The primary aim of this thesis is the elucidation of covariate effects on the dependence structure of random variables in bivariate or multivariate models. We develop a unified approach via a conditional copula model in which the copula is parametric and its parameter varies as the covariate. We propose a nonparametric procedure based on local likelihood to estimate the functional relationship between the copula parameter and the covariate, derive the asymptotic properties of the proposed estimator and outline the construction of pointwise confidence intervals. We also contribute a novel conditional copula selection method based on cross-validated prediction errors and a generalized likelihood ratio-type test to determine if the copula parameter varies significantly. We derive the asymptotic null distribution of the formal test. Using subsets of the Matched Multiple Birth and Framingham Heart Study datasets, we demonstrate the performance of these procedures via analyses of gestational age-specific twin birth weights and the impact of change in body mass index on the dependence between two consequent pulse pressures taken from the same subject.

Covariate adjustment is common in the analysis of randomised trials, and can increase statistical power without increasing sample size. Published research on covariate adjustment, and guidance for choosing covariates, focusses on trials where individuals are randomised to treatments. In cluster randomised trials (CRTs) clusters of individuals are randomised. Valid analyses of CRTs account for the structure imposed by cluster randomisation. There is limited published research on the e ects of covariate adjustment, or guidance for choosing covariates, in analyses of CRTs. I summarise existing guidance for choosing covariates in individually randomised trials and CRTs, and review the methods used to investigate the e ects of covariate adjustment. I review the use of adjusted analyses in published CRTs. I use simulation, analytic methods, and analyses of trial data to investigate the e ects of covariate adjustment in mixed models. I use these results to form guidance for choosing covariates in analyses of CRTs. Guidance to choose covariates a priori and adjust for covariates used to stratify randomisation is also applicable to CRTs. I provide guidance speci c to CRTs using linear and logistic mixed models. Cluster size, the intra-cluster correlations (ICCs) of the outcome and covariate, and the strength of the relationship between the outcome and covariate in uence the power of adjusted analyses and the precision of treatment e ect estimates. An a priori estimate of the product of cluster size and the ICC of the outcome can be used to assist choosing covariates. When this product is close to one, adjusting for a cluster level covariate or a covariate with a negligible ICC provide similar increases in power. For smaller values of this product, adjusting for a cluster level covariate gives minimal increases in power. The use of separate withincluster and contextual covariate e ect parameters may increase power further in some circumstances.

The primary aim of this thesis is the elucidation of covariate effects on the dependence structure of random variables in bivariate or multivariate models. We develop a unified approach via a conditional copula model in which the copula is parametric and its parameter varies as the covariate. We propose a nonparametric procedure based on local likelihood to estimate the functional relationship between the copula parameter and the covariate, derive the asymptotic properties of the proposed estimator and outline the construction of pointwise confidence intervals. We also contribute a novel conditional copula selection method based on cross-validated prediction errors and a generalized likelihood ratio-type test to determine if the copula parameter varies significantly. We derive the asymptotic null distribution of the formal test. Using subsets of the Matched Multiple Birth and Framingham Heart Study datasets, we demonstrate the performance of these procedures via analyses of gestational age-specific twin birth weights and the impact of change in body mass index on the dependence between two consequent pulse pressures taken from the same subject.

It is well known that incorporating auxiliary covariates in the analysis of randomized clinical trials (RCTs) can increase efficiency. Questions still remain regarding how to flexibly incorporate baseline covariates while maintaining valid inference. Recent methodological advances that use semiparametric theory to develop covariate-adjusted inference for RCTs have focused on independent outcomes. In biomedical research, however, cluster randomized trials and longitudinal studies, characterized by correlated responses, are commonly used. We develop methods that flexibly incorporate baseline covariates for efficiency improvement in randomized studies with correlated outcomes. In Chapter 1, we show how augmented estimators may be used for cluster randomized trials, in which treatments are assigned to groups of individuals. We demonstrate the potential for imbalance correction and efficiency improvement through consideration of both cluster- and individual-level covariates. To improve small-sample estimation, we consider several variance adjustments. We evaluate this approach for continuous and binary outcomes through simulation and apply it to the Young Citizens study, a cluster randomized trial of a community behavioral intervention for HIV prevention in Tanzania. Chapter 2 builds upon the previous chapter by deriving semiparametric locally efficient estimators of marginal mean treatment effects when outcomes are correlated. Estimating equations are determined by the efficient score under a mean model for marginal effects when data contain baseline covariates and exhibit correlation. Locally efficient estimators are implemented for longitudinal data with continuous outcomes and clustered data with binary outcomes. Methods are illustrated through application to AIDS Clinical Trial Group Study 398, a longitudinal randomized study that compared various protease inhibitors in HIV-positive subjects. In Chapter 3, we empirically evaluate several covariate-adjusted tests of intervention effects when baseline covariates are selected adaptively and the number of randomized units is small. We demonstrate that randomization inference preserves type I error under model selection while tests based on asymptotic theory break down. Additionally, we show that covariate adjustment typically increases power, except at extremely small sample sizes using liberal selection procedures. Properties of covariate-adjusted tests are explored for independent and multivariate outcomes. We revisit Young Citizens to provide further insight into the performance of various methods in small-sample settings.

