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Arithmetic-Geometric-Harmonic (AGH) Method of Rough Estimation of Median Lethal Dose (Ld50) Using Up and Down Procedure

Saganuwan Alhaji Saganuwan

Earlier methods adopted for the estimation of median lethal dose (LD50) used many animals (40 – 100). But for the up – and – down procedure, 5 – 15 animals can be used, the number I still consider high. So this paper seeks to adopt arithmetic, geometric and harmonic (AGH) mean for rough estimation of median lethal dose (LD50) using up – and – down procedure by using 2 – 6 animals that may likely give 1 – 3 reversals. The administrated doses should be summed up and the mean, standard deviation (STD) and standard error of mean (SEM) should be determined. The mean would be the LD50, whereas standard deviation would be the default dose progression and standard error of mean would provide the lower and upper boundary of the LD50, which may also serve as confidence interval. Arithmetic, geometric and harmonic means all go together harmoniously. If there is no death above 15,000 mg/kg body weight, the test agent is practically safe and that serves as the limit boundary for safety. The revised method saves time, reserves large numbers of animals that may be wasted and ignores complex mathematical manipulation involved and therefore encouraging the principles refinement, reduction and replacement (3R).