Probability models and the applicability of statistical procedures in the identification of chromosomal fragile sites

Böhm et al. (1995, Human Genetics 95, 249-256) introduced a statistical model (named FSM--fragile site model) specifically designed for the identification of fragile sites from chromosomal breakage data. In response to claims to the contrary (Hou et al., 1999, Human Genetics 104, 350-355; Hou et al., 2001, Biometrics 57, 435-440), we show how the FSM model is correctly modified for application under the assumption that the probability of random breakage is proportional to chromosomal band length and how the purportedly alternative procedures proposed by Hou, Chang, and Tai (1999, 2001) are variations of the correctly modified FSM algorithm. With the exception of the test statistic employed, the procedure described by Hou et al. (1999) is shown to be functionally identical to the correctly modified FSM and the application of an incorrectly modified FSM is shown to invalidate all of the comparisons of FSM to the alternatives proposed by Hou et al. (1999, 2001). Last, we discuss the statistical implications of the methodological variations proposed by Hou et al. (2001) and emphasize the logical and statistical necessity for fragile site identifications to be based on data from single individuals.