Quantal Response Analysis for a Mixture of Populations

SUMMARY This paper is concerned with the biological assay of a mixture of populations which cannot be differentiated on the basis of their external characteristics. It is shown that the overall dosage-response relation may be expressed in terms of the corresponding relations for the separate populations and of the proportion of each present in the mixture. The derivation of the maximum likelihood (ML) estimates of the unknown parameters is then described and the proposed methods are illustrated by an example of the analysis of a quantal assay of trypanosomes involving a mixture of two distinct populations. The calculation of the parameter estimates involved an iterative procedure which is only practicable using a digital computer and it is pointed out that the quantity and quality of the experimental data must conform to very stringent criteria if an analysis to to be worthwhile.