Flexible evaluation of surrogate markers with Bayesian model averaging.

When long-term follow up is required for a primary endpoint in a randomized clinical trial, a valid surrogate marker can help to estimate the treatment effect and accelerate the decision process. Several model-based methods have been developed to evaluate the proportion of the treatment effect that is explained by the treatment effect on the surrogate marker. More recently, a nonparametric approach has been proposed allowing for more flexibility by avoiding the restrictive parametric model assumptions required in the model-based methods. While the model-based approaches suffer from potential mis-specification of the models, the nonparametric method fails to give desirable estimates when the sample size is small, or when the range of the data does not follow certain conditions. In this paper, we propose a Bayesian model averaging approach to estimate the proportion of treatment effect explained by the surrogate marker. Our procedure offers a compromise between the model-based approach and the nonparametric approach by introducing model flexibility via averaging over several candidate models and maintains the strength of parametric models with respect to inference. We compare our approach with previous model-based methods and the nonparametric method. Simulation studies demonstrate the advantage of our method when surrogate supports are inconsistent and sample sizes are small. We illustrate our method using data from the Diabetes Prevention Program study to examine hemoglobin A1c as a surrogate marker for fasting glucose.

Simulation-based sequential design.

We review some simulation-based methods to implement optimal decisions in sequential design problems as they naturally arise in clinical trial design. As a motivating example we use a stylized version of a dose-ranging design in the ASTIN trial. The approach can be characterized as constrained backward induction. The nature of the constraint is a restriction of the decisions to a set of actions that are functions of the current history only implicitly through a low-dimensional summary statistic. In addition, the action set is restricted to time-invariant policies. Time-dependence is only introduced indirectly through the change of the chosen summary statistic over time. This restriction allows computationally efficient solutions to the sequential decision problem. A further simplification is achieved by restricting optimal actions to be described by decision boundaries on the space of such summary statistics.

Hi3 + 3: A model-assisted dose-finding design borrowing historical data.

BACKGROUND: In phase I clinical trials, historical data may be available through multi-regional programs, reformulation of the same drug, or previous trials for a drug under the same class. Statistical designs that borrow information from historical data can reduce cost, speed up drug development, and maintain safety. PURPOSE: Based on a hybrid design that partly uses probability models and partly uses algorithmic rules for decision making, we aim to improve the efficiency of the dose-finding trials in the presence of historical data, maintain safety for patients, and achieve a level of simplicity for practical applications. METHODS: We propose the Hi3+3 design, in which the letter "H" represents "historical data". We apply the idea in power prior to borrow historical data and define the effective sample size (ESS) of the prior. Dose-finding decision rules follow the idea in the i3+3 design (Liu et al., 2020 [1]) while incorporating the historical data via the power prior and ESS. The proposed Hi3+3 design pretabulates the dosing decisions before the trial starts, a desirable feature for ease of application in practice. RESULTS: In most cases we investigated, the Hi3+3 design is superior than the i3+3 design due to information borrow from historical data. Even when the historical data is incompatible with the current data, it is capable of maintaining a high level of safety for trial patients and comparable performances without sacrificing the ability to identify the correct MTD too much. Ilustration of this feature are found in the simulation results. CONCLUSION: With the demonstrated safety, efficiency, and simplicity, the Hi3+3 design could be a desirable choice for dose-finding trials borrowing historical data.