多変量解析の使い方の こつ - niph.go.jp

1 118 I II MDS III IV I II III IV MDS Cox regression analysis y= x+ x y x=0 y y x -33-33 y= x+ H0: =0 x y 100 y BMI x y= x + 100 =0 5% BMI 1mmHg x1 x3 y= 1x1+ 1 = BMI + 100 y= 2x2+ 2 = + 110 y= 3x3+ 3 = ( 1, 0) + 120 BMI 1mmHg BMI 125mmHg BMI BMI 1mmHg BMI BMI 25 60 125mmHg?

2 140mmHg?135mmHg? BMI = BMI + 100 BMI (confounding variables) multiple linear regression analysis x1 x3 y= 1x1+ 2x2+ 3x3+ 1 3: = BMI + + 16 ( 1, 0) + 95 BMI BMI BMI BMI BMI BMI BMI=25, 60 , 25+ 60+16 1+95= 4mmHg 2mmHg mmHg P P < < R2 = BMI + + 16 ( 1, 0) + 95 R2 R2= 30% BMI BMI, , (partial R2)

3 BMI =0 =1 BMI 30% BMI 8% 13% 12% 30% R2 R2 R2 P < R2= SBP DBP DBP SBP stepwise R2 R2 Stepwise -33-33 -33-33 -33-33 -33-33 -33-33 -33-33 X Y correlation coefficient -1 +1 kg g 1000 =0 Pearson

4 Spearman correlation analysis BMI partial correlation coefficient -1 +1 =0 partial correlation analysis y= 1x1+ 2x2+ 3x3+ x x y= 1x1+ 2x2+ x1x2x3 100 010 0 0 1 vs. vs. y= 1x1+ 2x2+ x1x2x3 100 010 0 0 1 vs. vs. P ( 1) ( 2) - I BMI 130 15 25 125 12 25 122 12 857065 ANCOVA(Analysis of Covariance) LSM: Least Square Mean 75 BMI 123 85 25 126 70 25 128 65 P< for trend.

5 SD y= 1x1+ 2x2+ x1: (-)=0, (+)=1, x2: (-)=0, (+)=1 2= ,P= 1= , P= SD =?? =?? SD = = = y= 1x1+ 2x2+ 12x1x2+ x1: (-)=0, (+)=1, x2: (-)=0, (+)=1 + + 2 1 12 Cox y= 1x1+ 2x2+ 3x3+ y y (=1) (=0) x y 1 0 log(p/(1-p)) = 1x1+ 2x2+ 3x3+ p p/(1-p) log(p/(1-p)) p exp( ) x =1, =0 2 N x1 2 3 log(p/(1-p))

6 = 1x1+ p 0 1 Wilcoxon McNemar P n=90n=90 13%25% < 70%65% 48%46% = 10 / 21 = 221 23 1057 67 127890 stepwise (95% ) vs. ( ) vs. ( ) +10 ( ) vs. ( ) +1SD ( ) 2 3 log(p/(1-p)) = 1x1+ 2x2+ 3x3+ p x1, x2 x3 Cochran-Mantel-Haenszel (n=200)20% 50% 30% (n=300)10% 70% 20% 6070 P= log(p/(1-p))

7 = 1x1+ 2x2+ 3x3+ p 1 - - - - d 30 e e ea Yokoyama T, et al. (2003) Cancer EpidemiolBiomarkers Prev.( )b 1 / 1 / 9 / 18 / . c 30 d 234 634 a95% (<1 / ) (0) ( / ) (1) ( / ) (5) (18 / ) (6) (7) ( / ) (4) 25% ( / ) (9)25-49% (18 / ) (10)50-74% (8)75-89% 10% +11+ (3) (0) 30 (2) (0) (0) (1) (0) (1) (HRA) HRA-F A E 10% (A-E 1 ) ( ) = A + B + C + D + positive rate (1-specificity)Sensitivity80th70th95th60 th50th90thAUC (area under the curve) is Yokoyama T, et al.

8 (2008) Cancer Epidemiol Biomarkers Prev. Cox Cox (t, X) 0(t) exp( 1x1+ 2x2+ 3x3) (t, X) t exp( ) =1, =0 x vs. Cox 7 ()()2122 + Log-rank Log-rank test: X2= , P< Cox RR= Cox (1996).

9 Cox .. ( =2) n=200n=600 P 65%73% 48%49% 0012345678910 Log-rank test: 2= , df=1, P= Cox stepwise (95% ) (95% ) vs. ( ) ( ) vs. ( ) ( ) +10 ( ) ( ) vs. ( ) ( ) +1SD ( ) ( ) = Cox factor analysis x1 xn f1 fm x1=a11f1+a12f2+.

10 +a1mfm+d1u1 x2=a21f1+a22f2+..+a2mfm+d2u2 Varimax Promax x f a 1. 2. 3. 95% 1( ) 1( ) 1( ) principal component analysis x1 xn