New approaches to mutation rate fold change in Luria-Delbrück fluctuation experiments

For nearly eight decades the Luria-Delbrück protocol remains the preferred method for experimentally determining microbial mutation rates. However, earnest development and rigorous applications of statistical methods for mutation rate comparison using fluctuation assay data are a relatively recent phenomenon. While likelihood ratio tests tailored for the fluctuation protocol give investigators appropriate tools, researchers sometimes may prefer to view the comparison of two mutation rates through the lens of the ratio of the two mutation rates. The idea of using the bootstrap technique to construct intervals for mutation rate fold change was proposed nearly a decade ago, but it failed to gain traction partly due to a failure to incorporate likelihood-based estimation. In addition to extending the bootstrap method, this paper proposes two new methods of constructing intervals for mutation rate fold change: a profile likelihood method and a Bayesian method utilizing Monte Carlo Markov chain. All three methods are assessed by large-scale simulations.