Norikazu Yasuda

Geographical Variations in Inborn Errors of Metabolism in Japan

Using materials from a nationwide screening project on inborn errors of metabolism in Japan, the incidence of histidinemia, phenylketonuria, galactosemia and homocystinuria were found to be 140, 16, 14 and 7 in 1 million live births, respectively. Geographical variations were observed, especially in histidinemia, which are most likely due to chance.

The random walk model of human migration

It has been known that the distribution of matrimonial distances, the distance between birthplaces of mates, is highly leptokurtic and has been fitted empirically to a gamma function (including an exponential function as a special case) (Cavalli-Sforza, 1963), a beta function (Yasuda, 1966), a sum of normal probabilities (Cavalli-Sforza et al., 1966) and so forth. Also, theoretical models have been built to justify the skewness of the distribution. In this connection, the distribution has been used for the prediction of probabilities of consanguineous marriage (Cavalli-Sforza et al., 1966) as well as for the study of the probability of gene identity in terms of migration and mutation (Malecot, 1967). In these studies, it is assumed that the second moment of the distribution is finite and the convolution of the distribution is simple. The purpose of the present paper is to demonstrate that such a skewed distribution can be derived from a model of the behavior of man in terms of a random walk of the “Brownian motion type.” The resulting distribution is a K-distribution of the Bessel function. This not only satisfies the two theoretical requirements above, but also contains merely two parameters to be calculated. Some attempts to fit the K-distribution have been made in a helminthe (Broadbent and Kendall, 1953) and in a codling moth (Williams, 1961). In these cases, the stopping time of the movement of larvae is exponentially distributed.

A Surveillance System for Metabolic Disorders in Japan

Statistical procedures based on a Poisson hypothesis for surveying serial occurrences of incidence were developed. Three methods, the z-test, the cusum technique and the sequential test were applied in a study of a nationwide screening system on newborns for hereditary metabolic disorders in Japan. It was found that the statistical tests well detected human errors involved in data processing.

A note on gene frequency estimation in the ABO and ABO-like system

SummaryBased on a random sample of individuals, new conventional formulae for estimating gene frequency in the ABO and the ABO-like system are presented. Applying the formulae on a large number of samples, it is found that the new method is simple and yields estimates as accurate in at least two decimal places as the maximum likelihood solutions. The method however might be fraught with bias when the O phenotype frequency was low or even absent. Degrees of this bias have been discussed in terms of the number of iterative processes by a method of gene counting and of a goodness of fit to the Hardy-Weinberg proportions.

The probability of parentage exclusion based on restriction fragment length polymorphisms

SummaryBased on restriction fragment length polymorphisms (RFLPs) reported in the Eighth International Workshop of Human Gene Mapping (HGM8) held in Helsinki, the probability of parentage exclusion was calculated and the result was compared with those currently obtained from blood groups, serum groups and biochemical markers among Japanese. RFLPs would be very promissing in use of forensic medicine as well as mutation study. The eight probes with the highest probability yielded a joint probability of parentage exclusion as 99.5%. Sex-linked RFLPs, especially DXY segments which share homologous regions in both X and Y chromosome, would be very efficient in paternity exclusion, while RFLPs on mitochondrial DNA would be effective in maternity exclusion in mutation study. Conventional formulae for autosomal as well as sex-linked gene and RFLPs on mitochondrial DNA were summarized.

HLA polymorphism information content (PIC)

To the Editor: Genetically polymorphic loci can be tested for linkage relationships in human pedigrees. While restriction fragment length polymorphisms (RFLPs) are commonly used as genetic markers, HLA complex are also currently employed for establishing linkage with disease in question (e.g. Carroll et aI., 1987). Pedigrees in which inherited traits are known to be segregating can then be analyzed, making possible the mapping of the gene(s) responsible for the trait with respect to HLA haplotype on chromosome 6. For constructing gene map, the polymorphism information content (PIC) developed by Botstein et al. (1980) is the one most often used for linkage analysis. The PIC represents the probability that a given offspring of a random mating between a carrier of a rare dominant gene and a noncarrier is informative for linkage between the locus of the dominant gene and a codominant marker. The PIC may be interpreted in the following manner. If grandparents are not examined for the first child, the PIC is the probability of establishing linkage phase. Once phase is established, it is the probability that an offspring is informative for accepting or rejecting linkage. PIC could be shown in terms of power-sum (Vasuda, 1986) as

The sampling variance of the linkage disequilibrium parameter in multi-allele loci

SummaryThe linkage disequilibrium parameter Δ between two loci has been evaluated for multiple alleles. It shows that when there is random mating and chromosome pairs satisfy Hardy-Weinberg frequencies the disequilibrium between two multi-allele loci is due to unequal frequencies between coupling and repulsion phases in the double heterozygote.The maximum likelihood estimators of Δ and the approximate variance of Δ are given for a large size of sample. A numerical example is also given.

No evidence for linkage between the loci for coagulation factor XIII-A and HLA

SummaryThe linkage analysis between the locus for coagulation factor XIII-A (F13A) and HLA region genes (HLA-A,-C,-B) was performed. In males, the maximum of lod scores between F13A and HLA was 0.33 at θ=0.30, and in females lod scores were negative at all values of θ. The results provided no evidence for close linkage between F13A and HLA genes.

A statistical analysis of the heterogeneity of inherited diseases

SummaryHeterogeneity of inherited diseases could statistically be demonstrated by utilizing a concept of sporadic cases. A model of segregation analysis based on family data was implemented to derive formulae of estimating the proportion of sporadic cases. With an illustrative example of congenital deafness, it is shown that the estimate of the proportion of sporadic cases is rather sensitive to the probability of ascertainment or the method of family selection. While an assumption of single ascertainment leads to an upper limit of the proportion of sporadic cases, another extreme under complete ascertainment yields a lower one. Between two extremes the estimated proportion of sporadics changes nearly linearly for a given set of family data. A proper estimate of the ascertainment probability therefore would be desirable for an appropriate evaluation of the proportions of sporadic cases. When the probability of ascertainment was not available, the proportion of sporadic cases were unable to be estimated properly. However, a suggestion made for accepting hypothesis of no sporadics unless the test was significant under the assumption of single ascertainment. Alternatively, if the test was significant under the assumption of complete ascertainment, it indicates that there would be genetic heterogeneities.

Estimation of the ascertainment probability of rare diseases

SummaryTwo models of ascertainment have been reviewed and maximum likelihood estimates of probabilities are given. Simple formulae were derived for the model of multiple sources of ascertainment per proband. Numerical tables were prepared for the model of proband distribution among affected siblings with illustrative examples. Discussions were made on the ascertainment probability pertaining to the indirect estimation of prevalence as well as incidence of rare diseases.