Topics in Bayesian adaptive clinical trial design using dynamic linear models and missing data imputation in logistic regression.

Conventional Phase II clinical trial designs usually employ a logistic regression model to analyze the efficacy of a new drug and, therefore, assumes monotone dose-response relationship. Also, the logistic regression model requires the response to be categorical and, thus, it is not applicable for continuous data. The traditional design in Phase II determines if a new drug will be further tested in Phase III based on only drug efficacy and allocates an equal number of patients to each dosage, ignoring dose efficacy. Because of the limitations of conventional clinical trial designs, new adaptive designs have been proposed by researchers to improve the flexibility and adaptability of conventional designs. In Chapter Two we propose an adaptive Bayesian design that uses a bivariate normal dynamic linear model for a Phase II clinical trial, and we compare its performance to a Bayesian fixed or non-adaptive design. The proposed Bayesian adaptive design can be utilized for continuous data and can model various dose-response relationships. We remark that for many dose-response relationships, our proposed adaptive Bayesian design can use fewer patients to obtain a correct decision concerning a drug's efficacy than the Bayesian fixed design. Missing data arises in almost all research; that is, part of the data are missing for a subject. A data analyst must decide how to cope with the missing data from among the numerous imputation methods that can be used. However, one might not know which imputation method is the best. The objective of this study is to evaluate the efficacy of five imputation methods. In Chapter Four, we have compared the performance of complete-data-only, single-mean imputation, conditional-mean imputation, multiple imputation by chained equations and hotdeck imputation methods for prediction of a logistic regression model, for the missing-completely-at-random and missing-at-random mechanisms. These five imputation methods yield different results for small sample sizes, and the difference decreases with an increasing sample size. Surprisingly, a single-mean imputation method performs as well as the multiple imputation methods compared here.