2 H23 BioS (i) data d1; input group patno t sex censor; cards;

Similar documents
*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

,, 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

y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4

5 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 )

H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =

ＪＭＰ V4 による生存時間分析

H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I

(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

スライド 1

( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x +

48 * *2

function2.pdf

r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B

meiji_resume_1.PDF

t sex N y y y Diff (1-2)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

9 5 ( α+ ) = (α + ) α (log ) = α d = α C d = log + C C 5. () d = 4 d = C = C = 3 + C 3 () d = d = C = C = 3 + C 3 =

4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

「産業上利用することができる発明」の審査の運用指針（案）

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

α 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 +

t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ

高校生の就職への数学II


i 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


ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(

201711grade1ouyou.pdf

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

第１０１回　日本美容外科学会誌／ｎｂｇｋｐ‐０１（大扉）

２７巻３号／ＦＵＪＳＹＵ０３‐１０７（プログラム）

ｔｎｂｐ５９－２０＿Ｗｅｂ：Ｐ１／ｋｙ１０８６７９５０９６１０００２９４３

パーキンソン病治療ガイドライン2002

p...{..P01-48(TF)

本文２７／Ａ（ＣＤ－ＲＯＭ

入試の軌跡

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :

II 2 3.,, A(B + C) = AB + AC, (A + B)C = AC + BC. 4. m m A, m m B,, m m B, AB = BA, A,, I. 5. m m A, m n B, AB = B, A I E, 4 4 I, J, K

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

生活設計レジメ

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

I II III 28 29


10:30 12:00 P.G. vs vs vs 2

総合薬学講座 生物統計の基礎

コンピュータ概論

II K116 : January 14, ,. A = (a ij ) ij m n. ( ). B m n, C n l. A = max{ a ij }. ij A + B A + B, AC n A C (1) 1. m n (A k ) k=1,... m n A, A k k

24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x

2010 II / y = e x y = log x = log e x 2. ( e x ) = e x 3. ( ) log x = 1 x 1.2 Warming Up 1 u = log a M a u = M a 0

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C

t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1

Chap11.dvi

DE-resume

A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa

Chap10.dvi

..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A

Microsoft PowerPoint - SAS2012_ZHANG_0629.ppt [互換モード]

2014 S hara/lectures/lectures-j.html r 1 S phone: ,


: α α α f B - 3: Barle 4: α, β, Θ, θ α β θ Θ

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,


学習内容と日常生活との関連性の研究－第２部－第６章

5 1F2F 21 1F2F

( ) Loewner SLE 13 February

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0

, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f

1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1

Part () () Γ Part ,

i 18 2H 2 + O 2 2H 2 + ( ) 3K

II III II 1 III ( ) [2] [3] [1] 1 1:

Web XXX.XXX.XXX.XXX - - [02/May/2010:12:52: ] "GET /url/url2/page2.htm HTTP/1.1" " "(compatibl

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552


untitled

DATA Sample1 /**/ INPUT Price /* */ DATALINES


chap1.dvi

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f

untitled

Chap9.dvi

limit&derivative

直交座標系の回転

untitled

_TZ_4797-haus-local

微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.

K E N Z OU

gr09.dvi

名古屋工業大の数学 2000 年 ~2015 年 大学入試数学動画解説サイト

Kumagai09-hi-2.indd

Transcription:

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 1 1 1 16 15 0 1 1 17 15 0 0 1 18 0 1 1 1 19 0 0 0 1 0 4 0 0 1 1 4 1 0 1 4 0 0 ; run; 1

proc lifetest data d1 plot(lls); time t * censor (0); strata sex group; run; log-log 1 log-log log(t) Cox Kaplan-Meier 4 1: sex 0 group 0 t 0.0000 1.0000 0 0 0 5.0000 *... 0 4.0000 0.7500 0.500 0.165 1 4.0000 0.5000 0.5000 0.500 15.0000... 1 15.0000 0 1.0000. 4 0

Note : sex 0 group 1 t 0.0000 1.0000 0 0 0 6 7.0000 0.8 0.1667 0.151 1 5 15.0000 0.6667 0. 0.195 4 15.0000 *... 0.0000 *... 4.0000 *... 1 4.0000 *... 0 Note : sex 1 group 0 t 0.0000 1.0000 0 0 0 6.0000 0.8 0.1667 0.151 1 5 5.0000... 4 5.0000 0.5000 0.5000 0.041 10.0000 *... 4.0000 *... 1 4.0000 *... 0 Note

