Bayesian Methods in Phase I Trials and Small n Sequential Multiple Assignment Randomized Trials
Wei, Boxian
2019
Abstract
In this dissertation, we present new methods for Phase I trials and Small n Sequential Multiple Assignment Randomized Trials (snSMARTs), both in a Bayesian framework. The Bayesian formulation of the Continual Reassessment Method (CRM) is implemented with a one-parameter model describing the association of dose with the probability of dose-limiting toxicity (DLT). Implementation of the CRM requires the user to select two ``tuning parameters": (1) the ``skeleton," or vector of {it a priori} probabilities of DLT for each dose, and (2) the prior standard deviation for the model parameter. Existing methods search the values for each from a range of plausible values through simulation, which is time-consuming. Therefore, in the first project, we propose a systematic way of recommending the skeleton and prior standard deviation that avoids simulations. We compare the percentage that each dose level is recommended as the MTD using the proposed approach and existing approaches as comparators. We demonstrate that our approach is computationally faster and maintains a good precision of selecting the MTD in various scenarios. In the second chapter, we continue trial design in small samples, but change gears to the small-n Sequential Multiple Assignment Randomized Trial (snSMART). In an snSMART, patients are first randomized to one of the multiple treatments (stage 1) and patients who respond to their initial treatment continue the same treatment for another stage, while those who fail to respond are re-randomized to one of the remaining treatments (stage 2). The data from both stages are used to estimate the efficacy of three active treatments in the setting of rare disease. Analysis approaches for snSMARTs are limited. Therefore, in the second project, we propose a Bayesian approach that allows for borrowing of information across both stages. Through simulation, we compare the bias, root mean-square error (rMSE), width and coverage rate of $95%$ confidence/credible interval (CI) of estimators from of our approach to estimators produced from (a) standard approaches that only use the data from stage 1, and (b) a log-Poisson model using data from both stages whose parameters are estimated via generalized estimating equations. We demonstrate the rMSE and width of $95%$ CIs of our estimators are smaller than the other approaches in realistic settings, so that the collection and use of stage $2$ data in snSMARTs provide improved inference for treatments of rare diseases. In the previous project, a Bayesian method for estimating the response rate of each individual treatment in a three-arm snSMART demonstrated efficiency gains for a given sample size relative to other existing frequentist approaches. However, these efficiency gains are dependent upon knowing the sample size. Because few sample size calculation methods for snSMARTs exist, in the third project, we propose a Bayesian sample size calculation for an snSMART designed to distinguish the best treatment from the second-best treatment. Although our methods are based on asymptotic approximations, we demonstrate via simulations that our proposed sample size calculation approach produces the desired statistical power, even in small samples. Moreover, our methods produce sample sizes quickly, thereby saving time relative to using simulations to determine the appropriate sample size. We compare our proposed sample size to an existing frequentist method based upon a weighted $Z$-statistic and demonstrate that the Bayesian method requires far fewer patients than the frequentist method for a study with the same design parameters.Subjects
dose-finding adaptive clinical trial rare disease joint model coverage interval
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