Studies on quasi-continuity

Abstract

This study was an attempt to fit a model of quasi-continuous variation to three sets of data. The model is based on the assumption that the trait under study is completely additive and wholly polygenic. Conditions due to a major gene, in the sense of classical Mendelian inheritance, would give unreasonable parameter estimates and a poor fit on such a model. Information on population prevalence and recurrence in sibs is used to estimate the parameters and predict risk for other degrees of relationship. Records on all surgically corrected cases of pyloric stenosis occurring in the period 1942 to 1966 in Hawaii provided the first set of data. Nearly 200 families were interviewed to obtain a pedigree and family history. Birth certificate numbers were matched with a file of all births for that time period to provide additional information on race and sociological variables. The sex ratio was similar to all earlier reports, approximately 4:1. The segregation analysis was compatible with a major gene hypothesis but the estimates had very large standard errors. The regression analysis of interracial crosses indicated a depression in the frequency in F1, indicative of recessivity. The fit to the model of quasi-continuity was neither good nor consistent. Such a theory cannot be eliminated as the possible genetic mechanism for pyloric stenosis, but the current model is inadequate to explain the data. Males with serum cholesterol levels greater than two standard deviations above the mean of a random sample of 7,000 forty to sixty year old Japanese males were selected for a study of hypercholesterolemia. Sibs were contacted, interviewed and serum cholesterol determinations made. The 219 sibships were analyzed by segregation analysis, providing an estimate of the segregation frequency of 0.52 and the proportion of sporadics as zero, evidence for a dominant gene. Estimates of heritability on the additive model exceeded 1.5. This condition appears to be a dominant gene with nearly complete penetrance. This finding is in agreement with other studies. Information from the Bureau of Identification provided a sample of individuals with a dermal ridge count of zero, an arch pattern on all ten fingers. These individuals were defined as "affected." Ridge counts were made for all available relatives. A control sample was selected from the Bureau files. The frequency of patterns and mean ridge counts for the Caucasian controls agreed well with published studies from England. The Japanese had higher mean counts and a significantly higher frequency of whorls. Correlation coefficients computed in the control sample for sib-sib and parent-child relationships agreed well with complete heritability. Segregation analysis in both the affected families and the controls failed to detect segregation of a major gene. Parameters were estimated for the quasi-continuous model using data from first degree relatives. Fitting these estimates to data from cousins and second degree relatives gave a non-significant deviation. Evidence from earlier studies has shown fairly conclusively that dermal ridge count is additive and multifactorial. The good fit of our data to this model of quasi-continuity was reassuring. Hypercholesterolemia, on the other hand, seems clearly due to a major gene. The failure to fit the data on pyloric stenosis may only reflect inefficient parameter estimates and lack of sufficient sophistication or accuracy in the current model.