4: sex 1 group 1 t 0.0000 1.0000 0 0 0 5 5.0000 *... 0 4 8.0000 0.7500 0.500 0.165 1 8.0000 *... 1 0.0000 0.750 0.650 0.864 1 4.0000 *... 0 Note (ii) log-log S ij (t) (i : j : ) log( log(s ij (t))) log(t) t j S i (t j ) log( log(s i (t i ))) t j S 00 (t j ) log(t j ) log( log(s 00 (t j ))) 0.7500 1.10 1.5 4 0.5000 1.9 0.7 t j S 10 (t j ) log(t j ) log( log(s 10 (t j ))) 7 0.8 1.95 1.70 15 0.6667.71 0.90 t j S 01 (t j ) log(t j ) log( log(s 01 (t j ))) 0.8 1.10 1.70 5 0.5000 1.61 0.7 t j S 11 (t j ) log(t j ) log( log(s 11 (t j ))) 8 0.7500.08 1.5 0 0.750.00 0.0 (i) (iii) Proc Phreg Cox proc phreg data d1; model t * censor(0) group sex / ties efron; run; 4

PHREG WORK.D1 t censor 0 EFRON 11 11 50.00 (GCONV1E-8) - LOG L 57.798 5.98 AIC 57.798 57.98 SBC 57.798 58.778 : BETA0 Pr > ChiSq.8161 0.1484 Score.9441 0.19 Wald.660 0.16 5

Pr > ChiSq group 1-1.87 0.6561.564 0.0591 0.90 sex 1-0.468 0.6557 0.540 0.461 0.66 Wald group 1.87 χ.564 p 0.0591 *1 (iv) Cox (a) Cox λ(t x i, y j ) λ 0 (t) exp(αx i + βy j ) (i 0, 1, j 0, 1) x 0 0, x 1 1, y 0 0, y 1 1 ( ) λ 00 (t) λ(t 0, 0) λ 0 (t) (1) ( ) λ 10 (t) λ(t 1, 0) λ 0 (t) exp(α) () ( ) λ 01 (t) λ(t 0, 1) λ 0 (t) exp(β) () ( ) λ 11 (t) λ(t 1, 1) λ 0 (t) exp(α + β) (4) * 0 t λ ij (t) λ(t x i, y j ) Λ(t x i, y j ) t 0 t 0 ( t 0 λ(u x i, y j )du λ 0 (u) exp(αx i + βy j )du ) λ 0 (u)du exp(αx i + βy j ) t 0 λ 0(u)du Λ 0 (t) ( ) Λ 00 (t) Λ(t 0, 0) Λ 0 (t) ( ) Λ 10 (t) Λ(t 1, 0) Λ 0 (t) exp(α) ( ) Λ 01 (t) Λ(t 0, 1) Λ 0 (t) exp(β) ( ) Λ 11 (t) Λ(t 1, 1) Λ 0 (t) exp(α + β) (b) (a) H 0 : β 0 H 1 : β 0 *1 Wald Wald * λ ij (t) λ(t x i, y j ) i j λ ij (t) x i, y j λ(t x i, y j ) 6

(c) λ(t 0, 0) λ 10(t) λ 00 (t) λ 0(t) exp(α) exp(α) λ 0 (t) λ 01(t) λ 00 (t) λ 0(t) exp(β) exp(β) λ 0 (t) λ 11(t) λ 00 (t) λ 0(t) exp(α + β) exp(α + β) λ 0 (t) t log(λ 00 (t)) log(λ 0 (t)) log(λ 10 (t)) log(λ 0 (t)) + α log(λ 01 (t)) log(λ 0 (t)) + β log(λ 11 (t)) log(λ 0 (t)) + α + β t β 1 α, β t log( log) α, β, α + β t 4 * Cox + 1 λ(t x i, y j ) λ 0 (t) t t exp(αx i + βy j ) α, β 1 (d) λ ij (t) T λ ij (t) λ(t x i, y j ) lim dt 0 P r(t < T t + dt x i, y j, t T ) dt F ij (t) i j *4 F ij (t) 1 S ij (t) 1 P r(t > t x i, y j ) P r(t t x i, y j ) λ(t x i, y j ) lim dt 0 P r(t < T t + dt x i, y j, t T ) dt P r(t < T t + dt x i, y j ) 1 lim dt 0 dt P r(t T x i, y j ) F ij (t + dt) F ij (t) 1 lim dt 0 dt 1 F ij (t) * y t + 1 y t + 5 y t y t + 10 *4 F ij (t) F (t x i, y j ) 7

