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A Research Report submitted to the Faculty of Science in partial fulfilment of the requirements for the degree of Master of Science. 26 October 2016. / The cost of healthcare has become generally expensive the world over, of which the greater part of the money is spent buying drugs. In order to reduce the cost of drugs, drug manufacturers came up with the idea of manufacturing generic drugs, which cost less as compared to brand name drugs. The challenge which arose was how safe, effective and efficient the generic drugs are compared to the brand name drugs, if people were to buy them. As a consequence of this challenge, bioequivalence studies evolved, being statistical procedures for comparing whether the generic and brand name drugs are similar in treating patients for various diseases. This study was undertaken to show the existence of bioequivalence in drugs. Bioavailability is considered in generic drugs to ensure that it is more or less the same as that of the original drugs by using statistical tests. The United States of America’s Food and Agricultural Department took a lead in the research on coming up with statistical methods for certifying generic drugs as bioequivalent to brand name drugs. Pharmacokinetic parameters are obtained from blood samples after dosing study subjects with generic and brand name drugs. The design for analysis in this research report will be a 2 2 crossover design. Average, population and individual bioequivalence is checked from pharmacokinetic parameters to ascertain as to whether drugs are bioequivalent or not. Statistical procedures used include confidence intervals, interval hypothesis tests using parametric as well as nonparametric statistical methods. On presenting results to conclude that drugs are bioequivalent or not, in addition to hypothesis tests and confidence intervals, which indicates whether there is a difference or not, effect sizes will also be reported. If ever there is a difference between generic and brand name drugs, effect sizes then quantify the magnitude of the difference. KEY WORDS: bioequivalence, bioavailability, generic (test) drugs, brand name (reference) drugs, average bioequivalence, population bioequivalence, individual bioequivalence, pharmacokinetic parameters, therapeutic window, pharmaceutical equivalence, confidence intervals, hypothesis tests, effect sizes. / TG2016

Medical research is often weakened by poor statistical practice, and inappropriate use of statistical computer software is part of this problem. The statistical knowledge that medical researchers require has traditionally been gained in both dedicated and ad hoc learning time, often separate from the research processes in which the statistical methods are applied. Computer software, however, can be written to flexibly support statistical practice. The work of this thesis was to explore the possibility of, and if possible, to create, a resource supporting medical researchers in statistical knowledge and calculation at the point of need. The work was carried out over eleven years, and was directed towards the medical research community in general. Statistical and Software Engineering methods were used to produce a unified statistical computational and knowledge support resource. Mathematically and computationally robust approaches to statistical methods were continually sought from current literature. The type of evaluation undertaken was formative; this included monitoring uptake of the software and feedback from its users, comparisons with other software, reviews in peer reviewed publications, and testing of results against classical and reference data. Large-scale opportunistic feedback from users of this resource was employed in its continuous improvement. The software resulting from the work of this thesis is provided herein as supportive evidence. Results of applying the software to classical reference data are shown in the written thesis. The scope and presentation of statistical methods are considered in a comparison of the software with common statistical software resources. This comparison showed that the software written for this thesis more closely matched statistical methods commonly used in medical research, and contained more statistical knowledge support materials. Up to October 31st 2000, uptake of the software was recorded for 5621 separate instances by individuals or institutions. The development has been self-sustaining. Medical researchers need to have sufficient statistical understanding, just as statistical researchers need to sufficiently understand the nature of data. Statistical software tools may damage statistical practice if they distract attention from statistical goals and tasks, onto the tools themselves. The work of this thesis provides a practical computing framework supporting statistical knowledge and calculation in medical research. This work has shown that sustainable software can be engineered to improve statistical appreciation and practice in ways that are beyond the reach of traditional medical statistical education.

