A likelihood-based approach for computing the operating characteristics of the 3+3 phase I clinical trial design with extensions to other A+B designs
Abstract
Background In phase I clinical trials, the “3+3” algorithmic design has been unparalleled in its popularity. The statistical properties of the “3+3” design have been studied in the literature either in comparison with other methods or by deriving exact formulae of statistical quantities. However, there is still much to be known about its capabilities of describing and accounting for uncertainties in the observed data. Purpose The objective of this study is to provide a probabilistic support for analyzing the heuristic performance of the “3+3” design. The operating characteristics of the algorithm are computed under different hypotheses, levels of evidence, and true (or best guessed) toxicity rates. The dose-finding rules are further compared with those generated by the modified toxicity probability interval design and generalized for implementation in all “A+B” designs. Methods Our likelihood method is based on the evidential paradigm. Two hypotheses are chosen to correspond to two hypothesized dose-limiting toxicity rates, for example, H 1 —unsafe versus H 2 —acceptable. Given observed toxicities per dose, the likelihood-ratio is calculated and compared to a certain k threshold (level of evidence). Under various true toxicities, the probabilities of weak evidence, favoring H 1 and H 2 , were computed under four sets of hypotheses and several k thresholds. Results For scenarios where the midpoint of the two hypothesized dose-limiting toxicity rates is around 0.30, and for a…
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