F ij (t) S ij (t) (1 S ij(t)) S ij (t) S ij (t) S ij (t) t 0 d log(s ij (t)) dt d log(s ij (t)) dt dt λ(t x i, y j ) t 0 λ(t x i, y j )dt log(s ij (t)) log(s ij (0)) Λ(t x i, y j ) (a) S ij (t) exp (Λ(t x i, y j )) ( S ij (0) 1) S 00 (t) exp (Λ(t 0, 0)) exp (λ 0 (t)) S 10 (t) exp (Λ(t 1, 0)) exp (λ 0 (t)) exp(α) S 01 (t) exp (Λ(t 0, 1)) exp (λ 0 (t)) exp(β) S 11 (t) exp (Λ(t 1, 1)) exp (λ 0 (t)) exp(α + β) (e) log( log(s ij (t))) S 00 (t) exp (λ 0 (t)) log(s 00 (t)) λ 0 (t) log( log(s 00 (t))) log(λ 0 (t)) (5) S 10 (t) exp (λ 0 (t) exp(α)) log(s 10 (t)) λ 0 (t) exp(α) log( log(s 10 (t))) log(λ 0 (t)) + α (6) S 01 (t) exp (λ 0 (t) exp(β)) log(s 01 (t)) λ 0 (t) exp(β) log( log(s 01 (t))) log(λ 0 (t)) + β (7) S 11 (t) exp (λ 0 (t) exp(α + β)) log(s 11 (t)) λ 0 (t) exp(α + β) log( log(s (t))) log(λ 0 (t)) + α + β (8) (f) (5) (8) log( log(s ij (t))) y log(t) y log( log(s ij (t))) y log( log(s 00 (t)) log(λ 0 (t)) 8

y log( log(s 10 (t)) log(λ 0 (t)) + α y log( log(s 01 (t)) log(λ 0 (t)) + β y log( log(s 11 (t)) log(λ 0 (t)) + α + β log(λ 0 (t)) log(λ 0 (t)) α, β, α + β *5 log( log(s ij (t))) 1 (g) at risk number *5 a, b log( log(λ 0 (t))) a + bt log( log(λ 0 (t))) exp(a + bt + bt ) Cox 9

(1) (0 1 ) at risk number ( ) (0 1 ) (0) 0 5 0 0 0 4 0 1 0 4 0 1 0 15 0 1 0 15 0 1 0 6 1 1 0 5 5 1 1 0 5 5 1 1 0 10 1 0 0 4 1 0 0 4 1 0 1 6 7 0 1 1 5 15 0 1 1 5 15 0 0 1 0 0 0 1 4 0 0 1 4 0 0 1 5 5 1 0 1 4 8 1 0 1 4 8 1 1 1 0 1 1 1 1 4 1 0 t L t 4 at risk number 5 6 5 L 4 λ(4 0, 0) λ(4 0, 0) + 5 λ(4 1, 0) + 6 λ(4 0, 1) + 5 λ(4 1, 1) λ 0 (4) λ 0 (4) + 5 λ 0 (4) exp(α) + 6 λ 0 (4) exp(β) + 5 λ 0 (4) exp(α + β) 1 + 5 exp(α) + 6 exp(β) + 5 exp(α + β) 10

1 1 7 at risk number 6 4 L 7 λ(7 0, 1) λ(7 0, 0) + λ(7 1, 0) + 6 λ(7 0, 1) + 4 λ(4 1, 1) λ 0 (7) exp(β) λ 0 (7) + λ 0 (7) exp(α) + 6 λ 0 (7) exp(β) + 4 λ 0 (7) exp(α + β) exp(β) + exp(α) + 6 exp(β) + 4 exp(α + β) 8 Kaplan-Meier at risk number at risk number 5 4 L 8 λ(8 1, 1) λ(8 0, 0) + λ(8 1, 0) + 5 λ(8 0, 1) + 4 λ(4 1, 1) λ 0 (8) exp(α + β) λ 0 (8) + λ 0 (8) exp(α) + 5 λ 0 (8) exp(β) + 4 λ 0 (8) exp(α + β) exp(α + β) + exp(α) + 5 exp(β) + 4 exp(α + β) 0 at risk number 0 L 0 λ(0 1, 1) λ(0 1, 0) + λ(8 0, 1) + λ(4 1, 1) λ 0 (0) exp(α + β) λ 0 (0) exp(α) + λ 0 (0) exp(β) + λ 0 (0) exp(α + β) exp(α + β) exp(α) + exp(β) + exp(α + β) Efron 1 1 1 at risk number 4 6 6 5 L λ( 0, 0) 4 λ( 0, 0) + 6 λ( 1, 0) + 6 λ( 0, 1) + 5 λ( 1, 1) ( 4 1 ) λ( 0, 0) + ( 6 1 λ( 1, 0) ) (10) λ( 1, 0) + 6 λ( 0, 1) + 5 λ( 1, 1) λ 0 () 4 λ 0 () + 6 λ 0 () exp(α) + 6 λ 0 () exp(β) + 5 λ 0 () exp(α + β) λ 0 () exp(α) 7 λ 0() + 11 λ 0() exp(α) + 6 λ() exp(β) + 5 λ 0 () exp(α + β) 1 4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β) exp(α) 7 + 11 exp(α) + 6 exp(β) + 5 exp(α + β) 1 (9) 1 1 (9) 11

