Small-sample behavior of novel phase I cancer trial designs

Novel dose-finding designs for Phase I cancer clinical trials, using estimation to assign the best estimated Maximum Tolerated Dose (MTD) at each point in the experiment, most prominently via Bayesian techniques, have been widely discussed and promoted since 1990.

To examine the small-sample behavior of these 'Bayesian Phase I' designs, and also of non-Bayesian designs sharing the same main 'Long-Memory' traits of using likelihood estimation and assigning the estimated MTD to the next patient.

Data from several recently published experiments are presented and discussed, and Long-Memory designs' operating principles are explained. Simulation studies compare the small-sample behavior of Long-Memory designs with short-memory 'Up-and-Down' designs.

In simulation, Long-Memory and Up-and-Down designs achieved similar success rates in finding the MTD. However, for all Long-Memory designs examined, the number n (*) of cohorts treated at the true MTD was highly variable between simulated experiments drawn from the same toxicity-threshold distribution. Further investigation using the same set of thresholds in permuted order indicates that this Long-Memory behavior is driven by sensitivity to the order in which participants enter the experiment. This sensitivity is related to Long-Memory designs' 'winner-takes-all' dose-assignment rule, which grants the early cohorts a disproportionately large influence, and causes many experiments to settle early on a specific dose. Additionally for the Bayesian Long-Memory designs, the prior-predictive distribution over the dose levels has a substantial impact upon MTD-finding performance, long into the experiment.

While the numerical evidence for Long-Memory designs' order sensitivity is broad, and plausible explanations for it are provided, we do not present a theoretical proof of the phenomenon.

Method developers, analysts, and practitioners should be aware of Long-Memory designs' order sensitivity and related phenomena. In particular, they should be informed that settling on a single dose does not guarantee that this dose is the MTD. Presently, Up-and-Down designs offer a simpler and more robust alternative for the sample sizes of 10-40 patients used in most Phase I trials. Future designs might benefit from combining the two approaches. We also suggest that the field's paradigm change from dose-selection to dose-estimation.