Estimating the Logistic Curve

In estimating the parameters of the logistic curve when the response at any given dose is binomial, the method of “maximum likelihood” and the method of “minimum logit chi-square” have both been suggested. Computational difficulties formerly associated with the maximum likelihood solution have now largely disappeared. In a comparison of the two methods it is shown that the maximum likelihood estimates, but not the minimum logit chi-square estimates, are sufficient estimators for the parameters. Particular attention is paid to samples where all but one of the responses are zero or 100 per cent. Also, the effects of using the “2n-rule” for handling the minimum logit chi-square estimation problem for cases of zero or 100 per cent kill in any class are examined. The two sets of estimators are also surveyed from the viewpoint of consistency and some remarks made on the criterion of minimum mean square error estimators when sufficient estimators exist.