1/ (10) 1/ 1 5 at risk number 5 6 5 1/ 1 L 5 λ(5 1, 0) λ(5 0, 0) + 5 λ(5 1, 0) + 6 λ(5 0, 1) + 5 λ(5 1, 1) λ(5 1, 0) λ(5 0, 0) + 4 λ(5 1, 0) + 6 λ(5 0, 1) + 5 λ(5 1, 1) λ 0 (5) exp(α) λ 0 (5) + 5 λ 0 (5) exp(α) + 6 λ 0 (5) exp(β) + 5 λ 0 (5) exp(α + β) λ 0 (5) exp(α) λ 0 (5) + 4 λ 0 (5) exp(α) + 6 λ(5) exp(β) + 5 λ 0 (5) exp(α + β) exp(α) + 5 exp(α) + 6 exp(β) + 5 exp(α + β) exp(α) + 4 exp(α) + 6 exp(β) + 5 exp(α + β) 15 at risk number 5 1 1 1/ / 1/ L 15 λ(15 0, 0) λ(15 0, 0) + λ(15 1, 0) + 5 λ(15 0, 1) + λ(15 1, 1) λ(15 0, 0) ( ) ( λ(15 0, 0) + λ(15 1, 0) + 5 1 ) λ(15 0, 1) + λ(15 1, 1) λ(15 0, 1) ( ) ( λ(15 0, 0) + λ(15 1, 0) + 5 1 ) λ(15 0, 1) + λ(15 1, 1) λ 0 (15) λ 0 (15) + λ 0 (15) exp(α) + 5 λ 0 (15) exp(β) + λ 0 (15) exp(α + β) λ 0 (15) 4 λ 0(15) + λ 0 (15) exp(α) + 14 λ(15) exp(β) + λ 0(15) exp(α + β) λ 0 (15) exp(β) λ 0(15) + λ 0 (15) exp(α) + 1 λ(15) exp(β) + λ 0(15) exp(α + β) 1 + exp(α) + 5 exp(β) + exp(α + β) 1 4 14 + exp(α) + exp(β) + exp(α + β) + exp(α) + 1 exp(β) exp(β) + exp(α + β) α, β L(α, β) L t L(α, β) L L 4 L 5 L 7 L 8 L 15 L 0 (11) 1

