*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
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- ゆきさ うるしはた
- 5 years ago
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1 Wilcoxon H23 BioS 1 Wilcoxon 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
2 *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 risk number * 3 d t t *1 S 1 t S 2 t t y S 1 t y S 2 t *2 S i t f i t f i t ds i dt t 1 *3 at risk number 2
3 e t t v t t e t E[d t ] n tm t, v t V [d t ] M tn t N t M t N t n t N t Nt 2 N t 1 t 3 N 3 7, d 3 0, e , v t 4 t 8 N 4 6, d 4 0, e N 8 3, d 8 1, e , v , v t N t d t e t v t Wilcoxon Wilcoxon 3 d 3, d 4, d d log d 3 + d 4 + d 8 d log E[d log ] E[d 3 + d 4 + d 8 ] E[d 3 ] + E[d 4 ] + E[d 8 ] e 3 + e 4 + e
4 V [d log ] V [d 3 + d 4 + d 8 ] V [d 3 ] + V [d 4 ] + V [d 8 ] d 3, d 4, d χ 2 log d log E[d log ] 2 V [d log ] χ 2 log 1 χ2 *4 5% χ 2 log > χ 2 1, 0.95 χ 2 log , χ2 1, p SAS data d1; p log 1- cdf chisq, , 1; run; p log Wilcoxon Wilcoxon d 3, d 4, d 8 Wilcoxon Wilcoxon Wilcoxon Wilcoxon Wilcoxon at risk number d log d W il N 3 d 3 + N 4 d 4 + N 8 d 8 d W il *4 χ 2 log 1 χ d t d t d t d log P t d t Wilcoxon 4
5 E[d W il ] E[N 3 d 3 + N 4 d 4 + N 8 d 8 ] N 3 E[d 3 ] + N 4 E[d 4 ] + N 8 E[d 8 ] N 3 e 3 + N 4 e 4 + N 8 e V [d W il ] V [N 3 d 3 + N 4 d 4 + N 8 d 8 ] N 2 3 V [d 3 ] + N 2 4 V [d 4 ] + N 2 8 V [d 8 ] d 3, d 4, d 8 N 2 3 v 3 + N 2 4 v 4 + N 2 8 v χ 2 W il d W il E[d W il ] 2 V [d W il ] {3 10} χ 2 W il 1 χ2 5% χ 2 W il > χ 2 1, 0.95 χ 2 W il , χ2 1, p SAS data d2; p Wil 1 - cdf chisq, , 1; run; p Wil Wilcoxon Wilcoxon at risk number 5
6 5 SAS SAS Proc Lifetest 5.1 data d1; input group patno t censor; cards; ; run; proc lifetest data d1; time t * censor0; strata group; run; t group Wilcoxon
7 group Wilcoxon group Pr > Chi-Square Wilcoxon LogLR χ 2 log Wilcoxon χ 2 W il Wilcoxon 2 p 2LogLR 3 2 i ii Wilcoxon 2 SAS t 2 2 t d t M t d t N t M t n t N t n t N t 7
8 E[d t ] n tm t N t, E[ d t ] n tn t M t N t V [d t ] M tn t N t M t N t n t Nt 2, V [ N t 1 d t ] M tn t N t M t N t n t Nt 2 N t 1 Cov[d t, d t ] V [d t ] M tn t N t M t N t n t N 2 t N t d log d 3 + d 4 + d 8 d log d 3 + t 4 + t 8 E[d log ] e 3 + e 4 + e 8 e log E[ d log ] ẽ 3 + ẽ 4 + ẽ 8 ẽ log V [d log ] V [d 3 + d 4 + d 8 ] V [d 3 ] + V [d 4 ] + V [d 8 ] v 3 + v 4 + v 8 v log V [ d log ] V [ d 3 + d 4 + d 8 ] V [ d 3 ] + V [ d 4 ] + V [ d 8 ] ṽ 3 + ṽ 4 + ṽ 8 ṽ log d log dlog d log d log E[d log ] elog ẽ log V [dlog ] V [d log ] vlog v log V [d log ] V [d log ] V [d log ] v log v log d log E[d log ] dlog e log d log ẽ log d t n t d t d log d 3 + d 4 + d 8 n 3 d 3 + n 4 d 4 + n 8 d 8 n log d log n log n 3 + n 4 + n 8 8
9 ẽ t E[n t d t ] n t E[d t ] n t e t ẽ log ẽ 3 + ẽ 4 + ẽ 8 n 3 e 3 + n 4 e 4 + n 8 e 8 n log e log dlog e log d log E[d log ] d log ẽ log V [d log ] vlog v log v log v log *5 vlog v log V [d log ] v log v log χ 2 χ 2 log d log E[d log ] V [d log ] 1 d log E[d log ] 1 V [d log ] *6 V [d log ] V V V VV V V *7 V v log 0 0 *5 *6 v log v log V [d log ] v log v log! det `V [d log ] v 2 log v2 log 0 *7 V V V 9
