Effective sample size for computing prior hyperparameters in Bayesian phase I-II dose-finding

Abstract

Background: The efficacy-toxicity trade-off based design is a practical Bayesian phase I-II dose-finding methodology. Because the design's performance is very sensitive to prior hyperparameters and the shape of the target trade-off contour, specifying these two design elements properly is essential.

Purpose: The goals are to provide a method that uses elicited mean outcome probabilities to derive a prior that is neither overly informative nor overly disperse, and practical guidelines for specifying the target trade-off contour.

Methods: A general algorithm is presented that determines prior hyperparameters using least squares penalized by effective sample size. Guidelines for specifying the trade-off contour are provided. These methods are illustrated by a clinical trial in advanced prostate cancer. A new version of the efficacy-toxicity program is provided for implementation.

Results: Together, the algorithm and guidelines provide substantive improvements in the design's operating characteristics.

Limitations: The method requires a substantial number of elicited values and design parameters, and computer simulations are required to obtain an acceptable design.

Conclusion: The two key improvements greatly enhance the efficacy-toxicity design's practical usefulness and are straightforward to implement using the updated computer program. The algorithm for determining prior hyperparameters to ensure a specified level of informativeness is general, and may be applied to models other than that underlying the efficacy-toxicity method.

Keywords: Adaptive design; Bayesian design; clinical trial; dose-finding; phase I/II trial.

© The Author(s) 2014.

Figures

Figure 1

Two sets of efficacy-toxicity trade-off contours for the phase I-II prostate cancer trial. The contours in the left-hand figure generated by target C1 are insufficiently steep, and produce a design with poor properties. The contours in the right-hand figure generated by target C2 produce a design with more desirable properties, as shown in Table 1.

Figure 2

Probabilities of selecting doses 3, 4, or 5, or stopping the trial early, under Scenario 2 of Table 2, where doses 1, 2, 3, and 4 are acceptable and the respective desirabilities of the five doses based on their efficacy-toxicity trade-off s are 41, 57, 96, 79, 66.