<p>Background: Post-operative pain management in total joint replacement surgery remains to be ineffective in up to 50% of patients and remains to have overwhelming impacts in terms of patient well-being and healthcare burden. The MOBILE trial was designed to assess whether the addition of gabapentin to a multimodal perioperative analgesia regimen can reduce morphine consumption or improve analgesia of patients following total joint arthroplasty. We present here empirical application of these various statistical methods to the MOBILE trial.</p> <p>Methods: Part 1: Analysis of covariance (ANCOVA) was used to adjust for baseline measures and to provide an unbiased estimate of the mean group difference of the one year post-operative knee flexion scores in knee arthroplasty patients. Robustness test were done by comparing ANCOVA to three comparative methods: i) the post-treatment scores, ii) change in scores, iii) percentage change from baseline.</p> <p>Part 2: Morphine consumption, taken at 4 time periods, of both the total hip and total knee arthroplasty patients was analyzed using linear mixed-effects model (LMEM) to provide a longitudinal estimate of the group difference. Repeated measures ANOVA and generalized estimating equations were used in a sensitivity analysis to compare robustness of the methods. Additionally, robustness of different covariance matrix structures in the LMEM were tested, namely first order auto-regressive compared to compound symmetry and unstructured.</p> <p>Results: Part 1: All four methods showed similar direction of effect, however ANCOVA (-3.9, 95% CI -9.5, 1.6, p=0.15) and post-treatment score (-4.3, 95% CI -9.8, 1.2, p=0.12) method provided the highest precision of estimate compared to change score (-3.0, 95% CI -9.9, 3.8, p=0.38) and percent change (-0.019, 95% CI -0.087, 0.050, p=0.58).</p> <p>Part 2: There was no statistically significant difference between the morphine consumption in the treatment group and the control group (1.0, 95% CI -4.7, 6.7, p=0.73). The results remained robust across different longitudinal methods and different covariance matrix structures.</p> <p>Conclusion: ANCOVA, through both simulation and empirical studies, provides the best statistical estimation for analyzing continuous outcomes requiring covariate adjustment. More wide-spread of the use of ANCOVA should be recommended amongst not only biostatisticians but also clinicians and trialists. The re-analysis of the morphine consumption aligns with the results of the MOBILE trial that gabapentin did not significantly reduce morphine consumption in patients undergoing major replacement surgeries. More work in area of post-operative pain is required to provide sufficient management for this patient population.</p> / Master of Science (MSc)

<p><strong>ABSTRACT</strong></p> <p><strong>Background and Objectives</strong>:<strong> </strong>Informed health care decision making depends on the available evidence base. Where the available evidence comes from different sources methods are required that can synthesise all of the evidence. The synthesis of different types of evidence poses various methodological challenges. The objective of this thesis is to investigate the use of Bayesian methods for combining evidence on effects from randomised and non-randomised studies and additional evidence from the literature with patient level trial data. <strong> </strong></p> <p><strong>Methods</strong>: Using a Bayesian three-level hierarchical model an approach was proposed to combine evidence from randomised and non-randomised studies while adjusting for potential imbalances in patient covariates. The proposed approach was compared to four other Bayesian methods using a case study of endovascular versus open surgical repair for the treatment of abdominal aortic aneurysms. In order to assess the performance of the proposed approach beyond this single applied example a simulation study was conducted. The simulation study examined a series of Bayesian approaches under a variety of scenarios. The subsequent research focussed on the use of informative prior distributions to integrate additional evidence with patient level data in a Bayesian cost-effectiveness analysis comparing endovascular and open surgical repair in terms of incremental costs and life years gained.</p> <p><strong>Results and Conclusions</strong>: The shift in the estimated odds ratios towards those of the more balanced randomised studies, observed in the case study, suggested that the proposed Bayesian approach was capable of adjusting for imbalances. These results were reinforced in the simulation study. The impact of the informative priors in terms of increasing estimated mean life years in the control group, demonstrated the potential importance of incorporating all available evidence in the context of an economic evaluation. In addressing these issues this research contributes to comprehensive evidence based decision making in health care.</p> / Doctor of Philosophy (PhD)