Limiting dilution assays for the determination of immunocompetent cell frequencies. III. Validity tests for the single-hit Poisson model.

A statistical method was developed to test the validity of the single-hit Poisson model in limiting dilution assays used to determine immunocompetent cell frequencies. Principles of bioassay, validity tests, and the distinction between model-discrimination experiments and parameter-estimation assays are reviewed in the Introduction. The new test derived and then demonstrated with previously published data is intended to be used for parameter-estimation assays based upon the single-hit Poisson model. It is a family of related chi 2, t, and F tests for deviations from zero of the slopes of weighted least squares regression plots. These plots regress the logarithms of single-dose estimates fi of the frequency phi on the total cell doses lambda i and fi on the total cell dose reciprocals 1/lambda i, that is, Yi = ln fi on Xi = lambda i and Yi = fi on Xi = 1/lambda i. The test discriminates against alternative models with multiple-hit/target response-generation processes, a variable number (dose-dependent) of false negatives, and a constant number (dose-independent) of false positives. Its purpose as a test for parameter-estimation assays, though, is to detect deviations from the single-hit Poisson model and not to select one of these alternative models. Tests for model-discrimination experiments to select or 'prove' an unknown alternative model are considered in light of relevant literature reviewed in the Discussion.