A Copula-Based Method for Analyzing Bivariate Binary Longitudinal Data

The work presented as part of this dissertation is primarily motivated by a randomized trial for HIV serodiscordant couples. Specifically, the Multisite HIV/STD Prevention Trial for African American Couples is a behavioral modification trial for African American, heterosexual, HIV discordant couples. In this trial, investigators developed and evaluated a couple-based behavioral intervention for reducing risky shared sexual behaviors and collected retrospective outcomes from both partners at baseline and at 3 follow-ups to evaluate the intervention efficacy. As the outcomes refer to the couples\u27 shared sexual behavior, couples\u27 responses are expected to be correlated, and modeling approaches should account for multiple sources of correlation: within-individual over time as well as within-couple both at the same measurement time and at different times. This dissertation details the novel application copulas to modeling dyadic, longitudinal binary data to estimate reliability and efficacy. Copulas have long been analytic tools for modeling multivariate outcomes in other settings. Particularly, we selected a mixture of max-infinitely divisible (max-id) copula because it has a number of attractive analytic features. The dissertation is arranged as follows: Chapter 2 presents a copula-based approach in estimating the reliability of couple self-reported (baseline) outcomes, adjusting for key couple-level baseline covariates; Chapter 3 presents an extension of the max-id copula to model longitudinal (two measurement occasions), binary couples data; Chapter 4 further extends the copula-based model to accommodate more than two repeated measures in a different application examining two clinical depression measures. In this application, we are interested in estimating whether there are differential treatment effects on two different measures of depression, longitudinally. The copula-based modeling approach presented in this dissertation provides a useful tool for investigating complex dependence structures among multivariate outcomes as well as examining covariate effects on the marginal distribution for each outcome. The application of existing statistical methodology to longitudinal, dyad-based trials is an important translational advancement. The methods presented here are easily applied to other studies that involve multivariate outcomes measured repeatedly

Concepts for the construction of confidence intervals for measuring stability after hallux vulgus surgery: theoretical development and application.

Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.The absolute change in the corrected angle measured immediately after surgery and after bone healing is a clinically relevant endpoint to judge an osteotomy's stability. The primary objective of this research is to illustrate the non-inferiority of a novel screw used for fixation of the osteotomy compared with a standard screw. If the difference in the angles after surgery and after bone healing can be assumed to be normally distributed, the absolute change follows the folded normal distribution. The most natural approach to present the clinical study results is using a confidence interval to compare two folded normal distributions. We construct a confidence interval to compare two independent folded normal distributions using the ratio of two chi-square random variables, the difference of two chi-square distribution, and the bootstrap method. We illustrate the approaches from a study on hallux valgus osteotomy. The proposed confidence intervals permit an investigation of the noninferiority for the two treatment groups in clinical trials with end points following a folded normal distribution. The application to real data results indicates that the confidence interval for the ratio of two chi-squares random variable and bootstrap is straightforward and easy to calculate. Bootstrapping was asymptotically more accurate than the standard interval obtained from samples that assume normality. Also, it was an appropriate way to ascertain the stability of the results. Judging by δ of the bootstrap method, we establish non-inferiority for the new surgical method. In conclusion, the approaches are promising, and we recommend them for use to compare other practical data that require the use of the folded normal distribution

