George E. Bonney

Compound regressive models for family data

The regressive models for the analysis of family data are extended to include cases in which the within-sibship covariation may exceed that implied by the class A regressive model, but for which birth order is not required. In addition to specified major genes, if any, and common parental phenotypes, the excess within-sibship covariation may come from a common cumulative risk from unspecified factors such as a shared environment, and other genes. The within-sibship cumulative risk has a probability distribution in the population. The sib-sib correlation (more generally within-sibship statistical dependence) is equal for all pairs within a given sibship. The compound regressive model is thus a version of the class D regressive model with the property of within-sibship interchangeability. The work is motivated here by comparing and contrasting the Elston-Stewart algorithm and the Morton-MacLean algorithm for the mixed model of inheritance. This points the way to derive practical algorithms for the compound regressive models proposed, with easy extensions to pedigrees of arbitrary structure, and to multilocus problems.

Genetic Analysis Combining Path Analysis with Regressive Models: The TAU Model of Multifactorial Transmission

We have extended regressive models by incorporating a simple path model (the TAU model). This was achieved for both class A and class D regressive models by expressing the residual correlations in the regressive models in terms of parameters of the path model. We have presented explicit solutions for path coefficients in terms of the residual correlations. These methods were applied to a French-Canadian family study on body mass index. It was found that the estimate of pseudopolygenic heritability was robust under class A (t2 = 0.28) and class D (t2 = 0.26) models.

The Use of Logistic Models for the Analysis of Codon Frequencies of DNA Sequences in Terms of Explanatory Variables

The development of the regressive logistic model applicable to the analysis of codon frequencies of DNA sequences in terms of explanatory variables is presented. A codon is a triplet of nucleotides that code for an amino acid, and may be considered as a trivariate response (B1, B2, B3), where Bi (i = 1, 2, 3) is a categorical random variable with values A, C, G, T. The linear order of bases in the DNA and possible statistical dependence of the bases in a given codon make the regressive logistic model a suitable tool for the analysis of codon frequencies. A problem of structural zeros arises from the fact that the stopping codons (terminators) do not code for amino acids; this is solved by normalizing the likelihood function. Codon frequencies may also depend on the function of the gene and they are known to differ between genes of the same genome. Differences also occur between synonymous codons for the same amino acid. Thus, the use of covariates that differ between synonymous codons as well as covariates that are constant within codons of the same amino acid may be useful in explaining the frequencies. As an illustration, the method is applied to the human mitochondrial genome using the following as explanatory variables: (1) TSCORE, a measure of the number of single base mutations required for a given codon to become a terminator; (2) AARISK, an indicator of a codons ability of changing by a single base substitution to triplets coding for amino acids with very different characteristics; (3) AVDIST, a measure of the typicality of the amino acid coded for by the triplets. The results indicate that models that incorporate dependency structure and covariates are to be preferred to either the models comprising covariates alone or dependency structure alone.