10 VV vlog v log vlog v log V v log v log v log 0 0 v log v log 1 0 vlog v log 1 0 v log v log vlog v log V v log v log V V 1 1 V [d log ] 1 V [d log ] χ 2 log d log E[d log ] V [d log ] d log E[d log ] d log e log dlog ẽ log v log 0 0 dlog e log d log ẽ log d log e log v log SAS 5.4 Wilcoxon Wilcoxon d log N 3 d 3 + N 4 d 4 + N 8 d 8 d log N 3 d3 + N 4 t 4 + N 8 t 8 E[d W il ] N 3 e 3 + N 4 e 4 + N 8 e 8 e W il E[ d W il ] N 3 ẽ 3 + N 4 ẽ 4 + N 8 ẽ 8 ẽ W il V [d W il ] V [N 3 d 3 + N 4 d 4 + N 8 d 8 ] N 2 3 V [d 3 ] + N 2 4 V [d 4 ] + N 2 8 V [d 8 ] N 2 3 v 3 + N 2 4 v 4 + N 2 8 v 8 v W il V [ d W il ] V [N 3 d3 + N 4 d4 + N 8 d8 ] N 3 3 V [ d 3 ] + N 2 4 V [ d 4 ] + N 2 8 V [ d 8 ] N 2 3 ṽ 3 + N 2 4 ṽ 4 + N 2 8 ṽ 8 ṽ W il d W il dw il d W il d W il E[d W il ] ew il ẽ W il V [dw il ] V [d W il ] vw il v W il V [d W il ] V [d W il ] V [d W il ] v W il v W il 10
11 5.4.1 Wilcoxon dw il e W il d W il E[d W il ] d W il ẽ W il d W il N 3 d3 + N 4 d4 + N 8 d8 N 3 n 3 d 3 + N 4 n 4 d 4 + N 8 n 8 d 8 n W il d W il n W il N 3 n 3 + N 4 n 4 + N 8 n ẽ t E[n t d t ] n t E[d t ] n t e t ẽ W il N 3 ẽ 3 + N 4 ẽ 4 + N 8 ẽ 8 N 3 n 3 e 3 + N 4 n 4 e 4 + N 8 n 8 e 8 n W il e W il dw il e W il d W il E[d W il ] d W il ẽ W il Wilcoxon V [d W il ] vw il v W il v W il v W il V [d W il ] vw il v W il v W il v W il V [d W il ] 1 v W il V [d W il ] 1 11
12 5.4.3 χ 2 χ 2 W il χ 2 W il d W il E[d W il ] V [d W il ] d W il E[d W il ] d W il e W il dw il ẽ W il v W il 0 0 dw il e W il d W il ẽ W il d W il e W il v W il 22 SAS 12
2 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
H22 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
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
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 )
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
(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,
,, 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
![,, 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](/thumbs/87/95421301.jpg ",, 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,
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Kaplan-Meier 1, 2,3 1 2 3 A SAS macro for extended Kaplan-Meier plots Kengo Nagashima 1, Yasunori Sato 2,3 1 Department of Parmaceutical Technochemistry, Josai University 2 School of Medicine, Chiba University
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But nothing s unconditional, The Bravery R R >0 = (0, ) ( ) R >0 = (0, ) f, g R >0 f (0, R), R >
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「東京都子供・子育て支援総合計画」中間見直し版（案）第2章 子供と家庭をめぐる状況
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Kaplan-Meierプロットに付加情報を追加するマクロの作成
1 / 47 Kaplan-Meier A SAS macro for extended Kaplan-Meier plots 1, 2,3 1 2 3 Kengo Nagashima 1, Yasunori Sato 2,3 1 Department of Parmaceutical Technochemistry, Josai University 2 School of Medicine, Chiba
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