Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential "children", each of whom deal with a different possible state of knowledge resulting from the experimentation of the "parent". The research of this dissertation extends the real-world rigor of the statistical field of design of experiments to develop an deterministic, adaptive algorithm that produces deterministically generated, reproducible, testable, defendable, adaptive, resource-constrained multi-stage experimental schedules without having to spend physical resource.

Indiana University-Purdue University Indianapolis (IUPUI) / Model-based drug development has become an essential element to potentially make drug development more productive by assessing the data using mathematical and statistical approaches to construct and utilize models to increase the understanding of the drug and disease. The modeling and simulation approach not only quantifies the exposure-response relationship, and the level of variability, but also identifies the potential contributors to the variability. I hypothesized that the modeling and simulation approach can: 1) leverage our understanding of pharmacokinetic-pharmacodynamic (PK-PD) relationship from pre-clinical system to human; 2) quantitatively capture the drug impact on patients; 3) evaluate clinical trial designs; and 4) identify potential contributors to drug toxicity and efficacy. The major findings for these studies included: 1) a translational PK modeling approach that predicted clozapine and norclozapine central nervous system exposures in humans relating these exposures to receptor binding kinetics at multiple receptors; 2) a population pharmacokinetic analysis of a study of sertraline in depressed elderly patients with Alzheimer’s disease that identified site specific differences in drug exposure contributing to the overall variability in sertraline exposure; 3) the utility of a longitudinal tumor dynamic model developed by the Food and Drug Administration for predicting survival in non-small cell lung cancer patients, including an exploration of the limitations of this approach; 4) a Monte Carlo clinical trial simulation approach that was used to evaluate a pre-defined oncology trial with a sparse drug concentration sampling schedule with the aim to quantify how well individual drug exposures, random variability, and the food effects of abiraterone and nilotinib were determined under these conditions; 5) a time to event analysis that facilitated the identification of candidate genes including polymorphisms associated with vincristine-induced neuropathy from several association analyses in childhood acute lymphoblastic leukemia (ALL) patients; and 6) a LASSO penalized regression model that predicted vincristine-induced neuropathy and relapse in ALL patients and provided the basis for a risk assessment of the population. Overall, results from this dissertation provide an improved understanding of treatment effect in patients with an assessment of PK/PD combined and with a risk evaluation of drug toxicity and efficacy.

Indiana University-Purdue University Indianapolis (IUPUI) / Some problems of complex systems are internal to the system whereas other problems exist peripherally; two such problems will be explored in this thesis. First, is the issue of excessive jerk from instantaneous velocity demand changes produced by an adaptive cruise control system. Calculations will be demonstrated and an example control solution will be proposed in Chapter 3. Second, is the issue of a non-perfect plant, called an uncertain or corrupted plant. In initial control analysis, the adaptive cruise control systems are assumed to have a perfect plant; that is to say, the plant always behaves as commanded. In reality, this is seldom the case. Plant corruption may come from a variation in performance through use or misuse, or from noise or imperfections in the sensor signal data. A model for plant corruption is introduced and methods for analysis and compensation are explored in Chapter 4. To facilitate analysis, Chapter 2 discusses the concept of system identification, an order reduction tool which is employed herein. Adaptive cruise control systems are also discussed with special emphasis on the situations most likely to employ jerk limitation.

Indiana University-Purdue University Indianapolis (IUPUI) / In medical research, data analysis often requires complex statistical methods where no closed-form solutions are available. Under such circumstances, Monte Carlo (MC) methods have found many applications. In this dissertation, we proposed several novel statistical models where MC methods are utilized. For the first part, we focused on semicompeting risks data in which a non-terminal event was subject to dependent censoring by a terminal event. Based on an illness-death multistate survival model, we proposed flexible random effects models. Further, we extended our model to the setting of joint modeling where both semicompeting risks data and repeated marker data are simultaneously analyzed. Since the proposed methods involve high-dimensional integrations, Bayesian Monte Carlo Markov Chain (MCMC) methods were utilized for estimation. The use of Bayesian methods also facilitates the prediction of individual patient outcomes. The proposed methods were demonstrated in both simulation and case studies. For the second part, we focused on re-randomization test, which is a nonparametric method that makes inferences solely based on the randomization procedure used in clinical trials. With this type of inference, Monte Carlo method is often used for generating null distributions on the treatment difference. However, an issue was recently discovered when subjects in a clinical trial were randomized with unbalanced treatment allocation to two treatments according to the minimization algorithm, a randomization procedure frequently used in practice. The null distribution of the re-randomization test statistics was found not to be centered at zero, which comprised power of the test. In this dissertation, we investigated the property of the re-randomization test and proposed a weighted re-randomization method to overcome this issue. The proposed method was demonstrated through extensive simulation studies.