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Updated: Dec 23, 2025

Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations
Published on: July 24, 2021
A surface-free design for phase I dual-agent combination trials
Pavel Mozgunov1, Mauro Gasparini2, Thomas Jaki1
1Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.
Abstract:
In oncology, there is a growing number of therapies given in combination. Recently, several dose-finding designs for Phase I dose-escalation trials for combinations were proposed. The majority of novel designs use a pre-specified parametric model restricting the search of the target combination to a surface of a particular form. In this work, we propose a novel model-free design for combination studies, which is based on the assumption of monotonicity within each agent only. Specifically, we parametrise the ratios between each neighbouring combination by independent Beta distributions. As a result, the design does not require the specification of any particular parametric model or knowledge about increasing orderings of toxicity. We compare the performance of the proposed design to the model-based continual reassessment method for partial ordering and to another model-free alternative, the product of independent beta design. In an extensive simulation study, we show that the proposed design leads to comparable or better proportions of correct selections of the target combination while leading to the same or fewer average number of toxic responses in a trial.
Insights
This study introduces a novel model-free design for oncology combination trials. The new approach effectively identifies optimal drug combinations with comparable or better accuracy and fewer toxic responses than existing methods.
Area of Science:
- Oncology
- Clinical Trial Design
- Biostatistics
Background:
- Combination therapies are increasingly common in oncology.
- Existing Phase I dose-escalation designs often rely on restrictive parametric models.
- There is a need for flexible and robust dose-finding designs for combination treatments.
Purpose of the Study:
- To propose a novel model-free dose-finding design for Phase I oncology combination trials.
- To evaluate the performance of the proposed design against existing model-based and model-free methods.
- To demonstrate the design's ability to identify target combinations with reduced toxicity.
Main Methods:
- Developed a model-free design based on the assumption of monotonicity for each agent.
- Parametrized ratios between neighboring combinations using independent Beta distributions.
- Compared the proposed design with the continual reassessment method and the product of independent beta design via simulation.
Main Results:
- The proposed design achieved comparable or superior proportions of correct target combination selection.
- The design resulted in an equal or lower average number of toxic responses.
- Demonstrated robustness without requiring pre-specified parametric models or knowledge of toxicity ordering.
Conclusions:
- The novel model-free design offers an effective and safer alternative for Phase I oncology combination trials.
- This approach provides flexibility by avoiding restrictive model assumptions.
- The design shows promise for optimizing drug combinations in clinical settings.
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