t sex N y y y Diff (1-2)
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1 Armitage t 1.2 SAS Proc GLM
2 t sex N y y y Diff (1-2) t t Pr > t y Pooled Equal < t p t 2
3 sex N x x x Diff (1-2) t t Pr > t x Pooled Equal < kg p * *2 *1 *2 3
4 F Pr > F Model <.0001 Error Corrected Total Type III F Pr > F sex x <.0001 sex p x 3 model / solution clparm *3 t Pr > t 95% Intercept B sex B sex B..... x < Note X X B *4 x *5 100 *3 solution clparm 95 *4 Note 0 B *5 (better ) PPK 4
5 2.1.4 t t t t *6 Error 37.3 = 6.1 * y t 4 y *6 *7 Error 5
6 t dose N y y y Diff (1-2) t t Pr > t y Pooled Equal *8 t p x y x x 5 x x t *
7 dose N x x x Diff (1-2) t t Pr > t x Pooled Equal <.0001 x y x 6 x y 4 x F Pr > F Model <.0001 Error Corrected Total
8 Type III F Pr > F dose <.0001 x <.0001 dose x 1 model /solution clparm t Pr > t 95% Intercept B < dose B < dose B..... x < Note X X B y x y = x (= x) y = x (= x) *9 x 6.45 x 1 y 2.91 x x x 1 * 10 2 x Proc MEANS : x x N x = ŷ = x = ŷ = x = Proc GLM model lsmeans lsmeans dose; * 11 2 dose y *9 2 *10 *11 8
9 2.2.4 t t t t 2.5 x x Error 7.7 = y x x y x BioS (2) * 12 (1) (2) (3) (1), (2) 1 2 (3) * 13 (1) (3) *12 Greenland, S. and Robins, J. M. Identifiability, exchangeability, and epidemiological confounding. International Journal of Epidemiology 1986;15: Rothman, K. J., Greenland, S. Modern Epidemiology, 2nd ed. Philadelphia: Lippincott and Raven, *13 9
10 3 3 * 14 * 15 (2) x y 60 y 7 y y t dose N y y y Diff (1-2) t t Pr > t y Pooled Equal p y x *14 *15 10
11 8 x 1 2 t dose N x x x Diff (1-2) t t Pr > t x Pooled Equal y x 11
12 9 x y * 16 2 * 17 F Pr > F Model <.0001 Error Corrected Total Type III F Pr > F dose x <.0001 dose p t Pr > t Intercept B <.0001 dose B dose B... x <.0001 Note X X B *16 y *
13 y = x (= x) y = x (= x) x 6.06 x Proc MEANS : x x N x = 5.07 * 18 2 ŷ = x = ŷ = x = SAS model lsmeans dose; 2 dose y t t t t Error = y y x x 3.3 *18 13
14 = * x * 20 x 4 * 21 *19 1 t *20 t x 6.1 =0 *21 14
15 1 SAS SAS y x dose proc glm data=d1; class dose; model y= dose x / solution clparm ; lsmeans dose; run; quit; model solution clparm dose 2 lsmeans 2 t t t y 11, y 12,, y 1n N(µ 1, σ 2 ) y 21, y 22,, y 2n N(µ 2, σ 2 ) y ij = µ i + ɛ ij ( ɛij N(0, σ 2 ) ) i = 1, 2, j = 1,, n i j x ij y ij = µ i + βx ij + ɛ ij ( ɛij N(0, σ 2 ) ) i = 1, 2, j = 1,, n ( ) x ij x y x 15
16 3 1 2 x 10 x * 22 2 x *22 y x = 10 x y 2 x x x x y 16
H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I
H BioS (i) I treat II treat data d; input group patno treat treat; cards; 8 7 4 8 8 5 5 6 ; run; I II sum data d; set d; sum treat + treat; run; sum proc gplot data d; plot sum * group ; symbol c black
More informationH22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =
H BioS t (i) treat treat data d; input patno treat treat; cards; 3 8 7 4 8 8 5 5 6 3 ; run; (i) treat treat data d; input group patno period treat y; label group patno period ; cards; 3 8 3 7 4 8 4 8 5
More information5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
More informationα β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β *3 2.3 * *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P + 10) 15 (µ A = µ P +
Armitage 1 1.1 2 t *1 α β 1.2 µ x µ 2 2 2 α β 2.1 1 α β α ( ) β *1 t t 1 α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β 1 0 0 1 1 5 2.5 *3 2.3 *4 3 3.1 1 1 1 *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P
More information(iii) x, x N(µ, ) z = x µ () N(0, ) () 0 (y,, y 0 ) (σ = 6) *3 0 y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *4 H 0 : µ
t 2 Armitage t t t χ 2 F χ 2 F 2 µ, N(µ, ) f(x µ, ) = ( ) exp (x µ)2 2πσ 2 2 0, N(0, ) (00 α) z(α) t * 2. t (i)x N(µ, ) x µ σ N(0, ) 2 (ii)x,, x N(µ, ) x = x + +x ( N µ, σ2 ) (iii) (i),(ii) x,, x N(µ,
More information,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i
Armitage.? SAS.2 µ, µ 2, µ 3 a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 µ, µ 2, µ 3 log a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 * 2 2. y t y y y Poisson y * ,, Poisson 3 3. t t y,, y n Nµ,
More informationi Armitage Q. Bonferroni 1 SAS ver9.1.3 version up 2 *1 *2 FWE *3 2.1 vs vs vs 2.2 5µg 10µg 20µg 5µg 10µg 20µg vs 5µg vs 10µg vs 20µg *1 *2 *3 FWE 1
i Armitage Q Boferroi SAS ver93 versio up * * FWE *3 vs vs vs 5µg 0µg 0µg 5µg 0µg 0µg vs 5µg vs 0µg vs 0µg * * *3 FWE 3 A B C D E (i A B C D E (ii A B C D E (iii A B C D E (iv A B C D A < B C D A < B
More information2 H23 BioS (i) data d1; input group patno t sex censor; cards;
H BioS (i) data d1; input group patno t sex censor; cards; 0 1 0 0 0 0 1 0 1 1 0 4 4 0 1 0 5 5 1 1 0 6 5 1 1 0 7 10 1 0 0 8 15 0 1 0 9 15 0 1 0 10 4 1 0 0 11 4 1 0 1 1 5 1 0 1 1 7 0 1 1 14 8 1 0 1 15 8
More information3 3.1 *2 1 2 3 4 5 6 *2 2
Armitage 1 2 11 10 3.32 *1 9 5 5.757 3.3667 7.5 1 9 6 5.757 7 7.5 7.5 9 7 7 9 7.5 10 9 8 7 9 9 10 9 9 9 10 9 11 9 10 10 10 9 11 9 11 11 10 9 11 9 12 13 11 10 11 9 13 13 11 10 12.5 9 14 14.243 13 12.5 12.5
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SAS ユーザー総会 2017 Mantel-Haenszel 法により調整したリスク差の信頼区間に関する一考察 武田薬品工業株式会社日本開発センター生物統計室佐々木英麿 舟尾暢男 要旨 Mantel-Haenszel 法により調整したリスク差に関する以下の信頼区間の算出方法を紹介し 各信頼区間の被覆確率をシミュレーションにより確認することで性能評価を行う Greenland 信頼区間 Sato 信頼区間
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