Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from Applied Stochastic Models in Business and Industry, with the full article now available to read here.
, . Sample size determination to estimate mediation effects in cell transformation assays: A Bayesian causal model. Appl Stochastic Models Bus Ind. 2021; 37: 973– 989. https://doi.org/10.1002/asmb.2641
The preliminary assessment of the carcinogenic potential of substances may be performed through Cell Transformation Assays (CTAs), quick-and-cheap in-vitro tests where increasing concentrations of the substance under testing are prepared within a liquid vehicle and then spread on Petri dishes already filled of activated cells. After 72 hours of treatment, Petri dishes are washed and the recovery time starts, a period during which alive cells replicate and may form cell colonies, called foci. After five weeks, Petri dishes are fixed and stained, so that a cell that mutated during treatment with the substance originates a colony of deeply packed-overlapped cells, called Type III foci, that appear as dark-blue spots within a Petri dish. The experimental outcome is the number of Type III foci within Petri dishes, thus an assay has the simple structure of a randomized one-way experiment, where the experimental factor is typically defined by 5 increasing concentrations: untreated negative control, highest non-toxic dose, median lethal dose and two further intermediate dose levels. All the models proposed so far do not consider differences in the number of viable cells after treatment and in the total number of foci (either Type I or Type II colonies). The key point is that only Type III foci cause tumor if injected into mice, as a result of a fully achieved disruption of cell’s metabolism. Nevertheless, the higher is the number of viable cells after treatment, the larger is the total number of foci (whatever their type) that we expect after fixation, and therefore the higher is the number of Type III foci. From this standpoint, we should be interested in changes of the number of Type III foci due to the ability of fully disrupting cell’s metabolism, called Direct Effect (DE), and not in the increase of Type III foci due to smaller levels of toxicity (higher number of viable cells) or due to a better ability in promoting initial events of disruption (higher number of Type I and Type II foci), i.e. Indirect Effects (IEs). By comparing the number of Type III foci at a given dose level with respect to negative controls, we are quantifying the Total Effect, which includes both DE and IEs.
A Bayesian structural causal model was proposed to distinguish TE, DE and IEs of a candidate carcinogen in CTA experiments based on Balb/c 3T3 cells. The elicited prior distribution of model parameters should be widely applicable to the whole set of substances that may be tested on Balb/c 3T3 cells, but it could be refined by the toxicologist for chemicals belonging to specific classes of compounds, e.g., genotoxic substances. The proposed model also overcomes the limitations of some statistical approaches described in the literature, for example it is flexible enough to account for samples of Petri dishes all showing the same small number of Type III foci. Furthermore, it never assigns large probability values to impossible events, like a number of foci less than zero. Finally, a Monte Carlo algorithm was developed to determine the sample size required to reduce the expected uncertainty of estimates below a preassigned threshold given the type of effect (e.g., DE or TE) and the magnitude to detect. Extensive experimentation to estimate DEs for hundred substances already in use may be now performed with a suitable sample size in a Bayesian causal framework.