生物検定法の故郷、2 値データの 用量反応に対す …

1 I 2 10 C: Documents and Settings Owner My Documents anz_seminal_9 Semi9_ _ .doc 4/20/2002 12:29 AM 2005 10 31 /19 4 ii 2002 1 13 iii 1.. 1 2.. 3 .. 3 .. 6 2 .. 9 95% .. 10 .. 11 .. 13 .. 15 ED50 .. 18 3.. 23 JMP .. 23 SAS POBIT .. 25 JMP .. 27 iv .. 4 50LD .. 4 .. 8 p .. 8 .. 9 95% .. 11 .. 5 .. 7 95% .. 11 ED50 Excel .. 19 ED50 Excel .. 20 ED50.

2 20 95% .. 21 2 95% .. 22 1 10 2002 4 20 9 2 10 9 2 LD50 LD50 95% complementary log-log 2 JMP biostat/ JMP JMP JMP PC D. Collett (1991) Modeling Binary Data, Chapman and Hall/CRC 4 LD50 Overdispersio Variation between the response probabilities 2 Example Germination of Orobanche ( ) 1:ageyp75 1:ageyp75 1:Bean 2:Cucumber 1:Bean 2:Cucumber y n y n y n y n 10 39 5 6 8 16 3 12 23 62 53 74 10 30 22 41 23 81 55 72 8 28 15 30 26 51 32 51 23 45 32 51 17 39 46 79 0 4 3 7 10 13 2 1 1.

3 2 JMP JMP JMP D. Collett (1991) Modeling Binary Data 2 4 Bioassay and some applications 1987 LD50 1996 SAS LD50 ED50 (Biological Assay) 50 Lack of Fit Lack of Parallelism 2 SAS proc PROBIT 1 proc LOGISTIC proc CATMOD proc GENMOD JMP Fit Y by X Fit Model Y0 X 95 SAS JMP Inverse Prediction JMP LD50 LD50 95% 2 2 2 2.

4 3 LD50 LD50 95% probit curve 50LD dp y102log22()exp{}22dxpdx = ( ) 1050log LD = probit probability unit 50LD25exp{}2probit( )2yxppdxy == ( ) y p 5 2 JMP ( ) 50LD1()p 5 JMP Normal Quartile 0 100% 4 2 50LD i mg/kg ( ) ip probit( )

5 Ip 1 110 10 0 2 136 10 2 3 183 10 5 4 247 10 8 5 333 10 9 6 450 10 10 2 JMP 10 probit( ) log ()iipdiose == + (5i) 10log ()idose probit( )ip ip 1 2 3 4 5 6 p( )

6 01 iix =+ 011 ((5)/ ) 1/ix = 105001 log LD((5) /)( 5) / ) == = = 2 5 mg/kg 1 1/1/ == = = = 95% (dose) 95% 50LD Y 95% X , 161, 223 2 SAS proc PROBIT JMP SAS proc LOGISTIC proc GENMOD LD50 95% 6 2 SAS proc PROBIT 00 = 10 = 6 = = 2 2 5 -5 LD50 95% , 160, 223 JMP 2 2 2 2exp()

7 1expxfxx = + , x < < ( ) < < 0 < 22/3 ()fx 1010log210logexpexplog1exp1expiidiidxpdx dx == ++ ( ) 0/ = 11/ = ()()01100110explog1explogiiidpd +=++ ( ) 0110logit( ) lnlog1iiiippdp ==+ 2 7 ( ) 50 LD50 11/ 22/3 2222 33 === JMP LD50 = = - - - 8 2 JMP = log10(dose) 2 <.

8 0001<.0001p (Prob>ChiSq) 50 105001 log LD/( ) == = = mg/kg 1% (1 ) === p p 10log ()idose Probit logit JMP 90% 50% 2 9 10% 95% , 50LD log10(dose) JMP JMP 00 = 10 = 6 = = 2 2 5 50% 2 2 SAS/LOGISTIC 10 2 SAS/PROBIT SAS/LOGISTIC SAS/GENMOD 2 SAS/LOGISTIC JMP SAS/LOGISTIC SAS/GENMOD 95% 95% ii =x 2xii = xx 010 1log()

9 Iidose1 = + 0 00v1 11v0 1 01v 2200100110112log ()log ()xiiiivdosevdosev = = + +xx JMP JMP 0 = 1 = = 1 0101 1log()iidose = + log (101) + = 1epe =+ 2200100110112log ()log ()xiiiivdosevdosev = = + +xx 2 log (101) ( ) log (101) + + = ( , )x = = ( 95) ==+ ( 95) ==+ 2 11 95% i dose n Y p log10 (dose)eta p^ Var(eta) (eta) L95 U95 1 101 10 0 2 136 10 2 3 183 10 5 4 247 10 8 5 333 10 9 6 450 10 10 95% 95% (dose) (dose) 95% x x 50% ED50 LD50 90% ED90 p d 12 2 01logit( ) log1ppdp ==+ p = ED50 logit ( ) = log (1) = 0 ED50 010ED50 += ED50 =01/ 0 1 ED50 01 50 ED = ED90 p = + ED90 0( ) /1 0 ( ) /ED901 = log(dose) 01logit( )=log( )pd + ED50 01+log()0ED50 = 01exp(/ )ED50 = 01 exp(/ )

10 ED50 = ED90 01 ED90 = 2 13 e 10 e ED50 ED90 log(dose) -101probit( )=( )log( )ppd =+ P = probit ( ) = 0 ED50 01 exp(/ )ED50 = 0 1 P = probit ( ) = ED90 01 exp[( ) /] ED50 ED50 ED50 ED50 ED50 2 01 (, )g = 01 (, )g = ( ) 22010101 Var()Var() 2 Cov(,) gg gg01 ++ ( ) 01 (, )g = 01 / 01 / = 000 Var()v = 111 Var( )v = 0101 Cov(,)v = ( ) 14 2 200011121 22 Var() vvED50 +