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 < C < D 3 3 3 FWE α *4 (i (ii (i FWE (iii *5 (ii,000,000 (iv (iii (00 α (00 α 3 Z, Z N(0, 005 Z > 96, Z > 96 5 FWE 005 F W E P ( Z > 96 or Z > 96 00 96 4 F W E P ( Z > 4 or Z > 4 0049 *4 *5
FWE 005 *6 FWE FWE *7 F W E P ( Z > 4 or Z > 4 4 4 F W E P ( max Z i > 4 i, max i, Z i Tukey-Kramer Duett 33 5µg 0µg 0µg Boferroi α α 005 005 6 00083, 005 3 0067 34 (i (ii x x x N(µ, x x x N(µ, I x I x I x II N(µ I, *6 P ( Z > 9 005 F W E P ( Z > 4 or Z > 4 P ( Z 4 ad Z 4 P ( Z 4 P ( Z 4 (* Z, Z 0975 0975 0049 *7 3
*8 x, x,, x I I I j j (x j x (x j x I (x Ij x I j 4 Tukey-Kramer 4 I * 9 H : µ µ H A : µ µ H 3 : µ µ 3 H3 A : µ µ 3 H I : µ µ I HI A : µ µ I H 3 : µ µ 3 H3 A : µ µ 3 H (I I : µ I µ I H(I I A : µ I µ I I IC I(I 4 t * 0 t i j x i x j t ij ( i + j ij *8 *9 H ij H A ij *0 F t χ F 4
* t ij i j i j ij ( ( i i ( i + ( j + ( j j i + j ( i j (x ik x i + (x jk x j k ij I ( ( ( + ( + + ( I + ( + + ( I I I (x j x + (x j x + + (x Ij x I I j j ( + + + I k j I I i (x ij x i i j x i x j T ij ( i + j Tukey-Kramer Tukey * t χ F t T ij ( I t * 3 43 FWE FWE α 3 I(I {T ij } T max i<j T ij max i<j x i x j ( i + j FWE * 4 T T 3 * 005 t > t( +, 0975 (t( +, 0975 ( + t 975 * Tukey Tukey-Kramer *3 t *4 max i<j i < j i, j x i x j x j x i i j 5
FWE T * 5 6 FWE FWE FWE FWE 44 44 I 3 0,, 3 H : µ µ H A : µ µ H 3 : µ µ 3 H A 3 : µ µ 3 H 3 : µ µ 3 H A 3 : µ µ 3 T * 6 µ µ µ 3 0, T (in(0, (0 + + 33 (ii 0 x x x 3 (iii (iv (i (iii T, T 3, T 3 T (v (i (iv,000,000 * 7 T (vi T 5 5 * 8 µ µ µ 3 0, * 9 N(0, 44 ( SAS SAS (iprobmc (iiproc glm * 0 (iprobmc (ca FWE (alpha (df (k *5 *6 6 FWE *7,000,000 *8 *9 µ µ µ 3 *0 proc mixed 6
data d; c ProbMC( Rage,, -alpha, df, k; ca c /sqrt(; ru; ca Rage : Tukey-Kramer : -alpha : Studet -( df : ( ( k : c Studet 00(-alpha Studet ca c ProbMC c (iiproc glm d dose bp proc glm datad; class dose; model bp dose; meas dose /tukey; ru; * 45 H ij : µ i µ j alpha T ij > ca (ca ProbMC i, j H ij 46 balaced ubalaced balaced ubalaced balaced Tukey ubalaced Tukey-Kramer proc glm probmc Tukey Tukey-Kramer * * SAS SAS LATEX * Tukey-Kramer 7
5 Duett Tukey-Kramer Tukey-Kramer 5 vs (I H : µ µ H A : µ µ H 3 : µ µ 3 H3 A : µ µ 3 H I : µ µ I HI A : µ µ I 5 Tukey-Kramer t Tukey-Kramer x x j T j ( + j 53 FWE Tukey-Kramer T j T max j I T j max j I x x j ( + j 54 54 ( Tukey-Kramer I 3 0,, 3 H : µ µ H A : µ µ H 3 : µ µ 3 H3 A : µ µ 3 8
Tukey-Kramer µ µ µ 3 0, (i N(0, (0 + + 33 (ii 0 x x x 3 (iii (iv (i (iii T, T 3, T (v (i (iv,000,000 T (vi T 5 5 54 ( SAS Tukey-Kramer (iprobmc (iiproc glm (iprobmc Tukey-Kramer (abalaced ubalaced (b Rage Duett * 3 (c (d k ( - * 4 (balaced balaced data d; ca ProbMC( Duett,, -alpha, df, k-; ru; Tukey-Kramer Duett : Duett : -alpha : -( df : Tukey-Kramer ( -( k- : ( - Tukey-Kramer Studet *3 Duett Duett Duett *4 9
