Bayesian adaptive designs for drug combinations in early phase clinical trials

Treating patients with combined agents is a growing trend in cancer clinical trials. Evaluating the synergism of multiple drugs is often the primary motivation for such drug-combination studies. Focusing on the drug combination study in the early phase clinical trials, our research is composed of three parts: (1) We conduct a comprehensive comparison of four dose-finding designs in the two-dimensional toxicity probability space and propose using the Bayesian model averaging method to overcome the arbitrariness of the model specification and enhance the robustness of the design; (2) Motivated by a recent drug-combination trial at MD Anderson Cancer Center with a continuous-dose standard of care agent and a discrete-dose investigational agent, we propose a two-stage Bayesian adaptive dose-finding design based on an extended continual reassessment method; (3) By combining phase I and phase II clinical trials, we propose an extension of a single agent dose-finding design. We model the time-to-event toxicity and efficacy to direct dose finding in two-dimensional drug-combination studies. We conduct extensive simulation studies to examine the operating characteristics of the aforementioned designs and demonstrate the designs' good performances in various practical scenarios.^

BAYESIAN PHASE I DOSE FINDING IN CANCER TRIALS

This dissertation explores phase I dose-finding designs in cancer trials from three perspectives: the alternative Bayesian dose-escalation rules, a design based on a time-to-dose-limiting toxicity (DLT) model, and a design based on a discrete-time multi-state (DTMS) model. We list alternative Bayesian dose-escalation rules and perform a simulation study for the intra-rule and inter-rule comparisons based on two statistical models to identify the most appropriate rule under certain scenarios. We provide evidence that all the Bayesian rules outperform the traditional ``3+3'' design in the allocation of patients and selection of the maximum tolerated dose. The design based on a time-to-DLT model uses patients' DLT information over multiple treatment cycles in estimating the probability of DLT at the end of treatment cycle 1. Dose-escalation decisions are made whenever a cycle-1 DLT occurs, or two months after the previous check point. Compared to the design based on a logistic regression model, the new design shows more safety benefits for trials in which more late-onset toxicities are expected. As a trade-off, the new design requires more patients on average. The design based on a discrete-time multi-state (DTMS) model has three important attributes: (1) Toxicities are categorized over a distribution of severity levels, (2) Early toxicity may inform dose escalation, and (3) No suspension is required between accrual cohorts. The proposed model accounts for the difference in the importance of the toxicity severity levels and for transitions between toxicity levels. We compare the operating characteristics of the proposed design with those from a similar design based on a fully-evaluated model that directly models the maximum observed toxicity level within the patients' entire assessment window. We describe settings in which, under comparable power, the proposed design shortens the trial. The proposed design offers more benefit compared to the alternative design as patient accrual becomes slower.

Bayesian Adaptive Designs for Early Phase Clinical Trials

My dissertation focuses mainly on Bayesian adaptive designs for phase I and phase II clinical trials. It includes three specific topics: (1) proposing a novel two-dimensional dose-finding algorithm for biological agents, (2) developing Bayesian adaptive screening designs to provide more efficient and ethical clinical trials, and (3) incorporating missing late-onset responses to make an early stopping decision. Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which toxicity and efficacy monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a phase I/II trial design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships. Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multi-arm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while at the same time allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while at the same time providing higher power to identify the best treatment at the end of the trial. Phase II trial studies usually are single-arm trials which are conducted to test the efficacy of experimental agents and decide whether agents are promising to be sent to phase III trials. Interim monitoring is employed to stop the trial early for futility to avoid assigning unacceptable number of patients to inferior treatments. We propose a Bayesian single-arm phase II design with continuous monitoring for estimating the response rate of the experimental drug. To address the issue of late-onset responses, we use a piece-wise exponential model to estimate the hazard function of time to response data and handle the missing responses using the multiple imputation approach. We evaluate the operating characteristics of the proposed method through extensive simulation studies. We show that the proposed method reduces the total length of the trial duration and yields desirable operating characteristics for different physician-specified lower bounds of response rate with different true response rates.

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

A simulation study of the standard design, the rolling six design, the CRM, and the modified CRM in Phase I clinical trials

The Phase I clinical trial is considered the "first in human" study in medical research to examine the toxicity of a new agent. It determines the maximum tolerable dose (MTD) of a new agent, i.e., the highest dose in which toxicity is still acceptable. Several phase I clinical trial designs have been proposed in the past 30 years. The well known standard method, so called the 3+3 design, is widely accepted by clinicians since it is the easiest to implement and it does not need a statistical calculation. Continual reassessment method (CRM), a design uses Bayesian method, has been rising in popularity in the last two decades. Several variants of the CRM design have also been suggested in numerous statistical literatures. Rolling six is a new method introduced in pediatric oncology in 2008, which claims to shorten the trial duration as compared to the 3+3 design. The goal of the present research was to simulate clinical trials and compare these phase I clinical trial designs. Patient population was created by discrete event simulation (DES) method. The characteristics of the patients were generated by several distributions with the parameters derived from a historical phase I clinical trial data review. Patients were then selected and enrolled in clinical trials, each of which uses the 3+3 design, the rolling six, or the CRM design. Five scenarios of dose-toxicity relationship were used to compare the performance of the phase I clinical trial designs. One thousand trials were simulated per phase I clinical trial design per dose-toxicity scenario. The results showed the rolling six design was not superior to the 3+3 design in terms of trial duration. The time to trial completion was comparable between the rolling six and the 3+3 design. However, they both shorten the duration as compared to the two CRM designs. Both CRMs were superior to the 3+3 design and the rolling six in accuracy of MTD estimation. The 3+3 design and rolling six tended to assign more patients to undesired lower dose levels. The toxicities were slightly greater in the CRMs.^