An exact goodness-of-fit test based on the occupancy problems to study zero-inflation and zero-deflation in biological dosimetry data
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The goal in biological dosimetry is to estimate the dose of radiation that a suspected irradiated individual has received. For that, the analysis of aberrations (most commonly dicentric chromosome aberrations) in scored cells is performed and dose response calibration curves are built. In whole body irradiation (WBI) with X- and gamma-rays, the number of aberrations in samples is properly described by the Poisson distribution, although in partial body irradiation (PBI) the excess of zeros provided by the non-irradiated cells leads, for instance, to the Zero-Inflated Poisson distribution. Different methods are used to analyse the dosimetry data taking into account the distribution of the sample. In order to test the Poisson distribution against the Zero-Inflated Poisson distribution, several asymptotic and exact methods have been proposed which are focused on the dispersion of the data. In this work, we suggest an exact test for the Poisson distribution focused on the zero-inflation of the data developed by Rao and Chakravarti (Some small sample tests of significance for a Poisson distribution. Biometrics 1956;12 : 264–82.), derived from the problems of occupancy. An approximation based on the standard Normal distribution is proposed in those cases where the computation of the exact test can be tedious. A Monte Carlo Simulation study was performed in order to estimate empirical confidence levels and powers of the exact test and other tests proposed in the literature. Different examples of applications based on in vitro data and also data recorded in several radiation accidents are presented and discussed. A Shiny application which computes the exact test and other interesting goodness-of-fit tests for the Poisson distribution is presented in order to provide them to all interested researchers.