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1
2 (confounding)
3 Confounding Exposure? Outcome Confounders adjustment (confounders)
4
5 Not Confounding? 2 exposure 3rd factor 3rd factor
6 NEJM 2000; 342: (adjustment) univariate or crude relative risk (univariate or crude OR)adjusted relative risk (or adjusted OR) multivariate adjustment adjusted value 10
7 (OR = 14.3; 95%CI: ) 13, ,0003.9
8 Overestimation
9 (RR=0.3; 95%CI: ) (<10%)
10 Overestimation
11 ,
12 Underestimation
13 (adjustment) (restriction)
14 Exposure Outcome Randomization Matching restriction Confounder Adjustment (confounders)
15 Confounder vs. Effect modification Confounder exposure outcome ( Effect modification: Effect modifier exposure, outcome ()
16 Crude data vs. Mantel-Haenszel adjustment crude data adjusted data exposure factor disease risk ratio (RR), odds ratio (OR) RRcrude = (a/n 1 ) / (c/n 0 ) ORcrude = ad/bc adjustment Mantel-Haenszel adjustment(mh) RR MH = [(a i )(N 0i )/T i ]/[(c i )(N 1i )/T i ] = [(w i )(RR i )]/[(w i )] w i = (c i )(N 1i )/T i = [T i ][(N 1i N 0i )/(T i T i )][c i /N 0i ] OR MH = [(a i )(d i )/T i ]/[ (b i )(c i )/T i ] = [(w i )(OR i )]/[ w i ] w i = (b i )(c i )/T i RR crude = RR MH, OR crud e = OR MH RR crude RR MH, OR crude OR MH
17 i closed cohort study :
18
19 ? RR crude = (210/500) / (90/500) = RR boy = = (120/200) / (80/400) = RR girl (90/300) / (10/100) = = 3.00
20 Mantel Haenszel RRcrude RRadjusted confounder RRboy = RRgirl effect modifier
21 adjustment boys girls (120 x 400)/600 + (90 x 100)/400 = = (80 x 200)/600 + (10 x 300)/400 = = / 34.2 = 3.00 = RR adjusted
22 confounder effect modifier
23 ? RR crude = (210/500) / (70/500) = RR boy = (120/200) / (40/200) = RR girl (90/300) / (30/300) = = 3.00
24 RRcrude = RRadjusted confounder RRboy = RRgirl effect modifier
25 adjustment boys girls (120 x 200)/400 + (90 x 300)/600 = = 105 (40 x 200)/400 + (30 x 300)/600 = = / 35 = 3.00 = RRadjusted
26 confounder effect modifier
27 ? RR crude = (210/500) / (70/500) = RR boy = (160/200) / (40/200) = RR girl (50/300) / (30/300) = = 1.67
28 RRcrude = RRadjusted confounder RRboy RRgirl effect modifier crude 10effect modification crude homogeneity test effect modification effect modification effect modification effect modification
29 adjustment boys girls (160 x 200)/400 + (50 x 300)/600 = = 105 (40 x 200)/400 + (30 x 300)/600 = = / 35 = 3.00 = RRadjusted
30 Stratification open cohort study i = 1,,,,, I strata stratum i,
31 i opened cohort study :
32 British Doctors Study revised 1.72
33 Stratification (open cohort study) s ns s ns s ns s ns s ns PY 52,407 18,790 43,248 10,673 28,612 5,710 12,663 2,585 5,317 1,462 British Doctors Study S: smoker, ns: non-smokerpy: person-years British Doctors Study revised
34 1.72
35 Just simply summarized s ns PY 142,247 39,220 IR IRR 1.72 incidence rate ratio (IRR)1.72
36 IRR effect modifier confounder chi 2 = (O E) 2 / var O: observed, E: expected, var:variance Open cohort study chi 2 = [X E(X/H 0 ) ] 2 / var(x/h 0 ) X = = a E(X/H 0 ) = confounder = M1(N1/T) Var(X/H 0 ) = M 1 (N 1 /T)(1- N 1 /T)=M 1 N 1 N 0 /T 2 (crude table) = [630 ( /181467)] 2 / (731 x x 39220/ ) = 26.24