l(α, β) (11) l(α, β) log L + log L 4 + log L 5 + log L 7 + log L 8 + log L 15 + log L 0 (1) log L α log (4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β)) log log L 4 log ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) ( 7 + 11 ) exp(α) + 6 exp(β) + 5 exp(α + β) log L 5 α log ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) + α log ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) α log ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) log ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) log L 7 β log ( + exp(α) + 6 exp(β) + 4 exp(α + β)) log L 8 α + β log ( + exp(α) + 5 exp(β) + 4 exp(α + β)) ( 4 log L 15 log ( + exp(α) + 5 exp(β) + exp(α + β)) log ( ) 1 +β log + exp(α) + exp(β) + exp(α + β) β log ( + exp(α) + 5 exp(β) + exp(α + β)) log ( ) 1 log + exp(α) + exp(β) + exp(α + β) log L 0 (α + β) log ( exp(α) + exp(β) + exp(α + β)) (1) l(α, β) 5α + 4β log (4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β)) log + exp(α) + 14 ) exp(β) + exp(α + β) ( ) 4 14 + exp(α) + exp(β) + exp(α + β) ( 7 + 11 ) exp(α) + 6 exp(β) + 5 exp(α + β) log ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) log ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) log ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) log ( + exp(α) + 6 exp(β) + 4 exp(α + β)) log ( + exp(α) + 5 exp(β) + 4 exp(α + β)) log ( + exp(α) + 5 exp(β) + exp(α + β)) ( ) ( ) 4 14 1 log + exp(α) + exp(β) + exp(α + β) log + exp(α) + exp(β) + exp(α + β) log ( exp(α) + exp(β) + 4 exp(α + β)) (h) Newton-Raphson α, β α, β 11 l α (α, β) 5 6 exp(α) + 5 exp(α + β) 4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β) exp(α) + 5 exp(α + β) exp(α) + 6 exp(β) + 5 exp(α + β) 7 + 11 5 exp(α) + 5 exp(α + β) + 5 exp(α) + 6 exp(β) + 5 exp(α + β) 5 exp(α) + 5 exp(α + β) + 5 exp(α) + 6 exp(β) + 5 exp(α + β) 4 exp(α) + 5 exp(α + β) + 4 exp(α) + 6 exp(β) + 5 exp(α + β) exp(α) + 4 exp(α + β) + exp(α) + 6 exp(β) + 4 exp(α + β) exp(α) + 4 exp(α + β) + exp(α) + 5 exp(β) + 4 exp(α + β) exp(α) + exp(α + β) + exp(α) + 5 exp(β) + exp(α + β) exp(α) + exp(α + β) 4 + exp(α) + 14 exp(β) + exp(α + β) exp(α) + exp(α + β) 1 + exp(α) + exp(β) + exp(α + β) exp(α) + 4 exp(α + β) exp(α) + exp(β) + exp(α + β) 1

l β (α, β) 4 6 exp(β) + 5 exp(α + β) 4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β) 6 exp(β) + 5 exp(α + β) 7 exp(α) + 6 exp(β) + 5 exp(α + β) + 11 6 exp(β) + 5 exp(α + β) + 5 exp(α) + 6 exp(β) + 5 exp(α + β) 6 exp(β) + 5 exp(α + β) + 5 exp(α) + 6 exp(β) + 5 exp(α + β) 6 exp(β) + 5 exp(α + β) + 4 exp(α) + 6 exp(β) + 5 exp(α + β) 6 exp(β) + 4 exp(α + β) + exp(α) + 6 exp(β) + 4 exp(α + β) 5 exp(β) + 4 exp(α + β) + exp(α) + 5 exp(β) + 4 exp(α + β) 5 exp(β) + exp(α + β) + exp(α) + 5 exp(β) + exp(α + β) 14 4 + exp(α) + 14 exp(β) + exp(α + β) exp(β) + exp(α + β) exp(β) + 4 exp(α + β) exp(α) + exp(β) + exp(α + β) F(θ) 1 + exp(α) + 1 exp(β) + exp(α + β) exp(β) + exp(α + β) θ (α, β) l(α, β) 1 F(θ) l α (α, β) l β (α, β) Newton-Raphson F(θ) α, β l exp(α) + 56 exp(α + β) + 0 exp(α + β) (α) 4 α (4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β)) + 77 4 101 exp(α) + exp(α + β) + 0 exp(α + β) exp(α) + 6 exp(β) + 5 exp(α + β)) ( 7 11 15 exp(α) + 45 exp(α + β) + 0 exp(α + β) 10 exp(α) + 40 exp(α + β) + 0 exp(α + β) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) 8 exp(α) + 4 exp(α + β) + 0 exp(α + β) 6 exp(α) + 6 exp(α + β) + 4 exp(α + β) ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) ( + exp(α) + 6 exp(β) + 4 exp(α + β)) 6 exp(α) + exp(α + β) + 0 exp(α + β) 4 exp(α) + 14 exp(α + β) + 10 exp(α + β) ( + exp(α) + 5 exp(β) + 4 exp(α + β)) ( + exp(α) + 5 exp(β) + exp(α + β)) 8 8 4 6 exp(α) + 1 exp(α + β) + exp(α + β) exp(α) + 10 exp(α + β) + exp(α + β) ( 4 14 + exp(α) + exp(β) + exp(α + β)) ( + exp(α) + 1 exp(β) + exp(α + β)) 6 exp(α + β) + 1 exp(α + β) ( exp(α) + exp(β) + exp(α + β)) l α β 16 exp(α + β) (4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β)) + 1 exp(α + β) ( 7 + 11 exp(α) + 6 exp(β) + 5 exp(α + β)) 15 exp(α + β) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) 0 exp(α + β) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) 14 exp(α + β) ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) 10 exp(α + β) ( + exp(α) + 6 exp(β) + 4 exp(α + β)) 7 exp(α + β) ( + exp(α) + 5 exp(β) + 4 exp(α + β)) 6 exp(α + β) ( + exp(α) + 5 exp(β) + exp(α + β)) ( 4 0 exp(α + β) 14 + exp(α) + exp(β) + exp(α + exp(α + β) β)) ( + exp(α) + 1 exp(β) + exp(α + β)) 6 exp(α + β) ( exp(α) + exp(β) + exp(α + β)) 101 l exp(β) + 56 exp(α + β) + 0 exp(α + β) 1 exp(β) + 4 β (4 + 6 exp(α) + 6 exp(β) + 5 exp(α + β)) + exp(α + β) + 55 exp(α + β) ( 7 + 11 exp(α) + 6 exp(β) + 5 exp(α + β)) 14

