Minimum sample sizes for identifying chromosomal fragile sites from individuals: Monte Carlo estimation

A Monte Carlo simulation procedure was used to estimate the exact level of the standardized X-2 test statistic (X-s(2)) for randomness in the FSM methodology for the identification of fragile sites from chromosomal breakage data for single individuals. A random-number generator was used to simulate 10000 chromosomal breakage data sets, each corresponding to the null hypothesis of no fragile sites for numbers of chromosomal breaks (n) from 1 to 2000 and at three levels of chromosomal band resolution (k). The reliability of the test was assessed by comparisons of the empirical and nominal alpha levels for each of the corresponding values of n and k. These analyses indicate that the sparse and discrete nature of chromosomal breakage data results in large and unpredictable discrepancies between the empirical and nominal alpha levels when fragile site identifications are based on small numbers of breaks (n < 0.5 k). With n greater than or equal to 0.5 k, the distribution of X-s(2) appears to be stable and non-significant differences in the empirical and nominal a levels are generally obtained. These results are inherent to the nature of the data and are, therefore, relevant to any statistical model for the identification of fragile sites from chromosomal breakage data. For FSM identification of fragile sites at alpha = 0.05, we suggest that n greater than or equal to 0.5 k is the minimum reliable number of mapped chromosomal breaks per individual.