37 crude table chi2= [Xi Ei (X i /H0 i) ]2 / vari (X i /H0 i) I Xi = = ai Ei(Xi/Hi0) = confounder = M1i(N1i/Ti) Vari(Xi/H0i) = M1i(N1i/Ti)(1- N1i/Ti)=M1iN1iN0i/Ti2 H0: HA: Xi 630
38 Effect Modification in Stratified Table IR: incidence rate, IRR: incidence rate ratio
39 Ei(Xi/Hi0) Vari(Xi/H0i) Ei(Xi/Hi0) = Vari(Xi/H0i) = chi2= [Xi Ei (X i /H0 i) ]2 / vari (X i /H0 i)=( )2 / = Pr (chi2> 11.02) = H0 control (control 101 :residual confounder)10 (residual confounder)( ),
40 c ( )c crude data adjust Effect modification (restriction) PY IRR(weight) PY(weight) Inverse variance weights {wi = 1/var[ln(RRi)] = 1/(1/ai + 1/bi)}a or b 0weight 0 strata Mantel- Haenszel weights
41 Adjusting to exclude confounding by age PY IR IRR E i (X i /H i0 ) Var i (X i /H 0i ) E(X/H 0 ) = V(X/H 0 ) = (32+2) x = (32+2) x x = 6.61 ( ) 2 variance
42 wi = bin1i/ti effect modification weight RRMH = wi RRi / wi =bin1i/ti(ai/n1i)/(bi/n0) /(bin1i/ti) =(ain1i/ti)/(bin1i/ti) ain1i/ti= bin1i/ti=82.09 RRMH = (ain1i/ti)/(bin1i/ti)=1.42 IRR , 42
43 value 95% confidence interval (CI) lnirrmh 1.96var(lnIRRMH) var(lnirrmh)= A/BC A = M1iN1iN0I / Ti2 B= ain0i /Ti C= bin1i/ti var(lnirrmh)= A/BC= ln(1.42) = (0.141, 0.560) e(0.141, 0.560)= (1.15, 1.76) adjust IRR1.72positive confounding
44 Calculate at each stratified table
45 rate difference (RD) RD = wi RDi / wi Var (RD) = a/n12 + b/n02 = (an02 + bn12)/n12n02 w i = 1/vari(RDi) = N1i2N0i2 /(N0i2ai + N1i2b1) RD = wi RDi / wi = , 10,000PY6.1 RD 1.96var(RD) Var(RD) = 1 / wi =(3.7/104 PY, 8.5/104 PY) RDcrude = 1.85/1,000PY (12.4/104 PY, 24.6/104 PY) RDcrudeRDadjusted RDconfounder
46 Calculate at each stratified table
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-1- -2- -3-24 32ha 13-4- 30-5- -6- -7- 100-8- 20 20 100-9- 100-10- 100 100-11- -12-30 -13- 10-14- 52 71 59-15- 30-16- -17- -18- 31 31-19- -20- 47 52 71 29 41 59 306 88 348-21- -22- -23- -24- 12-25- 1,300
総務委員会会議録
29 28 29 29 () 121 1 111 11928 3 () () () () 11928 3 1,320 32,7897,000 () 1 23725,000 9 1,320 313 2,7897,000 2 2 2 5.5 16 15200 31 29 2931 3110 21 21 5 6 8,2195,000 2134,1097,000 1,320 32,7897,000 31 ()
- 8 -. 1 (1) (2) (3) (4) (5) (6) (7) (8)
- 7 - (1) (2).. ha 43 ( (1) ( ) (2).. 18 11 30 43 (1).. (2).. 0.5. () () A) B) C) - 8 -. 1 (1) (2) (3) (4) (5) (6) (7) (8) (1) (2) 43-9 - - 10 - (1).. 43.. 43... 43 - 11 - (2) (1).. A B A A B A - 12 -.
14 12 ( 17 4 2 ) 2004
14 12 ( 17 4 2 ) 2004 1 4,700 1980 1,757 1,150 25,000ha 6,000ha 10 10 10 2 1981 56 90 4,700 1980 1,757 1,150 2003 187,614 96,940 51.7 17 102,128 54.7 2004 545 76 14 2004 4 13 49.1 1981 84,638 38,272 17,570
,
34 29 5 29 6 29 7 30 28 26 1 1-71 - , - 72 - 27 3 1, - 73 - 5811 5821 5822 5831 58 2 5841 5851 5861 5862 5863 5864 5892 5896 5897 5898 5891 5895 7711 622 6311 6312 6314 6324 6032 6033 7611 7621 7623 7624
事業報告書
22 23 202,803 144,683 58,120 120,411 117,455 2,956 59.6 81.3 21.7% 22 23 62,677 56,001 6,676 57,734 61,454 3,720 120,411 117,455 2,956 47,092 13,255 33,837 19,397 7,666 11,731 3,546 401 3,145 3,290 1,546
*1 * Wilcoxon 2 2 t t t t d t M t N t M t n t N t n t N t d t N t t at ri
Wilcoxon H23 BioS 1 Wilcoxon 2 2.1 1 2 1 0 1 1 5 0 1 2 7 0 1 3 8 1 1 4 12 0 2 5 2 0 2 6 3 1 2 7 4 1 2 8 10 0 Wilcoxon 2.2 S 1 t S 2 t Wilcoxon H 0 H 1 H 0 : S 1 t S 2 t H 1 : S 1 t S 2 t 1 *1 *2 2.3 2.3.1