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The thesis aimed to develop a method for optimizing design subject to matching the pre-defined baseline characteristics in clinical trials. As part of a clinical trial, a new treatment must be compared with a competitor treatment in order to determine its effect on the patient before the new treatment is launched. Ideally, we can directly compare the new treatment with competitor treatment in randomized controlled trials (RCTs). However, direct comparison is difficult to achieve due to various factors, such as time, price, regulation, and patents. A matching-adjusted indirect comparison (MAIC) method leverages all available data by adjusting average patient characteristics in trials with Individual patient data (IPD) to match those reported in the aggregate trials data (AgD). MAIC is a reweighting method in which the weights are calculated by deriving the propensity scores in the Individual patient’s data. This can reduce the bias. As IPD matches to the pre-defined baseline characteristics, we make use of optimal design theory and convert this into a constrained optimization problem. The Lagrangian method is used to determine the optimal design subject to satisfying the constraints of baseline characteristics. We formulate the Lagrangian and then transform the constrained problem to one where we simultaneously maximize several functions of the design weights. These functions have a common maximum of zero. In order to find the optimal design, we used the software R and a class of multiplicative algorithms. We then perform a sensitivity analysis and compare the Lagrangian method and the MAIC method by calculating the effective sample sizes (ESS). The higher the value of ESS the less information is lost due to reweighting. The Lagrangian method performs better than the MAIC method. Owing to the broad applicability of optimal design, we have tried to make use of this theory in order to obtain a better methodology in MAIC. The proposed methodology is quite flexible and c

In this thesis, we consider a competing cause scenario that incorporates a dependence structure. The correlated dependence generalized power series (CDGPS) cure rate model, used by Borges et al. (2012), is employed which captures the real life mechanisms that exist for dependent competing causes. Our approach assumes that the number of initial competing causes follows the generalized power series with a destructive process following an administered treatment. This destructive process allows us to capture the undamaged portion of the initial competing causes in a competitive scenario. The objective is to use the estimation-maximization (EM) algorithm on special cases of the CDGPS model to test its effectiveness at estimating model parameters, through a simulation study carried out under various parameter settings. Finally, the EM algorithm and the models are applied to two real melanoma data sets, where model discrimination is conducted through information-based methods.

Survival data analysis may reveal heterogeneity among the observational units in many situations. This heterogeneity is also known as frailty. Analysis that ignores frailty leads to incorrect inferences. The Cox proportional hazards model is commonly used in lifetime analysis to measure the effects of covariates. In some cases, covariates may fail to capture true risk differences in the population. The model might ignore covariates that could explain random frailty, but this can be explained by the existence of covariates not considered in the model. Frailty can prevent underestimation and overestimation of parameters, and it can also be used to estimate the effects of covariates on the response variables. This thesis explores the pretest and shrinkage estimation methods for the Cox proportional hazards frailty model for right-censored clustered survival data when some of the covariates in the model may not be relevant for accurately predicting survival times. In order to address this, we employ two models: an unrestricted model that encompasses all covariates, and a restricted model that includes a smaller set of covariates. For the unrestricted model, we apply the penalized partial likelihood to obtain the unrestricted model estimator. We maximize the penalized partial likelihood under the restriction on the irrelevant covariates to obtain the restricted model estimator. We optimally combine these estimators to obtain pretest and shrinkage estimators. Mean squared error (MSE) and relative MSE are calculated to assess the performance of these estimators. By conducting simulation studies and applying the proposed methods to a lung cancer data, we demonstrate that the shrinkage estimators perform better than the full model estimator when the shrinkage dimension exceeds two. The effects of increasing sample size, number of insignificant covariates, and censoring percentages are also studied through Monte Carlo simulations. The Cox proportional hazards and parametric m

In this thesis, the focus is developing an inference for the Downton's bivariate Weibull (DBW) distribution, particularly in the context of dependent competing risks. The study begins by investigating the statistical properties of the DBW distribution. Next, the thesis delves into likelihood inference for the DBW distribution using complete bivariate data, specifically in the context of dependent competing risks. Additionally, moment-based estimates based on complete bivariate data are developed and examined. To assess the performance of the point and interval estimates, extensive Monte Carlo simulations are conducted. Furthermore, two real datasets are presented as illustrative examples of the application of the DBW distribution with the inferential method. These illustrations serve to demonstrate the practical relevance and usefulness of the proposed model and methods. The thesis concludes with a comprehensive evaluation of the estimation techniques and suggestions for further research in this area.