18 exp(β) + 45 exp(α + 0β) + exp(α + β) 1 exp(β) + 40 exp(α + β) + 5 exp(α + β) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) ( + 5 exp(α) + 6 exp(β) + 5 exp(α + β)) 1 exp(β) + 4 exp(α + β) + 0 exp(α + β) 1 exp(β) + 0 exp(α + β) + 1 exp(α + β) ( + 4 exp(α) + 6 exp(β) + 5 exp(α + β)) ( + exp(α) + 6 exp(β) + 4 exp(α + β)) 10 exp(β) + exp(α + β) + 1 exp(α + β) 10 exp(β) + 14 exp(α + β) + 4 exp(α + β) ( + exp(α) + 5 exp(β) + 4 exp(α + β)) ( + exp(α) + 5 exp(β) + exp(α + β)) 56 9 ( 4 exp(β) + 1 exp(α + β) + 4 exp(α + β) exp(β) + 10 exp(α + β) + 4 exp(α + β) 14 + exp(α) + exp(β) + exp(α + β)) ( + exp(α) + 1 exp(β) + exp(α + β)) 6 exp(α + β) + 8 exp(α + β) ( exp(α) + exp(β) + exp(α + β)) Newton-Raphson θ (α, β) m θ m (α m, β m ) 6 9 ( ) 1 F θ m θ m1 θ (θ m1) F(θ) * * ; %macro ln(alpha, beta, a, b, c, d); log(&a + &b * exp(&alpha) + &c * exp(&beta) + &d * exp( &alpha + &beta)) %mend ln; * ; %macro f(alpha, beta); 5*&alpha + 4*&beta - %ln(&alpha, &beta, 4, 6, 6, 5) - %ln(&alpha, &beta, 7/, 11/, 6, 5) - %ln(&alpha, &beta,, 5, 6, 5) - %ln(&alpha, &beta,, 5, 6, 5) - %ln(&alpha, &beta,, 4, 6, 5) - %ln(&alpha, &beta,,, 6, 4) - %ln(&alpha, &beta,,, 5, 4) - %ln(&alpha, &beta,,, 5, ) - %ln(&alpha, &beta, 4/,, 14/, ) - %ln(&alpha, &beta, /,, 1/, ) - %ln(&alpha, &beta, 0,,, ) %mend f; * 1 ; %macro frac1(alpha, beta, a, b, c, d); (&b * exp(&alpha) + &d * exp(&alpha + &beta)) / (&a + &b*exp(&alpha) + &c*exp(&beta) + &d*exp(&alpha + &beta)) %mend frac1; %macro frac(alpha, beta, a, b, c, d); (&c * exp(&beta) + &d * exp(&alpha + &beta)) / (&a + &b*exp(&alpha) + &c*exp(&beta) + &d*exp(&alpha + &beta)) %mend frac; 15