Application of levy processes to unitised with-profits policies

The objective of this thesis is to develop more realistic long term asset models based on L´evy processes and discuss their applications to risk management of unitised with-profits policies. We investigate the behaviour of long-term returns of the UK total share return index by testing the common statistical properties for financial data, so-called “stylised facts”. We show that for the monthly U.K. share total return indices, the Gaussian return hypothesis is rejected in series of tests. The local distribution of the returns has higher kurtosis and heavier tails than the Gaussian. In addition, the returns series show significant nonlinear autocorrelation, extreme returns appear in clusters. The first long term asset model purposed in this thesis is the exponential L´evy model with non-Gaussian increment. We describe the Generalised Hyperbolic distributions with their subclasses. They are considered as candidate distributions for the increments of the driving L´evy processes. We estimate model parameters to the UK share gross total return index using two approaches, maximum likelihood (MLE) and Markov Chain Monte Carlo (MCMC) algorithm. Statistical and graphical goodness-of-fit tests demonstrate that these L´evy driven models give more accurate fits to the historical equity index returns data. For the liability model we consider long term participating life insurance products specifically unitised with-profits contracts. The payouts of unitised with-profits policies are simulated under a variety of asset models driven by L´evy processes. At first a basic model policy is considered with limited insurer operations and no risk controls. We look into various risk measures of the maturity loss for the insurer xiii and compare the statistical properties for different non-Gaussian increment L´evy models. It is found that the classical Gaussian model substantially underestimates the risk measures in unitised with-profits policies. The L´evy driven models which have semi-heavy tailed increments are aggregate to normal distributions in the long run. Then we consider different retrospective bonus mechanisms by varying the participating rate and the smoothing period. As a comparison we use a bonus earning power method with deterministic projected maturity asset share and 25 percent terminal bonus cushion. We study the joint distributions of the maturity asset shares and guarantees under these two bonus mechanism. With similar risk measures, there are larger expected maturity guarantees under bonus earning power method than retrospective bonus. Declaring bonuses on a more frequent basis is then tested, which has the desired effect of reducing the risk measures when declaring monthly bonuses using bonus earning power mechanism. We make observations on two different investment strategies, a diversified investment strategy and a hedging based investment strategy. The former method tries to reduce the variance of the invest return distribution while the hedging investment strategy, on the other hand, narrows the left tail of the maturity loss distribution by paying an extra amount of expenses. Finally, the L´evy models are extended by using GARCH(1,1)-m type volatility. Both maximum likelihood estimators and Bayesian estimators using Markov Chain Monte Carlo are presented. The statistical tests on the devolatilised data show that the GARCH model reduces the non-linear autocorrelation in the conditional return processes and furthermore improve the fitting of the asset models. Also, multi-variable models are considered. Stochastic bridges driven by L´evy processes are constructed while the yearly returns follow the Wilkie model

Circuit Design

Circuit Design = Science + Art! Designers need a skilled "gut feeling" about circuits and related analytical techniques, plus creativity, to solve all problems and to adhere to the specifications, the written and the unwritten ones. You must anticipate a large number of influences, like temperature effects, supply voltages changes, offset voltages, layout parasitics, and numerous kinds of technology variations to end up with a circuit that works. This is challenging for analog, custom-digital, mixed-signal or RF circuits, and often researching new design methods in relevant journals, conference proceedings and design tools unfortunately gives the impression that just a "wild bunch" of "advanced techniques" exist. On the other hand, state-of-the-art tools nowadays indeed offer a good cockpit to steer the design flow, which include clever statistical methods and optimization techniques.Actually, this almost presents a second breakthrough, like the introduction of circuit simulators 40 years ago! Users can now conveniently analyse all the problems (discover, quantify, verify), and even exploit them, for example for optimization purposes. Most designers are caught up on everyday problems, so we fit that "wild bunch" into a systematic approach for variation-aware design, a designer's field guide and more. That is where this book can help! Circuit Design: Anticipate, Analyze, Exploit Variations starts with best-practise manual methods and links them tightly to up-to-date automation algorithms. We provide many tractable examples and explain key techniques you have to know. We then enable you to select and setup suitable methods for each design task - knowing their prerequisites, advantages and, as too often overlooked, their limitations as well. The good thing with computers is that you yourself can often verify amazing things with little effort, and you can use software not only to your direct advantage in solving a specific problem, but also for becoming a better skilled, more experienced engineer. Unfortunately, EDA design environments are not good at all to learn about advanced numerics. So with this book we also provide two apps for learning about statistic and optimization directly with circuit-related examples, and in real-time so without the long simulation times. This helps to develop a healthy statistical gut feeling for circuit design. The book is written for engineers, students in engineering and CAD / methodology experts. Readers should have some background in standard design techniques like entering a design in a schematic capture and simulating it, and also know about major technology aspects

On the stability of canonical correlation analysis and partial least squares with application to brain-behavior associations

Associations between datasets can be discovered through multivariate methods like Canonical Correlation Analysis (CCA) or Partial Least Squares (PLS). A requisite property for interpretability and generalizability of CCA/PLS associations is stability of their feature patterns. However, stability of CCA/PLS in high-dimensional datasets is questionable, as found in empirical characterizations. To study these issues systematically, we developed a generative modeling framework to simulate synthetic datasets. We found that when sample size is relatively small, but comparable to typical studies, CCA/PLS associations are highly unstable and inaccurate; both in their magnitude and importantly in the feature pattern underlying the association. We confirmed these trends across two neuroimaging modalities and in independent datasets with n ≈ 1000 and n = 20,000, and found that only the latter comprised sufficient observations for stable mappings between imaging-derived and behavioral features. We further developed a power calculator to provide sample sizes required for stability and reliability of multivariate analyses. Collectively, we characterize how to limit detrimental effects of overfitting on CCA/PLS stability, and provide recommendations for future studies

