School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableThe impact of low-cost, genome-wide resequencing on association studies.(Springer Science and Business Media LLC, 2005-06)
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ItemEFFICIENT POOLING DESIGNS FOR LIBRARY SCREENING(ACADEMIC PRESS INC ELSEVIER SCIENCE, 1995-03-01)We describe efficient methods for screening clone libraries, based on pooling schemes that we call "random k-sets designs." In these designs, the pools in which any clone occurs are equally likely to be any possible selection of k from the v pools. The values of k and v can be chosen to optimize desirable properties. Random k-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, and easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only one pass, thus facilitating automation. For design comparison, we assume a binomial distribution for the number of "positive" clones, with parameters n, the number of clones, and c, the coverage. We propose the expected number of resolved positive clones--clones that are definitely positive based upon the pool assays--as a criterion for the efficiency of a pooling design. We determine the value of k that is optimal, with respect to this criterion, as a function of v, n, and c. We also describe superior k-sets designs called k-sets packing designs. As an illustration, we discuss a robotically implemented design for a 2.5-fold-coverage, human chromosome 16 YAC library of n = 1298 clones. We also estimate the probability that each clone is positive, given the pool-assay data and a model for experimental errors.
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ItemOptimal pooling designs with error detection(ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, 1996-04)Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive pooling (or group testing) problem involves identifying the bad objects using the least number of tests applied in parallel. The `hypergeometric' case occurs when an upper bound on the number of bad objects is known {\em a priori}. Here, practical considerations lead us to impose the additional requirement of {\em a posteriori} confirmation that the bound is satisfied. A generalization of the problem in which occasional errors in the test outcomes can occur is also considered. Optimal solutions to the general problem are shown to be equivalent to maximum-size collections of subsets of a finite set satisfying a union condition which generalizes that considered by Erd\"os \etal \cite{erd}. Lower bounds on the number of tests required are derived when the number of bad objects is believed to be either 1 or 2. Steiner systems are shown to be optimal solutions in some cases.
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ItemGametic phase estimation over large genomic regions using an adaptive window approach.(Springer Science and Business Media LLC, 2003-11)The authors present ELB, an easy to programme and computationally fast algorithm for inferring gametic phase in population samples of multilocus genotypes. Phase updates are made on the basis of a window of neighbouring loci, and the window size varies according to the local level of linkage disequilibrium. Thus, ELB is particularly well suited to problems involving many loci and/or relatively large genomic regions, including those with variable recombination rate. The authors have simulated population samples of single nucleotide polymorphism genotypes with varying levels of recombination and marker density, and find that ELB provides better local estimation of gametic phase than the PHASE or HTYPER programs, while its global accuracy is broadly similar. The relative improvement in local accuracy increases both with increasing recombination and with increasing marker density. Short tandem repeat (STR, or microsatellite) simulation studies demonstrate ELB's superiority over PHASE both globally and locally. Missing data are handled by ELB; simulations show that phase recovery is virtually unaffected by up to 2 per cent of missing data, but that phase estimation is noticeably impaired beyond this amount. The authors also applied ELB to datasets obtained from random pairings of 42 human X chromosomes typed at 97 diallelic markers in a 200 kb low-recombination region. Once again, they found ELB to have consistently better local accuracy than PHASE or HTYPER, while its global accuracy was close to the best.