* ; %macro frac11(alpha, beta, a, b, c, d); (&a * &b * exp(&alpha) + (&a * &d + &b * &c)*exp(&alpha + &beta) + &c * &d * exp(&alpha + *&beta)) / (&a + &b*exp(&alpha) + &c*exp(&beta) + &d*exp(&alpha + &beta))** %mend frac11; %macro frac1(alpha, beta, a, b, c, d); ( (&a * &d - &b * &c)*exp(&alpha + &beta) ) / (&a + &b*exp(&alpha) + &c*exp(&beta) + &d*exp(&alpha + &beta))** %mend frac1; %macro frac(alpha, beta, a, b, c, d); (&a * &c * exp(&beta) + (&a * &d + &b * &c)*exp(&alpha + &beta) + &b * &d * exp(*&alpha + &beta)) / (&a + &b*exp(&alpha) + &c*exp(&beta) + &d*exp(&alpha + &beta))** %mend frac; * 1 l alpha; %macro f1(alpha, beta); 5 - %frac1(&alpha, &beta, 4, 6, 6, 5) - %frac1(&alpha, &beta, 7/, 11/, 6, 5) - %frac1(&alpha, &beta,, 5, 6, 5) - %frac1(&alpha, &beta,, 5, 6, 5) - %frac1(&alpha, &beta,, 4, 6, 5) - %frac1(&alpha, &beta,,, 6, 4) - %frac1(&alpha, &beta,,, 5, 4) - %frac1(&alpha, &beta,,, 5, ) - %frac1(&alpha, &beta, 4/,, 14/, ) - %frac1(&alpha, &beta, /,, 1/, )- %frac1(&alpha, &beta, 0,,, ) %mend f1; * 1 l beta; %macro f(alpha, beta); 4 - %frac(&alpha, &beta, 4, 6, 6, 5) - %frac(&alpha, &beta, 7/, 11/, 6, 5) - %frac(&alpha, &beta,, 5, 6, 5) - %frac(&alpha, &beta,, 5, 6, 5) - %frac(&alpha, &beta,, 4, 6, 5) - %frac(&alpha, &beta,,, 6, 4) - %frac(&alpha, &beta,,, 5, 4) - %frac(&alpha, &beta,,, 5, ) - %frac(&alpha, &beta, 4/,, 14/, ) - %frac(&alpha, &beta, /,, 1/, ) - %frac(&alpha, &beta, 0,,, ) %mend f; * l alpha alpha; %macro f11(alpha, beta); - %frac11(&alpha, &beta, 4, 6, 6, 5) - %frac11(&alpha, &beta, 7/, 11/, 6, 5) - %frac11(&alpha, &beta,, 5, 6, 5) - %frac11(&alpha, &beta,, 5, 6, 5) - %frac11(&alpha, &beta,, 4, 6, 5) - %frac11(&alpha, &beta,,, 6, 4) - %frac11(&alpha, &beta,,, 5, 4) - %frac11(&alpha, &beta,,, 5, ) - %frac11(&alpha, &beta, 4/,, 14/, ) - %frac11(&alpha, &beta, /,, 1/, ) - %frac11(&alpha, &beta, 0,,, ) %mend f11; 16

* l alpha beta; %macro f1(alpha, beta); - %frac1(&alpha, &beta, 4, 6, 6, 5) - %frac1(&alpha, &beta, 7/, 11/, 6, 5) - %frac1(&alpha, &beta,, 5, 6, 5) - %frac1(&alpha, &beta,, 5, 6, 5) - %frac1(&alpha, &beta,, 4, 6, 5) - %frac1(&alpha, &beta,,, 6, 4) - %frac1(&alpha, &beta,,, 5, 4) - %frac1(&alpha, &beta,,, 5, ) - %frac1(&alpha, &beta, 4/,, 14/, ) - %frac1(&alpha, &beta, /,, 1/, ) - %frac1(&alpha, &beta, 0,,, ) %mend f1; * l beta beta; %macro f(alpha, beta); - %frac(&alpha, &beta, 4, 6, 6, 5) - %frac(&alpha, &beta, 7/, 11/, 6, 5) - %frac(&alpha, &beta,, 5, 6, 5) - %frac(&alpha, &beta,, 5, 6, 5) - %frac(&alpha, &beta,, 4, 6, 5) - %frac(&alpha, &beta,,, 6, 4) - %frac(&alpha, &beta,,, 5, 4) - %frac(&alpha, &beta,,, 5, ) - %frac(&alpha, &beta, 4/,, 14/, ) - %frac(&alpha, &beta, /,, 1/, ) - %frac(&alpha, &beta, 0,,, ) %mend f; *Newton-Raphson ; * Newton-Raphson Fisher s scoring ; %macro seq n(x1, x); x1 &x1; x &x; f1 %f1(x1, x); f %f(x1, x); f11 %f11(x1, x); f1 %f1(x1, x); f %f(x1, x); det f11*f - f1**; y1 x1 - (f * f1 - f1*f) / det; y x - (- f1*f1 + f11*f ) / det; %mend seq n; 17