Circuit Design

Circuit Design = Science + Art! Designers need a skilled "gut feeling" about circuits and related analytical techniques, plus creativity, to solve all problems and to adhere to the specifications, the written and the unwritten ones. You must anticipate a large number of influences, like temperature effects, supply voltages changes, offset voltages, layout parasitics, and numerous kinds of technology variations to end up with a circuit that works. This is challenging for analog, custom-digital, mixed-signal or RF circuits, and often researching new design methods in relevant journals, conference proceedings and design tools unfortunately gives the impression that just a "wild bunch" of "advanced techniques" exist. On the other hand, state-of-the-art tools nowadays indeed offer a good cockpit to steer the design flow, which include clever statistical methods and optimization techniques.Actually, this almost presents a second breakthrough, like the introduction of circuit simulators 40 years ago! Users can now conveniently analyse all the problems (discover, quantify, verify), and even exploit them, for example for optimization purposes. Most designers are caught up on everyday problems, so we fit that "wild bunch" into a systematic approach for variation-aware design, a designer's field guide and more. That is where this book can help! Circuit Design: Anticipate, Analyze, Exploit Variations starts with best-practise manual methods and links them tightly to up-to-date automation algorithms. We provide many tractable examples and explain key techniques you have to know. We then enable you to select and setup suitable methods for each design task - knowing their prerequisites, advantages and, as too often overlooked, their limitations as well. The good thing with computers is that you yourself can often verify amazing things with little effort, and you can use software not only to your direct advantage in solving a specific problem, but also for becoming a better skilled, more experienced engineer. Unfortunately, EDA design environments are not good at all to learn about advanced numerics. So with this book we also provide two apps for learning about statistic and optimization directly with circuit-related examples, and in real-time so without the long simulation times. This helps to develop a healthy statistical gut feeling for circuit design. The book is written for engineers, students in engineering and CAD / methodology experts. Readers should have some background in standard design techniques like entering a design in a schematic capture and simulating it, and also know about major technology aspects

Contributions to distributional regression models. Applications in biomedicine

The present thesis makes statistical contributions in the field of frequentist and Bayesian distributional regression (DR) for univariate and bivariate responses. This work also proposes the inclusion of functional data into the DR models. The proposed methodologies are applied to several real biomedical studies, with emphasis in diabetes research

Working relations and marketing channels in the seafood industry: a multi-sector analysis

With indications that fisheries production has plateued at a global capacity of 85 million metric tons in the 1990's, further exploitation of marine stocks on a sustainable basis is unrealistic. Economic development of coastal and regional economies will benefit from new approaches to maximizing benefits from harvested products that include adding value through additional processing, improving product characteristics, and improving marketing efforts. Each of these strategies require improved working relationships between captureharvest/aquaculture, processing, and marketing sectors. This presents an organizational challenge for a culture that has traditionally valued independence and does not have a successful history of joint marketing efforts. New models for organizational development of the seafood industry must ultimately be identified with greater levels of goal achievement of industry participants A model of factors affecting industry working relationships and goal realization was developed to clarify what elements of inustry's task environment could constrain the development of better working relationships. The model proposed that uncertainty and organizational involvement were key elements of working relationship and goal realization. These factors could also be tied to the amount of conflict between channel partners and have an impact on the length of a firm's planning horizon. Satisfaction with working relationships and goal realization among capture-harvesters, aquaculturists, and first buyers were tested using data gathered from a mail survey instrument. The response rate was relatively low, under 25% for all sectors. This limited our capabilities to to make inferences for the entire U.S. seafood industry. Incremental modeling of the full model through covariance (ANCOVA) and multivariate analysis of covariance (MANGOVA) supports hypotheses that the degree to which a firm is invovled in multiple sectors is a significant factor in determining levels of goal realization, uncertainty, and conflict behavior. Regression analysis was supportive of the hypothesis that a firm's planning horizon would be inversely proportional to a firm's uncertainty, and that differences in perceptions of uncertainty exist between sectors. Testing using MANGO VA also supported the notion that different sectors in the seafood industry would percieve different levels of conflict behavior, and that there would be differences in their satisfaction with working relationships. Generally, these sectoral differences indicate that aquaculturists are not as challenged by uncertainty, conflict, and work relationships as capture-harvesters. Tests using canonical correlation analysis (CCA) supports the hypothesis that working relationships and goal realization are associated and suggested several dimmensions along which canonical variate pairs were correlated. Development of marketing channels in the seafood industry are constrained by uncertainty and psychocultural characteristics of individuals that promote independence as an adaptive behavior. Changing conditions in the task environment of small scale operators suggest that new ways of working together will be more productive in the future. An important role exists for fisheries managers and regional governments in removing of the constraints to relationship marketing that currently exists