Bias-corrected confidence intervals for the concentration parameter in a dilution assay

Interval estimates of the concentration of target entities from a serial dilution assay are usually based on the maximum likelihood estimator. The distribution of the maximum likelihood estimator is skewed to the right and is positively biased. This bias results in interval estimates that either provide inadequate coverage relative to the nominal level or yield excessively long intervals. Confidence intervals based on both log transformation and bias reduction are proposed and are shown through simulations to provide appropriate coverage with shorter widths than the commonly used intervals in a variety of designs. An application to feline AIDS research, which motivated this work, is also presented.