pi pi H0 .
6.1.1
pipi pi H0 : pi1 = pi2 H1 : pi1 6= pi2. H0 pipi pi 1 (pi pi ). pipi pi H1 : |pi1 pi2| = > 0 pipi pipi H0 pi 1 . pi pi pi
P(pi H0| |pi1 pi2| = ) = 1
pi
n1 =1
2
(z1
pi1(1 pi1) + pi2(1 pi2)/k + z1/2
pi(1 pi)(1 + 1/k)
)2(6.1)
pi n2 = kn1, pi1 pi2 pi pi . pi pi pi pi . pipi pi pi pi pi pi = (pi1 + kpi2)/(1 + k).
6.1 pi pipi pi.
107
-
108 . : pi
6.2 pi .
6.1 pi 150 100000
pi = 20 pi .
pi 2 .
6.3 pipi pi pi
pi .
6.1.2
pipi piH0 : piAD = 1/2 H1 : piAD 6= 1/2, pi piAD = n21/nD. H0 pipi pi 1 (pi pi ). pipi pi H1 : piAD = piA1D pipi pipi H0 pi 1 . pi pi pi
P(pi H0|piAD = piA1D) = 1 pi
nD =
(2z1
piA1D(1 piA1D) + z1/2
)24(1/2 piA1D)2
.
pi pipi pi pi nD . pi pi pi - piD = nD/n pi
n = nD/piD =
(2z1
piA1D(1 piA1D) + z1/2
)24(1/2 piA1D)2piD
.
pipi pi pi pi pi 2n.
6.4 pi pipi pi.
6.5 pi pi .
6.2 2 pi . pi pi-
pi pi 85%.
pipi pipi H0 90% pi
2 pi 1. -
.
-
6: pi 109
6.1.3 : ,
pi
pipi pi pi pi pi pi pi. pi pi pi pi pi pi pi pi ( , pi pi ). pi pipi ( pi ) pi pi pi pi.
6.1 (drop-out rate) pi -
pi pi pi,
pi pi.
6.2 (drop-in rate) pi
( pi ) pi
pi.
pi
1: pi (drop-out rate).
2: pi (drop-in rate).
pi1: (pi.. pi pi) pi pi.
pi2: (pi.. pi pi) pi pi.
pi1 : pi.
pi2 : .
pi pi1 pi2 pi pi pi pi pi pi pi pi :
pi1 = P(|pi)
-
110 . : pi
= P(, |pi)+P(, |pi)
