Rationale and Applicability of Analysis Methods for Identification of Chromosomal Fragile Sites-A Reply to Drs Dahm et al

1. Applicability. Following previous studies, Tai et al. (1993) proposed use of the relationship between the binomial and F-distributions to test for nonrandomness of chromosomal breakpoints. All of these methods were developed based on the concept of the binomial model. Dahm and Greenbaum (1994) contended that appropriate models for statistical identification of fragile sites will require tests that establish site-specific chromosomal breakage as being nonrandom with respect to the number and distribution of total breaks. They thus questioned the statistical efficacy of Tai et al. (1993) with their own idea in this (cytogenetic) area. Even if their idea were correct, their question should be applicable to all methods under the binomial model, not only for Tai et al. (1993). We have little confidence in the biological and, specifically, cytogenetic reasoning put forth by Dahm and colleagues. They draw strong conclusions on the basis of very little biological evidence. Bohm et al. (1995) chose to present their method assuming an equiprobability model (EPM), although they noted their test procedures can be directly modified to scale the multinomial-homogeneity expectations to reflect band width or other relevant proportions. From our perspective, if Dahm and colleagues had been as clear in their published manuscript as they were in their Reader Reaction, readers might have more easily deduced the meaning of "directly," and we would not have misinterpreted them. We appreciate that this problem has now been clarified. Nevertheless, we would like to emphasize that Hou, Chiang, and Tai (1999) proposed using the highest standardized observed breakage (Ni np9)/{np?(1 9)11/2 as an exclusion statistic and the M test (Fuchs and Kenett, 1980) for resolving the problem. 2. Binomial, multinomial, or hierarchical. The iterative procedure proposed by Bohm et al. (1995) was established under a multistage changeable multinomial model. Because in each step the comparison base of sites changes, this method is a sequentially adjusted comparison base procedure rather than a fixed comparison base procedure. As a consequence, all the fragile sites identified by this procedure are obtained by different comparison bases. Instead of thinking that identification of fragile sites is a two-group classification procedure as Bohm et al. (1995) proposed, Hou, Chiang, and Tai (2001) considered that the classification procedure can be a multiple-group classification procedure. Obviously, the two-group setting is a special case of the multigroup setting. If Bohm and colleagues thought that the work of Bohm et al. (1995) extending the binomial model to the multinomial model is meaningful for identification of fragile sites, we do not see why they declared that it is not apparent that hierarchical clusters of fragile sites have any biological meaning. 3. Pooled or individual. Bohm et al. (1995) concluded from a numerical study that the analysis of chromosomal breakage data pooled over individuals causes a large number of sites to be inaccurately identified as fragile and insisted on the necessity of per-individual fragile sites analysis. In fact, very simple examples can be constructed in which just the opposite conclusion is reached: Failing to pool samples across individuals leads to the false exclusion of fragile sites. Thus, to our mind, the logic behind the claim of Dahm and colleagues is overly simplistic. 4. Sample size. Greenbaum et al. (1997) recommended a minimum of half as many breaks as bands in identifying