Asymmetry and other distributional properties in medical research data

Partlett, Christopher (2015). Asymmetry and other distributional properties in medical research data. University of Birmingham. Ph.D.

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The central theme of this thesis is to investigate the use of non-parametric methods for making inferences about a random sample with an unknown distribution function.The overarching aim is the development of new methods to make inferences regarding the nature of the unknown distribution to enhance medical research. Initially,the focus is exclusively on the asymmetry of a random variable. In particular, a recently proposed measure of asymmetry provides the foundation for the proposal and development of a new test for symmetry. The potential applications of the test and measure are applied to a number of medical research settings including randomised trials. Moreover, guidance is provided on its implementation, with particular emphasis on the problem of small sample estimation.

This investigation is then generalised to examine asymmetry across multiple studies. In particular, meta-analysis methods are used to synthesise information about the amount of asymmetry in several studies. Further, a detailed simulation study is carried out to investigate the impact of asymmetry on linear models and meta-analyses of randomised trials, in terms of the accuracy of the treatment effect estimate and the coverage of confidence and prediction intervals.

Finally, the scope of the investigation is widened to encompass the problem of comparing and synthesising information about the probability density function and cumulative distribution function, based on samples from multiple studies. The meta-analysis of the smooth distribution function estimate is then applied to propose new methods for conducting meta-analyses of diagnostic test accuracy, which have a number of merits compared to the existing methodology.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: None/not applicable
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics


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