Cerebral Palsy (CP) is one of the most common motor neurodevelopmental disorders which affects three of every thousand live births in North America. In this study, we use a Bayesian approach to advance the science of manual dexterity outcome measurement for young children. Fifty children with a diagnosis of CP and fifty healthy, typically developing children between the ages of 4 to 12 years of age were enrolled in the study. Firstly, the frequentist Analysis of Variance (ANOVA) method was used and then for comparison, a Bayesian Analysis of Variance (BANOVA) method was applied to analyze the various manual dexterity metrics obtained from a novel computer game-based assessment tool. Finally, the Bayesian Seemingly Unrelated Regression (BayesSUR) method was constructed to identify the influential factors affecting the manual dexterity performance matrix considering the response variables collectively, taking into account their interrelationships and dependencies. These findings indicate that Manual Ability Classification System (MACS) level emerges as a consistently influential factor for all response variables for both leftward and rightward movements, while gender predominantly influences the proportion of valid traces in rightward movements.

Most optimality criteria considered in the literature are model-based criteria that rely on having an assumed model to select an optimal design for the experiment. Having a specified model prior to experimentation might not be feasible in reality. Bayesian optimality criteria has been in the literature for decades to relieve the dependence on an assumed model. In this research, we develop new Bayesian optimality criteria with high parameter estimation efficiency for multistratum designs. Examples with comparisons and sensitivity analyses are provided for selecting optimal designs in completely randomized experiments and multistratum experiments such as split-plot designs using the new criteria.

Nitrogen-doped carbon nanodots (CNDs) were synthesized and utilized as sensing probes to detect different anions and metallic ions within aqueous solutions. The pristine CNDs were developed through a one-pot hydrothermal synthesis. o-Phenylenediamine was used as the precursor. A similar hydrothermal synthesis technique in the presence of polyethylene glycol (PEG) was adopted to form the PEG-coated CND clusters (CND-100k). Through photoluminescence (PL) quenching, both CND and PEG-coated CND suspensions display ultra-high sensitivity and selectivity towards HSO4− anions (Stern–Volmer quenching constant (KSV) value: 0.021 ppm−1 for CND and 0.062 ppm−1 for CND-100k) with an ultra-low detection limit (LOD value: 0.57 ppm for the CND and 0.19 ppm for CND-100k) in the liquid phase. The quenching mechanism of N-doped CNDs towards HSO4− ions involves forming the bidentate as well as the monodentate hydrogen bonding with the sulfate anionic moieties. The detection mechanism of metallic ions analyzed through the Stern–Volmer formulation reveals that the CND suspension is well suited for the detection of Fe3+ (KSV value: 0.043 ppm−1) and Fe2+ (KSV value: 0.0191 ppm−1) ions, whereas Hg2+ (KSV value: 0.078 ppm−1) sensing can be precisely performed by the PEG-coated CND clusters. Accordingly, the CND suspensions developed in this work can be employed as high-performance PL probes for detecting various anions and metallic ions in the liquid phase.

The thesis consists of three essays. In the first essay, we investigate the relation between excess cash holdings and future stock returns using a sample of firms in developed markets and emerging markets. The results show a positive relation between excess cash and future returns in developed markets but not in emerging markets. In developed markets, firms with higher excess cash have higher market betas and invest more in the future. Furthermore, the positive relation between excess cash and future stock returns is driven by rising market states. In contrast, we do not find similar patterns in emerging market. Overall, the evidence suggests that excess cash holdings proxy for growth opportunities in developed markets but not in emerging markets. In the second essay, we investigate corporate cash holdings in developed countries. This research assesses the cash difference between firms in developed Europe and the US and seeks to account for this difference. Results indicate that developed European firms hold less cash than are US firms, and this is largely explained by regional differences in intangible assets. We further find that the difference in intangible assets between developed Europe and the US is mainly driven by sector specialization. This finding supports literature that US companies outperform European firms in high R&D intensity sectors. In the third essay, we examine the relation between corporate debt maturity and cross-sectional equity returns in non-US markets. Prior research has shown that the maturity structure of corporate debt matters in explaining the equity risk premium of US stocks. In the US, debt refinancing intensity is associated with a positive risk premium. This essay re-evaluates this relation in international stocks. We find a similar positive relation between debt refinancing intensity and equity risk premium in developed European markets but not in emerging Asian markets. In developed Europe, the positive relation is driven by firms