Title: Two-stage Continual Reassessment Method and Patient Heterogeneity for Dose-finding Studies
Description: The continual reassessment method (CRM) is a widely used model-based design in Phase I dose-finding studies. This dissertation examines two extensions of CRM: one is a two-stage method and the other is a method that accounts for patient heterogeneity. Originally proposed in the Bayesian framework, CRM starts by testing the first patient at the prior guess of the maximum tolerated dose (MTD). However, there are safety concerns with this approach as practitioners often prefer to start from the lowest dose level and are reluctant to escalate to higher dose levels without testing the lower ones with a sufficient number of patients. This calls for a two-stage design, where the model-based phase is preceded by a pre-specified dose escalation phase, and the phase transitions when any dose-limiting toxicity (DLT) occurs. In the first part of this dissertation, I propose a theoretical framework to build a two-stage CRM based on the coherence principle and prove the unique existence of the most conservative and coherent initial design.

An accompanying calibration algorithm is formulated to facilitate design implementation. We demonstrate that by using real trial examples, the algorithm yields designs with competitive performance compared to the conventional design which uses a much more labor intensive trial-and-error approach. Furthermore, we show that this algorithm can be applied in a timely and reproducible manner. In addition to the two-stage method, we also take into account of patient's heterogeneity in drug metabolism rate that can result in different susceptibility to drug toxicity. This led to a risk-adjusting design for identifying patient-specific MTDs. The existing dose-finding designs which incorporate patient heterogeneity deal either with only categorical risk factor or with continuous risk factor using models based on strong parametric assumptions. We propose a method that uses a flexible semi-parametric model to identify patient-specific MTDs, adjusting for either categorical or continuous risk factor.

Initially, our method assigns dose to patients using the aforementioned two-stage CRM ignoring any patient heterogeneity, and tests the risk effect as trial proceeds. It then transitions to a risk-adjusting stage only if sufficient risk effect on toxicity outcome is observed. The performance of this multi-stage design is evaluated under various scenarios, using dosing accuracy measures calculated based on the final model estimate at the end of a trial and on the intra-trial dose allocation. The results are compared to the conventional two-stage CRM without considering patient heterogeneity. Simulation results demonstrate a substantial improvement in dosing accuracy in scenarios where there are true risk effects on toxicity probability; and in situations where risk factors do not have an effect, the performance of the proposed method is also comparable to that of the conventional design.