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A method is proposed for block randomization of treatments to experimental units that can accommodate both multiple quantitative blocking variables and unbalanced designs. Hierarchical clustering in conjunction with leaf-order optimization is used to block experimental units in multivariate space. The method is illustrated in the context of a diabetic mouse assay. A simulation study is presented to explore the utility of the proposed randomization method relative to that of a completely randomized approach, both in the presence and absence of covariate adjustment. An example R function is provided to illustrate the implementation of the method.

The traditional likelihood-based approach to hypothesis testing may not be an optimal strategy for evaluating oligogenic models of inheritance. Under oligogenic inheritance the number of possible multilocus models can become very large; there may be several competing linkage models having similar likelihoods; and comparisons among non-nested models can be required to determine if a given multilocus model provides a significantly better fit to observed phenotypic variation than an alternative model. We propose an efficient Bayesian approach to oligogenic model selection that makes use of existing model likelihoods, and show how model uncertainty can be incorporated into parameter estimation.

We propose a constrained permutation test that assesses the significance of an observed quantitative trait locus effect against a background of genetic and environmental variation. Permutations of phenotypes are not selected at random, but rather are chosen in a manner that attempts to maintain the additive genetic variability in phenotypes. Such a constraint maintains the nonindependence among observations under the null hypothesis of no linkage. The empirical distribution of the lod scores calculated using permuted phenotypes is compared to that obtained using phenotypes simulated from the assumed underlying multivariate normal model. We make comparisons of univariate analyses for both a quantitative phenotype that appears consistent with a multivariate normal model and a quantitative phenotype containing pronounced outliers. An example of a bivariate analysis is also presented.