Clinical practice should be based on the best available evidence. Ideally such evidence is obtained through rigorously conducted, purpose-designed clinical studies such as randomised controlled trials and prospective cohort studies. However gathering information in this way requires a massive effort, can be prohibitively expensive, is time consuming, and may not always be ethical or practicable. When answers are needed urgently and purpose-designed prospective studies are not feasible, retrospective healthcare data may offer the best evidence there is. But can we rely on analysis with such data to give us meaningful answers? The current thesis studies this question through analysis with repeated psychological symptom screening data that were routinely collected from over 20,000 outpatients who attended selected oncology clinics in Scotland. Linked to patients’ oncology records these data offer a unique opportunity to study the progress of distress symptoms on an unprecedented scale in this population. However, the limitations to such routinely collected observational healthcare data are many. We approach the analysis within a missing data context and develop a Bayesian model in WinBUGS to estimate the posterior predictive distribution for the incomplete longitudinal response and covariate data under both Missing At Random and Missing Not At Random mechanisms and use this model to generate multiply imputed datasets for further frequentist analysis. Additional to the routinely collected screening data we also present a purpose-designed, prospective cohort study of distress symptoms in the same cancer outpatient population. This study collected distress outcome scores from enrolled patients at regular intervals and with very little missing data. Consequently it contained many of the features that were lacking in the routinely collected screening data and provided a useful contrast, offering an insight into how the screening data might have been were it not for the limitations. We evaluate the extent to which it was possible to reproduce the clinical study results with the analysis of the observational screening data. Lastly, using the modelling strategy previously developed we analyse the abundant screening data to estimate the prevalence of depression in a cancer outpatient population and the associations with demographic and clinical characteristics, thereby addressing important clinical research questions that have not been adequately studied elsewhere. The thesis concludes that analysis with observational healthcare data can potentially be advanced considerably with the use of flexible and innovative modelling techniques now made practicable with modern computing power.

