Using jackknife methods for estimating the parameter in dilution series

Dilution assays are quantal dose-response assays that detect a positive or negative response in each individual culture within groups of replicate cultures that vary in the dose of cells/organisms tested. We propose three jackknife versions of the maximum likelihood estimator of the unknown parameter, i.e., the frequency of a well-defined cell within the context of limiting dilution assays or the density of organisms within the context of serial dilution assays. The methods have been evaluated with artificial data from extensive Monte Carlo experiments. As a result of these experiments and theoretical considerations, the jackknife version based on deleting one individual culture at a time is proposed as the statistical procedure of choice. The next best method is the jackknife version based on leaving out the same replicate from each of the culture groups at a time.