Systematic comparison of the statistical operating characteristics of various Phase I oncology designs

Abstract

Dose finding Phase I oncology designs can be broadly categorized as rule based, such as the 3 + 3 and the accelerated titration designs, or model based, such as the CRM and Eff-Tox designs. This paper systematically reviews and compares through simulations several statistical operating characteristics, including the accuracy of maximum tolerated dose (MTD) selection, the percentage of patients assigned to the MTD, over-dosing, under-dosing, and the trial dose-limiting toxicity (DLT) rate, of eleven rule-based and model-based Phase I oncology designs that target or pre-specify a DLT rate of ∼0.2, for three sets of true DLT probabilities. These DLT probabilities are generated at common dosages from specific linear, logistic, and log-logistic dose-toxicity curves. We find that all the designs examined select the MTD much more accurately when there is a clear separation between the true DLT rate at the MTD and the rates at the dose level immediately above and below it, such as for the DLT rates generated using the chosen logistic dose-toxicity curve; the separations in these true DLT rates depend, in turn, not only on the functional form of the dose-toxicity curve but also on the investigated dose levels and the parameter set-up. The model based mTPI, TEQR, BOIN, CRM and EWOC designs perform well and assign the greatest percentages of patients to the MTD, and also have a reasonably high probability of picking the true MTD across the three dose-toxicity curves examined. Among the rule-based designs studied, the 5 + 5 a design picks the MTD as accurately as the model based designs for the true DLT rates generated using the chosen log-logistic and linear dose-toxicity curves, but requires enrolling a higher number of patients than the other designs. We also find that it is critical to pick a design that is aligned with the true DLT rate of interest. Further, we note that Phase I trials are very small in general and hence may not provide accurate estimates of the MTD. Thus our work provides a map for planning Phase I oncology trials or developing new ones.

Keywords: Accuracy of MTD selection; BOIN design, Bayesian optimal interval design; CRM, continual reassessment method; DLT, dose limiting toxicity; Dose finding; EWOC design, escalation with overdose control design; MTD, maximum tolerated dose; Model-based designs; Oncology; Phase 1 designs; Rule-based designs; TEQR design, toxicity equivalence range design; mTPI design, modified toxicity probability interval design.

Fig. 1

Depicts the probability of not escalating at each step for different true DLT rates for the escalation only designs considered that are extensions of the 3 + 3 design and that target a DLT rate of ∼0.2. These probabilities are derived analytically based on the decision rules of each design as given in Table 1.

Fig. 2

Depicts the percentage of times each design considered selects the MTD (Dose Level 3) for the true DLT rates generated from the logistic dose-toxicity curve given in Table 2. These percentages are from simulations and the results are shown in Table 3, Table 4, Table 5.

Fig. 3

Depicts the percentage of times that the 3 + 3 design selects each dose level as the MTD for the true DLT rates given in Table 2, generated from the three dose-toxicity curves. These percentages are from simulations and the results are shown in Table 3, Table 4, Table 5.

Appendix Fig. 1

The figure depicts the percentage of times that the 5+5 a design selects each dose level as the MTD for the true DLT rates given in Table 2, generated from the three dose-toxicity curves. These percentages are from simulations and the results are shown in Table 3, Table 4, Table 5.

Appendix Fig. 2

The depicts the percentage of times that the mTPI design selects each dose level as the MTD for the true DLT rates given in Table 2, generated from the three dose-toxicity curves. These percentages are from simulations and the results are shown in Table 3, Table 4, Table 5.

Appendix Fig. 3

The figure depicts the percentage of times that the CRM design selects each dose level as the MTD for the true DLT rates given in Table 2, generated from the three dose-toxicity curves. These percentages are from simulations and the results are shown in Table 3, Table 4, Table 5.

Appendix Fig. 4

The figure depicts three linear dose-toxicity curves with different offsets that are used to investigate the effect of the location of the starting dose relative to the true MTD on the accuracy of MTD selection for the 3+3 design.