School of Mathematics and Statistics - Research Publications
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ItemCERVICAL CYTOLOGY REPORTED AS NEGATIVE AND RISK OF ADENOCARCINOMA OF THE CERVIX - NO STRONG EVIDENCE OF BENEFIT(NATURE PUBLISHING GROUP, 1995-04)The relationship between negative cervical cytology reports and risk of adenocarcinoma of the cervix was evaluated in a case-control study of 113 cases and 452 controls. All cases and controls had received at least two negative cytology reports. There was no significant difference between the cases and controls in the number of negative cytology reports or in history of cervical abnormality; while a test for trend in the time since last negative cytology report was significant (P < 0.001), the estimated benefit was very modest. Although the estimates of relative protection were higher in women aged less than 35 years than in women aged 35-69 years, this difference was not statistically significant. These results suggest that cervical screening as practised in the 1970s and 1980s was much less effective in preventing adenocarcinoma than squamous carcinoma of the cervix.
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ItemThe cost of breast cancer recurrences.(Springer Science and Business Media LLC, 1992-03)Information about the costs of recurrent breast cancer is potentially important for targeting cost containment strategies and analysing the cost-effectiveness of breast cancer control programmes. We estimated these costs by abstracting health service and consumable usage data from the medical histories of 128 patients, and valuing each of the resources used. Resource usage and costs were summarised by regarding the recurrence as a series of episodes which were categorised into five anatomical site-based groups according to the following hierarchy: visceral, central nervous system (CNS), bone, local and other. Hospital visits and investigations comprised 78% of total costs for all episodes combined, and there were significant differences between the site-based groups in the frequency of hospital visits and most investigations. Total costs were most accurately described by separate linear regression models for each group, with the natural logarithm of the cost of the episode as the dependent variable, and predictor variables including the duration of the episode, duration squared, duration cubed and a variable indicating whether the episode was fatal. Visceral and CNS episodes were associated with higher costs than the other groups and were more likely to be shorter and fatal. A fatal recurrence of duration 15.7 months (the median for our sample) was predicted to cost $10,575 (Aus + 1988; or 4,877 pounds). Reduction of the substantial costs of recurrent breast cancer is likely to be a sizable economic benefit of adjuvant systemic therapy and mammographic screening. We did not identify any major opportunities for cost containment during the management of recurrences.
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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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ItemInterpolation theorems for the f-chromatic index of multigraphs(World Scientific, 1994)
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ItemOptimal labelling of unit interval graphs(Springer Science and Business Media LLC, 1995-09)
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ItemDISJOINT HAMILTONIAN CYCLES IN FAN 2K-TYPE GRAPHS(JOHN WILEY & SONS INC, 1993-12)
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ItemUnifying approaches for constructing labeled graphs from known ones(MD Publications PVT LTD, 1995)
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ItemMATROID TREE GRAPHS AND INTERPOLATION THEOREMS(ELSEVIER SCIENCE BV, 1995-01-20)
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ItemOn f-domination number of a graph(CZECHOSLOVAK MATHEMATICAL JOURNAL, 1996)