Power analysis of statistical methods for comparing treatment differences from limiting dilution assays

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Abstract
Six different statistical methods for comparing limiting dilution assays were evaluated, using both real data and a power analysis of simulated data. Simulated data consisted of a series of 12 dilutions for two treatment groups with 24 cultures per dilution and 1,000 independent replications of each experiment. Data within each replication were generated by Monte Carlo simulation, based on a probability model of the experiment. Analyses of the simulated data revealed that the type I error rates for the six methods differed substantially, with only likelihood ratio and Taswell's weighted mean methods approximating the nominal 5% significance level. Of the six methods, likelihood ratio and Taswell's minimum Chi-square exhibited the best power (least probability of type II errors). Taswell's weighted mean test yielded acceptable type I and type II error rates, whereas the regression method was judged unacceptable for scientific work.