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theses

In this dissertation we work on two problems. In the first problem we propose a general framework for frequentist model averaging and explore its applications. In the second problem, we propose an adaptive design using a copula model that helps us analyze data from drug combination therapy. It is shown later that these new methods are more efficient than the existing methods. Model selection methods often ignore the uncertainty introduced in the selection process and there always remains the possibility that the selected model can possibly be a wrong one. A model averaging approach addresses this issue by combining estimators for a set of candidate models so that it incorporates the underlying model uncertainty. In Chapter 2 we establish a general frequentist model averaging framework that greatly broadens the scope of the existing methodologies under the frequentist model averaging development. We propose a set of weights to combine the individual estimators so that the asymptotic mean squared error of the model average estimator is minimized. Results from simulations and real data analysis show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods. The early phase clinical studies in drug development are focused on the toxicity and sometimes efficacy of a new treatment or a new combination of treatments. Often the aim is to identify a maximum tolerated dose (MTD), which is the maximum dose combination level that does not cause an unacceptable toxicity. In Chapter 3, we explore the combination of two treatments using a copula model. We combine the individual toxicity profiles of the treatments to develop the combination model framework. The theoretic framework is further extended to a combination of more than two treatments and combination of ordinal toxicity measures. A case study based on a combination oncology trial is presented to demonstrate the proposed dose finding strategy for combination therapy.

ETD_6745

Ph.D.

Includes bibliographical references

by Priyam Mitra

doi:10.7282/T39025RK

ETD doctoral

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