Modified toxicity probability interval design: a safer and more reliable method than the 3 + 3 design for practical phase I trials

Abstract

The 3 + 3 design is the most common choice among clinicians for phase I dose-escalation oncology trials. In recent reviews, more than 95% of phase I trials have been based on the 3 + 3 design. Given that it is intuitive and its implementation does not require a computer program, clinicians can conduct 3 + 3 dose escalations in practice with virtually no logistic cost, and trial protocols based on the 3 + 3 design pass institutional review board and biostatistics reviews quickly. However, the performance of the 3 + 3 design has rarely been compared with model-based designs in simulation studies with matched sample sizes. In the vast majority of statistical literature, the 3 + 3 design has been shown to be inferior in identifying true maximum-tolerated doses (MTDs), although the sample size required by the 3 + 3 design is often orders-of-magnitude smaller than model-based designs. In this article, through comparative simulation studies with matched sample sizes, we demonstrate that the 3 + 3 design has higher risks of exposing patients to toxic doses above the MTD than the modified toxicity probability interval (mTPI) design, a newly developed adaptive method. In addition, compared with the mTPI design, the 3 + 3 design does not yield higher probabilities in identifying the correct MTD, even when the sample size is matched. Given that the mTPI design is equally transparent, costless to implement with free software, and more flexible in practical situations, we highly encourage its adoption in early dose-escalation studies whenever the 3 + 3 design is also considered. We provide free software to allow direct comparisons of the 3 + 3 design with other model-based designs in simulation studies with matched sample sizes.

Fig 1.

Schema of the enhanced 3 + 3 design. The two versions of 3 + 3^L and 3 + 3^H represent cases where the maximum-tolerated dose (MTD) is defined as the highest dose at which no more than one and two dose-limiting toxicities (DLTs) are observed among six patients, respectively.

Fig 2.

Dose-finding spreadsheet of the modified toxicity probability interval (mTPI) method. The spreadsheet is generated based on a beta/binomial model and precalculated before a trial starts. 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 de-escalate the dose (D), stay at the same dose (S), and escalate the dose (E), the table includes action unacceptable toxicity (U), which is defined as the execution of the dose-exclusion rule in mTPI. MTD, maximum-tolerated dose.

Fig 3.

Difference in the average sample size per trial between the 3 + 3 and modified toxicity probability interval designs. Each boxplot summarizes the differences for 14 scenarios for a given target toxicity value p_T.

Fig 4.

Comparison between the 3 + 3 and modified toxicity probability interval (mTPI) designs based on matched sample sizes. (A) Points to the right of 0 correspond to the 3 + 3 design being less safe than the mTPI design; (B) points to the left of 0 correspond to the 3 + 3 design being less reliable than the mTPI design. (A) Differences in the numbers of patients treated at doses above the maximum-tolerated dose (MTD; n_{> MTD}; ie, values of [n_{> MTD} 3 + 3 − n_{> MTD} mTPI] for all 42 scenarios); (B) differences in the selection percentages of the true MTD (%Sel_MTD; ie, values of [%Sel_MTD 3 + 3 − %Sel_MTD mTPI] for all 42 scenarios). Colors indicate results corresponding to the three different p_T values.

Fig 5.

Overall toxicity percentages for the 3 + 3 and modified toxicity probability interval (mTPI) designs across all simulated trials. Scenarios in which (A) p_T = 0.1, (B) p_T = 0.2, and (C) p_T = 0.3. The mTPI design represents a safer and more reliable method than the 3 + 3 design for practical phase I trials.

Fig A1.

Dose-response patterns for the 42 clinical scenarios in which (A) p_T = 0.1, (B) p_T = 0.2, and (C) p_T = 0.3; 14 scenarios were constructed for each.

Fig A2.

Relationship between sample size and the percentage of time the true maximum-tolerated dose (MTD) is selected in two standard scenarios. Sel, selection.