John Molitor

Markov chain Monte Carlo without likelihoods

Many stochastic simulation approaches for generating observations from a posterior distribution depend on knowing a likelihood function. However, for many complex probability models, such likelihoods are either impossible or computationally prohibitive to obtain. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods. It can also be used in frequentist applications, in particular for maximum-likelihood estimation. The approach is illustrated by an example of ancestral inference in population genetics. A number of open problems are highlighted in the discussion.

Genome-Wide Association Mapping in Arabidopsis Identifies Previously Known Flowering Time and Pathogen Resistance Genes

There is currently tremendous interest in the possibility of using genome-wide association mapping to identify genes responsible for natural variation, particularly for human disease susceptibility. The model plant Arabidopsis thaliana is in many ways an ideal candidate for such studies, because it is a highly selfing hermaphrodite. As a result, the species largely exists as a collection of naturally occurring inbred lines, or accessions, which can be genotyped once and phenotyped repeatedly. Furthermore, linkage disequilibrium in such a species will be much more extensive than in a comparable outcrossing species. We tested the feasibility of genome-wide association mapping in A. thaliana by searching for associations with flowering time and pathogen resistance in a sample of 95 accessions for which genome-wide polymorphism data were available. In spite of an extremely high rate of false positives due to population structure, we were able to identify known major genes for all phenotypes tested, thus demonstrating the potential of genome-wide association mapping in A. thaliana and other species with similar patterns of variation. The rate of false positives differed strongly between traits, with more clinal traits showing the highest rate. However, the false positive rates were always substantial regardless of the trait, highlighting the necessity of an appropriate genomic control in association studies.

Effects of simultaneous over-expression of Cu/ZnSOD and MnSOD on Drosophila melanogaster life span.

The FLP-out technique, based on yeast FLP recombinase, allows induced over-expression of transgenes in Drosophila adults. With FLP-out control and over-expressing flies have identical genetic backgrounds and therefore differences in life span must result from transgene induction. The amount of over-expression achieved varies between independent transgenic lines, and previously for both Cu/ZnSOD and MnSOD life span was found to be increased in proportion to the increase in enzyme activity. To determine if greater increases in enzyme and life span could be achieved with FLP-out, enzyme over-expression and life span were analyzed in eight lines containing two MnSOD transgenes, three lines containing three MnSOD transgenes, and three lines containing a MnSOD transgene plus a Cu/ZnSOD transgene. Life span was again found to be increased in proportion to the increase in MnSOD enzyme activity, with increases of up to 40% in mean and maximum life span. However the increases in enzyme activity and life span conferred per transgene were reduced when more than one transgene was present at the same time. When the reduced efficiency of enzyme over-expression per transgene was taken into account, simultaneous over-expression of MnSOD and Cu/ZnSOD was found to have partially additive effects on life span.

Bayesian Modeling of Complex Metabolic Pathways

Many chronic diseases are the result of a complex sequence of biochemical reactions involving exposures to various environmental agents, metabolized by a number of different genes. Routine epidemiologic analyses of such associations have tended to rely on standard contingency table or logistic regression methods, typically focusing on one variable at a time or pairwise combinations. We consider two statistical alternatives to this approach, one based on Bayesian model averaging, one based on pharmacokinetic modeling of the biochemical pathways. These approaches are illustrated using data from a case-control study of colorectal polyps in relation to tobacco smoking and consumption of well done red meat, both viewed as sources of heterocyclic amines and polycyclic aromatic hydrocarbons. The new analyses are structured in a manner that attempts to take advantage of prior knowledge of the metabolism of these classes of compounds and the various genes that regulate these pathways.

Adenomyosis: A clinical and pathologic appraisal

Abstract Over a ten-year period on a private hospital service, adenomyosis was encountered in 281 cases or 8.8 per cent of the surgically removed uteri. In 71 per cent of these patients, the symptoms were due to or contributed to by the adenomyosis, yet the disease was diagnosed or mentioned preoperatively in only 23 per cent of cases. The ectopic endometrium showed functional response over all in 33 per cent of cases where this could be evaluated and secretory response to ovarian progesterone in 26.6 per cent of cases where the surface endometrium was secretory. Functionally active ectopic endometrium, however, did not always produce clinical symptoms. Sixty-seven patients had a history of treatment with synthetic progestins, and pseudodecidual change in the ectopic endometrial islands was demonstrated in some of these. The symptoms of the disease were not alleviated, and no evidence was found in this study that the widespread use of these drugs in the last decade has altered the clinical picture of adenomyosis.

Bayesian spatial modeling of haplotype associations.

We review methods for relating the risk of disease to a collection of single nucleotide polymorphisms (SNPs) within a small region. Association studies using case-control designs with unrelated individuals could be used either to test for a direct effect of a candidate gene and characterize the responsible variant(s), or to fine map an unknown gene by exploiting the pattern of linkage disequilibrium (LD). We consider a flexible class of logistic penetrance models based on haplotypes and compare them with an alternative formulation based on unphased multilocus genotypes. The likelihood for haplotype-based models requires summation over all possible haplotype assignments consistent with the observed genotype data, and can be fitted using either Expectation-Maximization (E-M) or Markov chain Monte Carlo (MCMC) methods. Subtleties involving ascertainment correction for case-control studies are discussed. There has been great interest in methods for LD mapping based on the coalescent or ancestral recombination graphs as well as methods based on haplotype sharing, both of which we review briefly. Because of their computational complexity, we propose some alternative empirical modeling approaches using techniques borrowed from the Bayesian spatial statistics literature. Here, space is interpreted in terms of a distance metric describing the similarity of any pair of haplotypes to each other, and hence their presumed common ancestry. Specifically, we discuss the conditional autoregressive model and two spatial clustering models: Potts and Voronoi. We conclude with a discussion of the implications of these methods for modeling cryptic relatedness, haplotype blocks, and haplotype tagging SNPs, and suggest a Bayesian framework for the HapMap project.

A survey of current Bayesian gene mapping method

Recently, there has been much interest in the use of Bayesian statistical methods for performing genetic analyses. Many of the computational difficulties previously associated with Bayesian analysis, such as multidimensional integration, can now be easily overcome using modern high-speed computers and Markov chain Monte Carlo (MCMC) methods. Much of this new technology has been used to perform gene mapping, especially through the use of multi-locus linkage disequilibrium techniques. This review attempts to summarise some of the currently available methods and the software available to implement these methods.

Fine mapping – 19th century style

BackgroundThere is great interest in the use of computationally intensive methods for fine mapping of marker data. In this paper we develop methods based upon ideas originally proposed 100 years ago in the context of spatial clustering.MethodsWe use spatial clustering of haplotypes as a low-dimensional surrogate for the unobserved genealogy underlying a set of genotype data. In doing so we hope to avoid the computational complexity inherent in explicitly modelling details of the ancestry of the sample, while at the same time capturing the key correlations induced by that ancestry at a much lower computational cost.ResultsWe benchmark our methods using the simulated Genetic Analysis Workshop 14 data, using 100 replicates of 4 phenotypes to indicate the power of our method. When a functional mutation relating to a trait is actually present, we find evidence for that mutation in 97 out of 100 replicates, on average.ConclusionOur results show that our method has the ability to accurately infer the location of functional mutations from unphased genotype data.