Design specification of Partial Ordering Continual Reassessment Method based on consistency conditions

TL;DR

This paper analyzes the Partial Ordering Continual Reassessment Method (POCRM) for drug combination trials, revealing its potential inconsistencies and offering practical guidelines for selecting orderings to improve performance in small samples.

Contribution

It identifies the inconsistency issues in current POCRM orderings and proposes new consistency conditions along with practical recommendations for better ordering selection.

Findings

POCRM can be inconsistent under current orderings.

Derived conditions improve small sample performance.

Guidelines help select orderings based on toxicity scenarios.

Abstract

The study of combinations of drugs/drug-schedules gained increasing attention in various therapeutic areas recently. In oncology, the aim of phase I combination clinical trial is to find the maximum tolerated combination (MTC). Many innovative designs were proposed, among which the Partial Ordering Continual Reassessment Method (POCRM) is increasingly applied due to its simplicity and versatility. The POCRM requires specification of plausible monotonic orderings of combinations. However, the choice remains a major difficulty, especially in trials with many compounds or/and combinations. Practical recommendations are given to select six orderings based on statistical considerations, while simulation studies found the design performs poorly when the MTC is in the middle of the combination grid. We prove that the POCRM under currently recommended orderings can be inconsistent (i.e., cannot achieve 100\% correct selection even under infinite samples) which translates into poor performance under small sample size. Based on the derived consistency conditions, we provide two practical recommendations on how to select orderings for real studies (i) based on plausible combination-toxicity scenarios, (ii) regardless of the possible scenarios. We also provide guidance on how to choose other design parameters based on the asymptotic properties and demonstrate how it improves small sample behaviours.