A. P. Morris

Fine-Scale Mapping of Disease Loci via Shattered Coalescent Modeling of Genealogies

We present a Bayesian, Markov-chain Monte Carlo method for fine-scale linkage-disequilibrium gene mapping using high-density marker maps. The method explicitly models the genealogy underlying a sample of case chromosomes in the vicinity of a putative disease locus, in contrast with the assumption of a star-shaped tree made by many existing multipoint methods. Within this modeling framework, we can allow for missing marker information and for uncertainty about the true underlying genealogy and the makeup of ancestral marker haplotypes. A crucial advantage of our method is the incorporation of the shattered coalescent model for genealogies, allowing for multiple founding mutations at the disease locus and for sporadic cases of disease. Output from the method includes approximate posterior distributions of the location of the disease locus and population-marker haplotype proportions. In addition, output from the algorithm is used to construct a cladogram to represent genetic heterogeneity at the disease locus, highlighting clusters of case chromosomes sharing the same mutation. We present detailed simulations to provide evidence of improvements over existing methodology. Furthermore, inferences about the location of the disease locus are shown to remain robust to modeling assumptions.

Bayesian Fine-Scale Mapping of Disease Loci, by Hidden Markov Models

We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers-in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain-Monte Carlo simulation methods, we obtain posterior distributions of model parameter estimates including disease-gene location and the age of the disease-predisposing mutation. In addition, we allow for heterogeneity in recombination rates, across the candidate region, to account for recombination hot and cold spots. We also obtain, for the ancestral marker haplotype, a posterior distribution that is unique to our method and that, unlike maximum-likelihood estimation, can properly account for uncertainty. We apply the method to data for cystic fibrosis and Huntington disease, for which mutations in disease genes have already been identified. The new method performs well compared with existing multi-locus mapping methods.

Randomization tests of disease-marker associations.

A powerful test for population association of a disease with alleles at a bi‐allelic marker locus is the transmission/disequilibrium test (TDT). A generalization of the test to multi‐allelic marker locus is proposed which utilizes the maximal association of individual alleles with the disease, given by the maximum TDT statistic, TDT(max). To overcome the multiple testing problem encountered when using the maximal association to test the null hypothesis of no disease‐marker association, a randomization procedure is developed. An investigation of the power of the test suggests that the randomization procedure performs almost as well as a recently proposed likelihood based test of linkage disequilibrium. The advantage of the new test is that it can be applied sequentially, based on a one‐sided version of the TDT statistic, for investigating patterns of association of several individual alleles with the disease.

A likelihood ratio test for detecting patterns of disease-marker association

A likelihood ratio test of disease‐marker association is proposed, based on the observation of marker alleles transmitted from parents to affected children. The proposed association test has the advantage of identifying the population pattern of disease‐marker association, differentiating between marker alleles that are positively and negatively associated with the disease. The power of the test for detecting association is evaluated and compared with three existing multi‐allelic tests for some specific disease‐marker association patterns. The power of the parametric tests depends crucially on the pattern of disease‐marker association. An over‐parameterised association model is less detrimental in terms of power than an under parameterised model.

The problems of using the transmission/disequilibrium test to infer tight linkage.

Family-based association methods such as the transmission/disequilibrium test (TDT) have become very popular during the past few years, often being preferred to case-control studies because family-based approaches avoid the difficulties of ascertainment of appropriate populations of cases and controls for case-control studies. Significant TDT results indicate both linkage and allelic association. However, significant TDT results are often interpreted as implying tight linkage of marker and disease locus, and we shall argue here that, in general, this interpretation is not justified.

Locating genes involved in human diseases

The increasing amount of information that is becoming available about the structure and composition of the DNA constituting the human chromosomes has provided new opportunities to locate genes that affect susceptibilities to a range of diseases. The accurate location of these genes is important in genetic counselling and in understanding the effects of genes that may result in disease. Various methods of analysing the data when DNA information is available at a single marker locus for an affected child and his or her parents are reviewed and applied to data on insulin-dependent diabetes mellitus. The importance of distinguishing between the association of alleles at a marker locus and at a disease locus resulting from chromosomal linkage from that resulting from other causes is emphasized.

Using information from both parents when testing for association between marker and disease loci

Several extensions of the transmission/disequilibrium test (TDT) to multi‐allelic markers now exist. In some of these, however, separate tests must be performed on male and female parents because of the non‐independence of parental transmission patterns, reducing power, and complicating interpretation of the test results. Here we show that this non‐independence is asymptotically irrelevant when using the allelic TDT of Bickeböller and Clerget‐Darpoux [(1995) Genet Epidemiol 12:577–582], allowing the analysis of data from both parents simultaneously. Genet. Epidemiol. 15:193–200,1998.

Fine scale association mapping of disease loci using simplex families.

We present a new method for the fine scale mapping of disease loci based on samples of simplex families, each containing an affected child. The method is based on a generalisation of a single locus allele transmission model to multiple marker loci. The model is developed under the assumption of a single ancestral mutation and allows for the calculation of posterior probabilities that each allele at a particular marker was present on the founder chromosome. We illustrate the method using simulated family data for cystic fibrosis and Huntingtons disease, for which the locations of mutations in the disease genes are now known. For both diseases, our new method provides good estimates of the location of the mutations.

Pooling DNA in the identification of parents

The preliminary pooling of DNA samples to reduce the number of tests required to identify which of a set of potential parents could be the parent of an individual progeny plant is discussed. The progeny plant may be homozygous or heterozygous at the marker locus involved and the marker alleles of the other parent plant may or may not be known. The expected number of tests is derived for varying pool sizes when the DNA of each parent plant is in one and only one DNA pool. Optimal pool sizes are calculated for a range of number of potential parents and of marker allele frequencies. Designs with each parent in more than one pool and the sequential use of up to three independent marker loci are also discussed.