Computer programs for algorithm for least-squares estimation of LD50
Abstract
Suppose the relation of mortality rate p to log dose x is a distribution function F(μ, σ, x) of N(μ, σ2).
With PC-1500 computer using the data log dose x, number of animals n, and mortality rate p, it is found by Marquardt method that the expression
Q =∑_(i-1)^m▒〖n[p-F(μ,σ,x)]2〗
reaches the minimum on μ=μ, σ=σ.
Consequently the log LD 50=μ is obtained.
For example.
Log dose .301 .398 .477 .544 .602 .699
Animals 6 5 6 5 6 1
Mortality rate . 167 .400 .667 .800 .833 1.0
μ=MU = 4.301690737 E-0l
σ=SIGMA= 1.426220 042 E-l0
Q= 2.925960202 E -02
lg LD 50 =4.301690737 E-01.
LD 50 =2.69258284
95% INTERVAL OF LD 50
LOWER = 2.259396921
UPPER = 3.208821914
LD 10 = 1.767631955
95% INTERVAL OF LD 10
LOWER = 1.203735749
UPPER = 2.595688241 LD 90 = 4.101533879
95% INTERVAL OF LD 90
LOWER = 3.029757494
UPPER = 5.552451043
Keywords:
With PC-1500 computer using the data log dose x, number of animals n, and mortality rate p, it is found by Marquardt method that the expression
Q =∑_(i-1)^m▒〖n[p-F(μ,σ,x)]2〗
reaches the minimum on μ=μ, σ=σ.
Consequently the log LD 50=μ is obtained.
For example.
Log dose .301 .398 .477 .544 .602 .699
Animals 6 5 6 5 6 1
Mortality rate . 167 .400 .667 .800 .833 1.0
μ=MU = 4.301690737 E-0l
σ=SIGMA= 1.426220 042 E-l0
Q= 2.925960202 E -02
lg LD 50 =4.301690737 E-01.
LD 50 =2.69258284
95% INTERVAL OF LD 50
LOWER = 2.259396921
UPPER = 3.208821914
LD 10 = 1.767631955
95% INTERVAL OF LD 10
LOWER = 1.203735749
UPPER = 2.595688241 LD 90 = 4.101533879
95% INTERVAL OF LD 90
LOWER = 3.029757494
UPPER = 5.552451043