Sample size determination to estimate mediation effects in Cell Transformation Assays: a Bayesian causal model

Cell transformation assays (CTAs) are in vitro methods used in the preliminary assessment of the carcinogenic potential of substances. CTAs are promising tests for cosmetic, food, and pharma companies because they are not only quick-and-cheap, but also able to reduce animal-based testing. An assay has the simple structure of a randomized one-way experiment, where the experimental factor is defined by 5 increasing concentrations. Different families of distributions have been proposed to evaluate the effect of a substance on counts of Type III foci, but all models proposed so far do not consider differences in the number of viable cells and in the total number of foci occurring among Petri dishes. In this article, a Bayesian structural causal model is proposed to distinguish total, direct, and indirect effects of a carcinogen in CTA experiments. The recommended sample size is calculated by Monte Carlo simulation given the type of effect and the magnitude to detect. An informative joint prior distribution on parameters elicited for BALB/c 3T3 CTAs is exploited to obtain the posterior distribution from each simulated dataset.