DEDUCTION

Dose Escalation Designs in Universal Context of Titration for Oncology Drug Development

Introduction

The category-theoretic perspective can function as a simplifying abstraction, isolating propositions that hold for formal reasons from those whose proofs require techniques particular to a given mathematical discipline.

— Emily Riehl, Preface to 'Category Theory in Context' (2016)

This project aims to formulate dose-escalation trial protocols using ideas from Applied Category Theory (ACT), carrying out the attendant computations on a 'workbench' developed using the monotonic subset of Prolog, including CLP(ℤ). In accordance with the quotation above, this categorial formulation serves to exhibit certain properties of dose-escalation designs as deducible from more basic premises than we may otherwise appreciate. Working in Prolog promotes a clarification of thought and elegance of expression that harmonize perfectly with the intellectual spirit of categorial investigations such as these. (For an extensive discussion of the advantages of Prolog in medical and other such safety-critical applications, and our rationale for selecting Scryer Prolog in particular, please see Section 2 of [1].)

Background

DEDUCTION represents the latest—and I now think, conclusive—development within the Dose Titration Algorithm Tuning (DTAT) research programme, which has been ongoing now for nearly a decade. The full bibliography found here links to 'lay explainers', short videos or online apps accompanying most of the scholarly outputs, reflecting the DTAT programme's long commitment to lay outreach. Although this outreach has been pursued with cancer patient advocates most especially in mind, these resources may prove useful even to experts in adjacent fields, since DTAT draws upon ideas from several disciplines not often brought under one roof.

Process

We are 'working with the garage door open', carrying out the DEDUCTION effort in this public repository.

A Mathematical Milestone

The work was presented in a June 2 talk at the Eighth International Conference on Applied Category Theory (ACT2025), and a thoroughly revised version of the submitted conference paper is now posted on the arXiv.

The preprint demonstrates a procedure for naturally converting any given dose-escalation design (defined over a fixed set of doses determined ex ante) to achieve rolling enrollment [3], while accounting for the possibility of pending toxicity assessments [4] and allowing for discretionary dose-titration [5].

This demonstrates the real possibility of achieving the "flexible and adaptive designs" called for by the Methodology for the Development of Innovative Cancer Therapies (MDICT) Taskforce [6].

Our Emphasis Evolves

The main thrust of the effort now shifts to finding applications through outreach to oncology trialists, and to building a robust software suite for the design and analysis of dose-titration trials.

Ongoing and Pending Technical Work

• Contribute probability distributions from Scryer fork via PR
• Investigate useful visualizations for high-dimensional tallies
• Visualize the dynamical operation of extended trial designs
• Apply the technique of [2] to 'modern' dose-escalation trial designs such as BOIN and CRM
• Accelerate dose-titration protocol simulations

References

1. Norris DC, Triska M. An Executable Specification of Oncology Dose-Escalation Protocols with Prolog. February 13, 2024. https://arxiv.org/abs/2402.08334

2. Norris DC. Dose-Escalation Trial Protocols that Extend Naturally to Admit Titration. July 2, 2025. https://arXiv.org/abs/2507.01370

3. Skolnik JM, Barrett JS, Jayaraman B, Patel D, Adamson PC. Shortening the Timeline of Pediatric Phase I Trials: The Rolling Six Design. Journal of Clinical Oncology. 2008;26(2):190-195. doi:10.1200/JCO.2007.12.7712

4. Frankel PH, Chung V, Tuscano J, et al. Model of a Queuing Approach for Patient Accrual in Phase 1 Oncology Studies. JAMA Network Open. 2020;3(5):e204787-e204787. doi:10.1001/jamanetworkopen.2020.4787

5. Norris DC. Ethical Review and Methodologic Innovation in Phase 1 Cancer Trials. JAMA Pediatrics. 2019;173(6):609. doi:10.1001/jamapediatrics.2019.0811

6. Araujo D, Greystoke A, Bates S, et al. Oncology phase I trial design and conduct: time for a change - MDICT Guidelines 2022. Annals of Oncology. 2023;34(1):48-60. doi:10.1016/j.annonc.2022.09.158