Fahad Granata
Introduction Replicated binomial count data is generated through a variety of bioassays. In Eco toxicological experiments, for example, fish larvae or Daphnis are exposed to various dosages of a drug in numerous tanks, and the number of dead or immobilized animals per tank is used to determine the item's hazard. For each dosage under consideration, a modest number of duplicated tanks is usually used. Counted numbers may indicate larger variance than expected under the binomial assumption, i.e. extra-binomial variability or over dispersion, if some experimental circumstances differ between tanks, affecting the proportion of dead or immobile Daphnis.
In the in-vivo micronucleus experiment, similar scenarios arise: the number of cells with micronuclei is measured for a certain number of exposed cells for each (randomized) animal, with the goal of determining the drugs' propensity to cause cytogenetic damage. A limited number of replications per dosage are also carried out here, so that variances between animals in the in-vivo micronucleus animals may lead to over dispersion. In summary, bioassays that produce binomial data frequently include clustered replication, which allows for data over dispersion to be accounted for. The number of replications or clusters per treatment group that can be used to determine the extent of over dispersion is, however, quite restricted.
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