Statistical methods for clinical trials under the Bayesian framework

Abstract

Clinical trials are the essential step during the development of new drugs. This thesis proposes several new statistical methods to facilitate the implementation of clinical trials in different phases under the Bayesian framework.

For phase I clinical trials, novel designs are developed to strengthen the efficiency and robustness for the dose-finding task. In particular, an innovative approximate Bayesian computation (ABC) design is proposed to locate the maximum tolerated dose (MTD) in the phase I trial. Not only is the ABC design free of any dose--toxicity curve assumption, but it can also aggregate all the available information accrued in the trial for dose assignment. In addition, calibration-free odds (CFO) designs are developed for identifying the MTD, the optimal biological dose (OBD) as well as accommodating the late-onset toxicity outcome in the dose-finding procedure. The CFO-family designs cast the current dose in competition with its two neighboring doses with the evidence in the form of odds ratio. In contrast to most of the existing designs, the prominent merit of CFO-family designs is that their main dose-finding components are model-free and calibration-free. The ABC and CFO-family designs both present satisfactory performances in the numerical studies.

A considerable proportion of promising drugs identified in phase II trials fail the confirmative efficacy test in phase III. Recognizing the low posterior probabilities of $H_1$ when accepting the drug under Simon's two-stage design, the Bayesian enhancement two-stage (BET) design is proposed to strengthen the passing criterion. Under the BET design, the lengths of highest posterior density (HPD) intervals, posterior probabilities of $H_0$ and $H_1$ are computed to calibrate the design parameters. However, from a practical perspective, the HPD interval length lacks transparency and interoperability. To circumvent this problem, the BET design with error control (BETEC) is proposed by replacing the HPD interval length with the posterior error rate. The BETEC design can achieve a balance between the posterior false positive rate and false negative rate and, more importantly, it has an intuitive and clear interpretation. The BETEC is compared with the BET design and Simon's design through extensive simulation studies, where the method yields desirable performances.

In phase III clinical trials, there often exist multiple historical studies for the same or related treatment investigated in the current trial. Incorporating historical data in the analysis of the current study is of great importance, because it can help to gain more information, improve efficiency, and provide a more comprehensive evaluation of treatment. Enlightened by the unit information prior (UIP) concept in the reference Bayesian test, a new informative prior called UIP is developed from an information perspective that can adaptively borrow information from multiple historical datasets. The UIP is applicable to both binary and continuous data and further extended to linear regression settings. Extensive simulation studies demonstrate that the UIP method is comparable to other commonly used informative priors, while its interpretation is more intuitive and its implementation is relatively easy.