* ; %macro exe(init1, init, method, no); data d&no; length i.0 diff x1 x y1 y f1 f %if &method n %then %do; f11 f1 f %end; %else %if &method f %then %do; I11 I1 I %end; det sol1 sol check1 check 8.0; i 1; diff 10; x1 &init1; x &init; do until(diff < 10**(-8) or det 0 or i > 1000); %seq &method(x1, x) output; diff sqrt((y1-x1)** + (y-x)**); x1 y1; x y; i i +1; end; sol1 y1;*newton-raphson ; sol y; check1 %f1(sol1, sol);* 0 ; check %f(sol1, sol);* 0 ; output; run; %mend exe; %exe(0.1, 0.1, n, 1) proc print proc print datad1; run; 18

i diff x1 x y1 y f1 f f11 f1 f det sol1 sol check1 check 1 10.0000 0.10000 0.10000-0.44565-1.998-0.6149 -.189 -.70575 0.61610 -.4765 6.080.... 1.5019-0.44565-1.998-0.4689-1.80-0.10096 0.16504 -.661 0.6648 -.4485 6.07685.... 0.065-0.4689-1.80-0.4687-1.864 0.0001-0.00150 -.6571 0.6781 -.4951 6.1789.... 4 0.0006-0.4687-1.864-0.4687-1.864 0.00000-0.00000 -.65711 0.677 -.4911 6.17191.... 5 0.0000-0.4687-1.864-0.4687-1.864-0.00000-0.00000 -.65711 0.677 -.4911 6.17191.... 6 0.0000-0.4687-1.864-0.4687-1.864-0.00000-0.00000 -.65711 0.677 -.4911 6.17191-0.4687-1.864 6.9541E-16-4.7E-16 α sol1 0.4687 β sol 1.864 SAS 19

(j) α, β (i) *6 λ(t x i, 1) λ(t x i, 0) λ 0(t) exp( αx i + β) exp( β) exp(1.86) 0.90 λ 0 (t) exp( αx i ) λ(t 1, y j) λ(t 0, y j ) λ 0(t) exp( α + βy j ) exp( α) exp(0.4684) 0.66 λ 0 (t) exp( βy j ) (k) Wald Wald H 0 H 1 H 0 : β 0 H 1 : β 0 L L ( 0 1 ) ( L θ 0 1 ) ( α β ) β H 0 H 1 H 0 : L θ 0 H 1 : L θ 0 θ (α, β) θ ( α, β) Fisher I(θ) I 11(θ) I 1 (θ) (I(θ)) 1 I11 (θ) I 1 (θ) Wald χ I 1 (θ) I (θ) I 1 (θ) I (θ) χ W ald (L θ) (L I( θ) 1 L) 1 (L θ) ( ( 0 1 ) ( α β )) ( ( 0 1 ) ( I 11 ( θ) I 1 ( θ) I 1 ( θ) I ( θ) ) ( 0 1 )) 1 ( ( 0 1 ) ( α β )) ( β) I ( θ) χ W ald 5% χ W ald > χ (1, 0.95) *6 x i 0

*7 F(θ) [ ] F I(θ) E θ (θ) [ E [ E ] l α l α β ] l α (α, β) l α β (α, β) [ E E l α β ] [ ] l β l α β (α, β) l β (α, β) Newton-Raphson θ (0.4684, 1.86) f11, f1, f I 11 ( θ), I 1 ( θ), I ( θ) ( ).6571 0.677 I( θ) 0.677.491 ( ).6571 0.677 0.677.491 det 6.1719 ( ) ( ) 1 1.4914 0.677 I( θ) 6.1719 0.677.6571 I ( θ).6571 6.1719 0.405 χ W ald (1.84) 0.405.566 χ (1, 0.95).84 H 0 SAS p data d1; p 1 - cdf( chisq,.566, 1) run; p 0.0591 SAS β I ( θ) 0.405 0.6569 SAS *7 1

( ) b exp(α) + d exp(α + β) α a + b exp(α) + c exp(β) + d exp(α + β) ( ) b exp(α) + d exp(α + β) β a + b exp(α) + c exp(β) + d exp(α + β) ( ) c exp(β) + d exp(α + β) β a + b exp(α) + c exp(β) + d exp(α + β) ab exp(α) + (ad + bc) exp(α + β) + cd exp(α + β) (a + b exp(α) + c exp(β) + d exp(α + β)) (ad bc) exp(α + β) (a + b exp(α) + c exp(β) + d exp(α + β)) ac exp(β) + (ad + bc) exp(α + β) + bd exp(α + β) (a + b exp(α) + c exp(β) + d exp(α + β))

2024 © docsplayer.net プライバシー | 利用規約 | フィードバック