# School of Mathematics and Statistics - Research Publications

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Now showing 1 - 2 of 2
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EFFICIENT POOLING DESIGNS FOR LIBRARY SCREENING
BRUNO, WJ ; KNILL, E ; BALDING, DJ ; BRUCE, DC ; DOGGETT, NA ; SAWHILL, WW ; STALLINGS, RL ; WHITTAKER, CC ; TORNEY, DC (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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Optimal pooling designs with error detection
Balding, DJ ; Torney, DC (ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, 1996-04-01)
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.