A modified toxicity probability interval method for dose-finding trials

Abstract

Background: Building on earlier work, the toxicity probability interval (TPI) method, we present a modified TPI (mTPI) design that is calibration-free for phase I trials.

Purpose: Our goal is to improve the trial conduct and provide more effective designs while maintaining the simplicity of the original TPI design.

Methods: Like the TPI method, the mTPI consists of a practical dose-finding scheme guided by the posterior inference for a simple Bayesian model. However, the new method proposes improved dose-finding decision rules based on a new statistic, the unit probability mass (UPM). For a given interval and a probability distribution, the UPM is defined as the ratio of the probability mass of the interval to the length of the interval.

Results: The improvement through the use of the UPM for dose finding is threefold: (1) the mTPI method appears to be safer than the TPI method in that it puts fewer patients on toxic doses; (2) the mTPI method eliminates the need for calibrating two key parameters, which is required in the TPI method and is a known difficult issue; and (3) the mTPI method corresponds to the Bayes rule under a decision theoretic framework and possesses additional desirable large- and small-sample properties.

Limitation: The proposed method is applicable to dose-finding trials with a binary toxicity endpoint.

Conclusion: The new method mTPI is essentially calibration free and exhibits improved performance over the TPI method. These features make the mTPI a desirable choice for the design of practical trials.

Figure 1

A demonstration of the UPMs for three intervals as defined in the ‘Introduction’ section. The two vertical lines result in three intervals on the X-axis. The UPM for each of the three intervals is indicated by the dashed horizontal line. The equivalence interval in the middle has the highest UPM under the distribution defined by the density curve

Figure 2

A screenshot of the Excel macro for the mTPI method. The table is uniquely determined upon specification of the sample size, the EI, and p_T (see ‘Introduction’ section). The letters in different colors are computed based on the decision rules under the mTPI method and represent different dose-finding actions. In addition to actions D, S, and E, the table includes action U, which is defined as the execution of the dose exclusion rule in the proposed dose-finding algorithm (Section ‘Dose-finding algorithm’)