Let (X, Y) be bivariate normal random vectors which represent the responses as a result of Treatment 1 and Treatment 2. The statistical inference about the bivariate normal distribution parameters involving missing data with both treatment samples is considered. Assuming the correlation coefficient ρ of the bivariate population is known, the MLE of population means and variance (ξ, η, and σ2) are obtained. Inferences about these parameters are presented. Procedures of constructing confidence interval for the difference of population means ξ – η and testing hypothesis about ξ – η are established. The performances of the new estimators and testing procedure are compared numerically with the method proposed in Looney and Jones (2003) on the basis of extensive Monte Carlo simulation. Simulation studies indicate that the testing power of the method proposed in this thesis study is higher.

The most common type of confirmatory trial is a randomised trial comparing the experimental treatment of interest to a control treatment. Confirmatory trials are expensive and take a lot of time in the planning, set up and recruitment of patients. Efficient methodology in clinical trial design is critical to save both time and money and allow treatments to become available to patients quickly. Often there are data available on the control treatment from a previous trial. These historical data are often used to design new trials, forming the basis of sample size calculations, but are not used in the analysis of the new trial. Incorporating historical control data into the design and analysis could potentially lead to more efficient trials. When the historical and current control data agree, incorporating historical control data could reduce the number of control patients required in the current trial and therefore the duration of the trial, or increase the precision of parameter estimates. However, when the historical and current data are inconsistent, there is a potential for biased treatment effect estimates, inflated type I error and reduced power. We propose two novel weights to assess agreement between the current and historical control data: a probability weight based on tail area probabilities; and a weight based on the equivalence of the historical and current control data parameters. For binary outcome data, agreement is assessed using the posterior distributions of the response probability in the historical and current control data. For normally distributed outcome data, agreement is assessed using the marginal posterior distributions of the difference in means and the ratio of the variances of the current and historical control data. We consider an adaptive design with an interim analysis. At the interim, the agreement between the historical and current control data is assessed using the probability or equivalence probability weight approach. The allocation ratio is adapted to randomise fewer patients to control when there is agreement and revert back to a standard trial design when there is disagreement. The final analysis is Bayesian utilising the analysis approach of the power prior with a fixed weight. The operating characteristics of the proposed design are explored and we show how the equivalence bounds can be chosen at the design stage of the current study to control the maximum inflation in type I error. We then consider a design where a treatment arm is added to an ongoing clinical trial. For many disease areas, there are often treatments in different stages of the development process. We consider the design of a two-arm parallel group trial where it is planned to add a new treatment arm during the trial. This could potentially save money, patients, time and resources. The addition of a treatment arm creates a multiple comparison problem. Dunnett (1955) proposed a design that controls the family-wise error rate when comparing multiple experimental treatments to control and determined the optimal allocation ratio. We have calculated the correlation between test statistics for the method proposed by Dunnett when a treatment arm is added during the trial and only concurrent controls are used for each treatment comparison. We propose an adaptive design where the sample size of all treatment arms are increased to control the family-wise error rate. We explore adapting the allocation ratio once the new treatment arm is added to maximise the overall power of the trial.

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This master’s thesis deals with active electronic loads focusing mostly on alternating input signals. The principles and modes of both DC and AC loads are described, as well as the most important parameters of MOSFET transistor which is used as the main power component. It deals with designing a regulation circuit of an AC load in detail. This work also discusses the possibilities of realisation of the remaining parts of the device. At the end of the thesis the function of the designed regulation circuit is verified by simple measurements on a prototype.

The concept of outlier detection by statistical hypothesis testing in geodesy is briefly reviewed. The performance of such tests can only be measured or optimized with respect to a proper alternative hypothesis. Firstly, we discuss the important question whether gross errors should be treated as non-random quantities or as random variables. In the first case, the alternative hypothesis must be based on the common mean shift model, while in the second case, the variance inflation model is appropriate. Secondly, we review possible formulations of alternative hypotheses (inherent, deterministic, slippage, mixture) and discuss their implications. As measures of optimality of an outlier detection, we propose the premium and protection, which are briefly reviewed. Finally, we work out a practical example: the fit of a straight line. It demonstrates the impact of the choice of an alternative hypothesis for outlier detection. / Das Konzept der Ausreißererkennung durch statistische Hypothesentests in der Geodäsie wird kurz überblickt. Die Leistungsfähigkeit solch eines Tests kann nur gemessen oder optimiert werden in Bezug auf eine geeignete Alternativhypothese. Als erstes diskutieren wir die wichtige Frage, ob grobe Fehler als nicht-zufällige oder zufällige Größen behandelt werden sollten. Im ersten Fall muss die Alternativhypothese auf das Mean-Shift-Modell gegründet werden, im zweiten Fall ist das Variance-Inflation-Modell passend. Als zweites stellen wir mögliche Formulierungen von Alternativhypothesen zusammen und diskutieren ihre Implikationen. Als Optimalitätsmaß schlagen wir das Premium-Protection-Maß vor, welches kurz überblickt wird. Schließlich arbeiten wir ein praktisches Beispiel aus: Die Anpassung einer ausgleichenden Gerade. Es zeigt die Auswirkung der Wahl einer Alternativhypothese für die Ausreißererkennung.