(ubalaced ubalaced data d; 0; 3; 34; k3; df + + 3 - k; lambda sqrt(/(+; lambda sqrt(3/(+3; ca ProbMC( Duett,, -alpha, df, k-, lambda, lambda; ru; (iiproc glm Tukey-Kramer d dose bp (balaced proc glm datad; class dose; model bp dose; meas dose /duett; ru; (ubalaced proc glm datad; class dose; model bp dose; lsmeas dose / pdiff cl adjust duett; ru; 55 Tukey-Kramer H j : µ µ j alpha T j > ca 56 balaced ubalaced balaced ubalaced Duett Tukey-Kramer proc glm probmc balaced ubalaced 0
6 FWE T FWE FWE α H : µ µ H 3 : µ µ 3 H 4 : µ µ 4 F W E all P ( H A H A 3 H A 4 µ µ µ 3 µ 4 H, H 3 H 4 H 4 FWE F W E,3 P (H A H A 3 µ µ µ 3 µ 4 F W E,3 F W E all F W E all FWE * 5 T *5 FWE α FWE α
7 FWE Tukey-Kramer FWE T max i<j T ij x x T (, T 3 + c x x 3 ( + 3 P (max{t, T 3 } > c P (T > c or T 3 > c P (T c ad T 3 c P (T c P (T 3 c FWE T T 3 T, T 3 t * 6 8 Tukey-Kramer Tukey-Kramer µ µ µ 3, x ij N(0, t N(µ, t 5 N(0, t 5 N(µ, t N(0, t x,, x N(µ, x,, x N(µ, N(0, x,, x, x,, x y,, y N(0, y,, y N(0, x ij y ij + µ (i,, j,, i *6
{x ij } x,, x y,, y y,, y x,, x x,, x t {y ij } * 7 x j x j ( y ij + µ j ȳ + µ ȳ y j j x ȳ + µ j j j (x j x ( ( y j + µ ( ȳ + µ (y j ȳ j (y j ȳ ( ( ( + ( + ( ( ( y j ȳ + ( ( + ( j (y j ȳ + (y j ȳ + + j i (y ij ȳ i i j j j (y j ȳ *7 x ij y ij µ, 3
t x x t ( + ( + x x i (x ij x i + i j ( ȳ + µ ( ȳ + µ i (y ij ȳ i ( + ( + + + i j ȳ ȳ i (y ij ȳ i i j ȳ ȳ ( + i + (y ij ȳ i ( + i j ȳ ȳ i (y ij ȳ i + i j µ, N(0, {y ij } t N(µ, t N(0, t N(µ, t N(0, t N(0,,000,000 ( + t Tukey-Kramer t pool Tukey-Kramer * 8 N(0, 9 Studet 9 Tukey-Kramer Studet Tukey-Kramer *8 Duett 4
Studet u,, u k, χ : u,, u k N(0,, χ χ (ν Q R k,ν max i<j u i u j χ ν Studet Q R k,ν Studet * 9 Tukey-Kramer x i x j T ij ( i + j Studet Tukey Tukey-Kramer i j T ij T ij x i x j ( + x i x j ( x i,, x i N(µ i, x j,, x j N(µ j, x i N (µ i,, x j N (µ j, H ij : µ i µ j ( µ x i, x j N (µ, Q R k,ν x i, x j N(0, ( x i µ, x j µ T ij x i x j N(0, ( x i µ ( x j µ T ij ( x i µ q ( x i µ q ( q x j µ c ( q xj µ c *9 SAS ProbMC ( Rage Q R k,ν 5
(i ( q x i µ ( q x j µ N(0, (ii c ν ( + + 3 3 ν c χ (ν * 30*3 (iii i, j * 3 ν ν (ii c χ c (ν ν Q R k,ν χ ν max T max i<j T ij T max i<j T ij max i<j max i<j Q R 3,ν ( x i µ q c ( q xj µ c ( x i µ q ( q x j µ c * 33 T 95 Q R 3,ν 95 9 Tukey Tukey-Cramer Tukey Tukey-Cramer FWE *30 *3 ν ( ( ν c χ (ν *3 *33 Q R 3,ν 3 ν ( -( 6
0 Duett (balaced Tukey Duett Q D k,ν Duett * 34 u,, u k, χ : u,, u k N(0,, χ χ (ν Duett Q D u u i k,ν max i k χ ν Studet Q D k,ν 95 5 *34 Duett s two-sided rage distributio 7