Testing for non-randomness of events in sparse data situations

In experiments involving cytogenetic assays or mutation assays it is often of interest to determine if there are hot spots for certain events, that is, to determine if the events occur more often at certain sites than would be expected under the assumption of randomness. In examining chromosome aberrations using banded chromosome preparations, for example, it may be of interest to determine if a particular type of aberration occurs more often in a particular band than would be expected given the relative length of the band. In a mutation assay it may be of interest to determine if a mutation occurs more often at a particular nucleotide in a given sequence than would be expected given the length of the sequence in question. Such experiments typically result in data following a multinomial distribution with a large number of classes and relatively few observations. For such data, De Braekeleer & Smith (1988) have suggested analysis of the frequencies in individual classes using an exact binomial test. Two cautions are noted for application of the binomial analysis in the usual situation in which the locations of potential hot spots are not specified beforehand.