Identifying chromosomal fragile sites from individuals: a multinomial statistical model

The inability to identify fragile sites from data for single individuals remains the major obstacle to determining whether these chromosomal loci are predisposed to cancer-causing and evolutionary rearrangements. We describe a novel statistical model that is amenable to data from single individuals and that establishes site-specific chromosomal breakage as nonrandom with respect to the distribution of total breakage. Our method tests incrementally smaller subsets of the data for homogeneity under a multinomial model that assigns equal probabilites to a maximal set of nonfragile sites and unrestricted probabilities to the remaining fragile sites with significantly higher numbers of breaks. We show how standardized Pearson's chi-square (X²) and likelihood-ratio (G²) statistics can be appropriately used to measure goodness-of-fit for sparse contingency (individual-based) data in this model. A sample application of this approach indicates extensive variation in fragile sites among individuals and marked differences in fragile-site inferences from pooled as opposed to per-individual data.