LD50 を求めるための最尤法入門 - yukms.com

1 LD50 18 2004 7 3 10/31/2005 7:41 PM 2004 7 3 E: R3_TK_2004_01_from R_ANZ_seminar_18_likelihood Semi_18_ .doc i 1.. 1 2. P .. 2 3. 2 .. 11 .. 11 JMP 2 .. 13 .. 16 4. P .. 19 .. 19 ..19 Colett ..20 2 D50 .. 22 .. 23 .. 25 .. 29 .. 29 .. 31 95% .. 32 JMP.

2 34 5. 2 D50 Dxx .. 36 95% .. 36 Colett Ex.. 38 Excel ..41 SAS NLIN 95% SAS 2004 .. 41 ii D50 ..42 ..43 Y p ..20 3 ..21 95% ..33 ..37 SdNd ln(dose) ..40 ..14 2 ..15 2 ..15 D50 ..20 DDT -BHC.

3 21 ..26 2 ..26 Excel Minverse ..27 10% 50% 90% ..29 90% 95% ..30 50% 95% ..30 10% 95% ..31 95% ..33 DDT -BHC ..39 ED50 95% ..40 Excel BHC ..41 1 1. LD50 P 2 2 P JMP Excel 2004 K04* 1 20 Q&A 10 2 & 20 Q A 10 3 & 20 Q A 10 30

4 2 2. P LD50 LD50 1 4 5 % % p% p% LD lethal dose p

5 0 50 100 LD10 LD50 LD90 LD50 LD50 probit curve 5-3 a . y 3 1022log2()exp{}22dxyd = x (1) 1050log LD = probit probability unit LD50 25exp{}2probit( ) 2yxpdx = y (2) y p 5 p 50 probit(p) 5 p 25 probit(p) p 75 probit(p)

6 LD50 LD50 4 LD50 . n k L k k 4 6 L L LD1d2dkd1d2dkd1Y2Y2Y50 1 1d 1n 1Y 111/pYn= 2 2d 2n 2Y 222/pYn= k kd kn 2Y /kkpYnk= i 1 2 k 0 1 4 ip 1 10logiixd= i 1 2 k probit( )iy=ip 2 ix iyyx =+ 2 ()( ()iii)

7 Xxy yxx = yx = 3 i ix i 4 1probit ( )ii = 5 iZ iinw 2exp{ (5) / 2}/ (2 )iiZ = 3 2/{ (1)}iiiiiinwnZ = 4 6 (1)()/iiiyp =+ iZ 7 / iiiiiXnwxnw= (1) / iiiiiYnwy nw= 2 ()xxiiiSnwxX= (1)2 ()yyiiiSnwyY= (1) ()(xyiiiiSnwxXyY= ) (1)/xyxxSS =(1)(1)yX = (1)(1)Y = X (5) 8 (1)(1)yx =+ix (1)i 5 9 i 1 2 k (1)|ii| < (1)(5) /XY =+ 10 LD50 (1)|ii| 4 i (1)i 4 8 (1)|ii| 9 LD50 1C(1)iiiikiynynyiii = (6) 1022log2()exp{22idixdx = (7)}

8 10 LD50 9 1) 1 10 9 10 0 p p 1 2 idip 5 1 4 2 3 + 6 2 + 7 2 4 6 1probit ( ) 1 {(5)}

9 Ii = 5 iZ iyi 9 (1)iy 2 5 LD50 LD50 95 10 in LD50 3 0 1 2 2 LDip50 LD50 LD50

10 1 0 1 LDipin50 LD50 inin LD 7 effective dose ED LD lethal conentration LC 6 5-12 5-12 LD50 i mg/kg ( ) ip probit( )ip 1 101 10 0 2 136 10 2 3 183 10 5 4 247 10 8