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1.1 The focus of this thesis will be the nexus of statistical methods and clinical practice, as it applies to Critical Care Medicine and is reflected in the literature ( for instance : Anaesthesia and Intensive Care ( Anaesthesia and Intensive Care 2005 ) and Critical Care & Resuscitation ( Critical Care and Resuscitation 2005 ) in Australia ; and internationally : Critical Care Medicine ( Critical Care Medicine 2005 ), Intensive Care Medicine ( Intensive Care Medicine 2005 ), Chest ( Chest 2005 ), American Journal of Respiratory and Critical Care Medicine ( American Journal of Respiratory and Critical Care Medicine 2005 ) and Journal of the American Medical Association ( JAMA 2005 ) ). 1.2 Altman has documented the career of statistics in medical journals over a 20 year period and has lamented the general state of affairs ( Altman 1982 ; Altman 1991b ; Altman 1994 ; Altman 2000 ). The transfer of statistical techniques into medical literature is characterised by a significant lag - time ( Altman et al. 1994b ) and statistical input into medical research and publication, although " widely recommended ... ( is ) ... inconsistently obtained " ( Altman et al. 2002 ), perhaps reflecting an undervaluation of statistical contributions to medicine, as articulated by one of the doyen ' s of biostatistics, Norman Breslow ( Breslow 2003 ). The latter observed that, as opposed to the awarding of a Nobel Prize ( in 2000 ) to econometricians Daniel McFadden and James Heckman for work on discrete choice models and selection bias, similar contributions to medicine by statisticians and epidemiologists have been, as yet, unrecognized. 1.3 Our comparators in statistical " critique " ( Berk 2004 ; BROSS 1960 ) are drawn from analytic approaches, more than thirty years apart. First, the lucid contributions of Jerome Cornfield ( Greenhouse 1982 ) ; in particular : the classic intervention ( in 1959 ) into the tobacco smoking / lung cancer debate " Smoking and lung cancer : recent evidence and a discussion of some questions " ( Cornfield et al. 1959 ) ; and " Further statistical analysis of the mortality findings " of the University Group Diabetes Program ( Cornfield 1971 ), which was an elegant response to the controversy which raged ( for some years ( Kolata 1979 ) ) over the discontinuance of tolbutamide and diet arm in that trial. The textual lucidity to which we refer was presumably a function of the literary background of Cornfield, as documented in the classic review by Salsburg of the rise of the modern statistical paradigm in the twentieth century ( Salsburg 2001 ). Second, the muscular re - examination, or rather, dissection, by Freedman et al ( Freedman et al. 2004 ) of the controversy surrounding breast cancer screening and its efficacy ; being a detailed reading of the meta - analysis by Gotszche and Olsen ( Gotzsche et al. 2000 ), who had questioned the role of mammography in breast cancer screening in terms of potential lives saved. Third, the subtle 1994 reappraisal by Petitti of the mortality treatment effect of patient " compliance " in randomized trials, as it related to both therapy and placebo groups in the Coronary Drug Project ( The Coronary Drug Project Research Group 1981 ) and the Beta - blocker Heart Attack Trial ( Byington 1984 ). The demonstration that the ( cardiovascular ) mortality reduction of compliance with placebo was of the same magnitude as that experienced by users of oestrogen replacement therapy, followed the publication of a quantitative assessment of the of the efficacy of oestrogen on coronary heart disease by Stampfer and Colditz, in which a relative risk of 0.56 ( 95 % CI 0.5 - 0.61 ) was postulated ( Stampfer et al. 1991 ). Petitti ' s review anticipated the null effects ( of replacement oestrogen ) demonstrated in the subsequent randomized trials of the Women ' s Health Initiative ( The Women ' s Health Initiative Study Group 1998 ). These null effects caused extensive debate and some degree of angst in the epidemiological literature and the consequent death of observational epidemiology was rhetorically announced ( Lawlor et al. 2004 ). 1.4 The thesis is divided into two parts: 1.4.1 First, a detailed expository analysis of various questions relating to the interpretation of the results of recent noteworthy trials in the medical and Critical Care literature. Initially we come to terms with the seemingly intractable P - value question which has regularly surfaced in the literature over the years. We also address the thorny but perennial parametric versus non - parametric test controversy. Next we look at the methodology of recent trials in Critical Care and find some problematic areas in terms of interim analyses and the reporting of results. These concerns are expanded into a detailed consideration of the issues surrounding group sequential and equivalence trials. The subsequent section analyses particular aspects of ( i ) effect size ( ii ) prognostic factors and responsiveness ( iii ) sample size, power and interpretation of trials and we conclude ( iv ) with a critique of various aspects of Critical Care practice, as it relates to certain key trials and overviews ( meta - analyses ) of these trials : the PROWESS trial of activated protein C in sepsis ; hypothermia as therapy in cerebral injury ; selective decontamination of the digestive tract ; and nutrition as therapy. 1.4.2 Second, concrete focused analyses are performed on particular datasets and particular statistical techniques are subject to scrutiny. The first encompasses multivariate analysis of phosphate metabolism in ICU patients ; in particular, issues relating to regression to the mean, appropriate estimators ( ordinary least squares or generalized linear models ), model and variable selection, and missing data. The second looks at the analysis of cost data and explores the use of generalized linear models as appropriate estimators. The third introduces time - to - event analysis in and reviews the use of the Cox model and random effects estimators in a data set of patients with malignancies. The fourth is a in depth analysis of three aspects of meta - analysis as it applies in the Critical Care field : heterogeneity, publication bias and metaregression. 1.5 In this endeavour, we are mindful of certain cautions regarding treatment effects : ( i ) it is reasonable to find odds ratio ( s ) below 0.6 " extremely surprising " ( Speigelhalter et al. 2004 ) ( ii ) " If a result appears too good to be true, it probably is " ( Yusuf 1997 ) and ( iii ) we may " require that data indicate an increased relative risk for a characteristic of at least 50 percent, on the assumption that an excess of this magnitude would not arise from extraneous factors alone " ( Mantel et al. 1959 ). The latter proposition was first articulated in 1959 by Mantel and Haenszel, but needed to be reiterated ( by Mantel ) some thirty four years later ( Mantel 1993 ). Finally, we endorse the admonition of Jerome Cornfield that " Any set of hospital or clinical data that is worth analysing at all is worth analysing properly " ( Cornfield 1951). 1.6 The importance of statistical principles in both the interpretation and conduct of analysis would seem to be obvious and we must " grapple " with statistics in the same manner as Appleby urged with respect to health economics ( Appleby 1987 ). To this extent, the evidence - based - medicine movement has mandated " critical appraisal ", which incorporates, to varying degree, statistical methods ( Morris 2002b ) and at least one prominent medical journal has recently welcomed papers " detailing important contributions in the design of studies or analysis of epidemiological data " ( Dominici et al. 2004 ). Thus statistics is increasingly engaged with " front - line science " ( Efron 2005 ) and these recent trends prefigure the overall thrust of the sections below. / Thesis (M.D.) -- University of Adelaide, School of Medicine, Discipline of Medicine,

Thesis (M.A.) in Mathematics--University of Maine, 2004. / Includes vita. Includes bibliographical references (leaf 51).

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Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Operations Research." Includes bibliographical references (p. 134-143).