Bivariate analyses of cholesterol and triglyceride levels in families in which probands have type IIb lipoprotein phenotype.

Univariate and bivariate analyses of cholesterol and triglycerides are performed after appropriate age adjustment on 247 individuals in 33 families where the probands have elevations of cholesterol, low density lipoprotein and triglycerides, and type IIb lipoprotein phenotype. Mixture of lognormal distributions are fitted by maximum likelihood to the data. Best fitting single and mixtures of lognormal distributions are compared with empirical cumulative plots, and the likelihood-ratio criterion is used to test for significance. A mixture of two lognormal distributions fits significantly better than one lognormal distribution for cholesterol but not for triglycerides. When a mixture of bivariate lognormals is fitted to the data, only one local maximum is found, suggesting action of a single genetic determinant in this sample. The best cutoff line is almost parallel to the triglyceride axis, indicating the relatively high involvement of cholesterol compared to triglycerides in separating the normal and abnormal groups. Using the best linear function, the difference in the two bivariate means is found to account for 61% of the total variation in log cholesterol and log triglycerides. To determine if the results are due to enrichment of the sample with familial hypercholesterolemia syndrome, seven families where the proband and/or any relative has tendon xanthomas are removed and the analyses repeated on the remaining 26 kindreds. The results of these analyses are virtually the same as those of the total sample. Also, a subsample of 21 families in which the proband and at least one additional kindred member are affected is analyzed in the same manner with similar results. For comparison, data from a study of families with combined hyperlipidemia [1] are analyzed in an analogous manner, bearing in mind that the populations sampled are probably different. Fitting a mixture of two bivariate distributions and finding the best cutoff to these data indicate that triglycerides are more involved in separating the two groups. Probably because of major differences in ascertainment, the distribution of lipid levels in oour patient group is practically indistinguishable from that of hypercholesterolemia, and the Seattle data [1] are more nearly similar to hypertriglyceridemia. It may be premature to consider familial combined hyperlipidemia as an entity distinct from both hypercholesterolemia and hypertriglyceridemia. We hope it will eventually be possible to analyze these data using a refined genetic model that includes both major gene and polygenic effects and to combine this form of analysis with quantitative tissue culture methods.     

An efficient algorithm to compute the posterior genotypic distribution for every member of a pedigree without loops

This paper describes a non-iterative, recursive method to compute the likelihood for a pedigree without loops, and hence an efficient way to compute genotype probabilities for every member of the pedigree. The method can be used with multiple mates and large sibships. Scaling is used in calculations to avoid numerical problems in working with large pedigrees.