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An Executable Specification of Oncology Dose-Escalation Protocols with Prolog

David C. Norris, Markus Triska

TL;DR

This work presents an executable Prolog specification of the traditional $3 + 3$ dose-escalation design for oncology trials, grounded in regret-constrained (RC) CLP constraints over integer tallies to reflect clinically meaningful decisions. It introduces a reified regret mechanism and anticipatory regret to constrain escalation, de-escalation, and stopping rules, enabling formal safety and liveness verification prior to trial deployment. The RC framework yields a complete, monotonic, declarative specification that can reproduce standard natural-language descriptions, support rolling enrollment, and provide online decision support while preserving tractable, provable properties. Overall, the approach offers a general, testable, and adaptable platform for validating and operationalizing early-phase dose-escalation designs with formal guarantees.

Abstract

We present, as a pure Prolog program, the first executable specification of the 3 + 3 dose-escalation protocol commonly used in early-phase oncology drug development. In this program, the imperative operations of the protocol emerge as consequences of clinically meaningful anticipatory-regret scenarios that are declared as CLP(Z) constraints. This 'regret-constrained' (RC) specification yields a robust formulation which can be used to prove clinically meaningful safety and liveness properties of the protocol before incorporating it into a trial, and then as an on-line decision support system while the trial is underway. Our RC specification also readily accommodates certain pragmatic modifications to trial enrollment which severely strain traditionally imperative formulations. The features of modern Prolog systems let us describe the 3 + 3 protocol with a short and general program that has desirable algebraic properties and can therefore be used, tested and reasoned about in several different ways.

An Executable Specification of Oncology Dose-Escalation Protocols with Prolog

TL;DR

This work presents an executable Prolog specification of the traditional dose-escalation design for oncology trials, grounded in regret-constrained (RC) CLP constraints over integer tallies to reflect clinically meaningful decisions. It introduces a reified regret mechanism and anticipatory regret to constrain escalation, de-escalation, and stopping rules, enabling formal safety and liveness verification prior to trial deployment. The RC framework yields a complete, monotonic, declarative specification that can reproduce standard natural-language descriptions, support rolling enrollment, and provide online decision support while preserving tractable, provable properties. Overall, the approach offers a general, testable, and adaptable platform for validating and operationalizing early-phase dose-escalation designs with formal guarantees.

Abstract

We present, as a pure Prolog program, the first executable specification of the 3 + 3 dose-escalation protocol commonly used in early-phase oncology drug development. In this program, the imperative operations of the protocol emerge as consequences of clinically meaningful anticipatory-regret scenarios that are declared as CLP(Z) constraints. This 'regret-constrained' (RC) specification yields a robust formulation which can be used to prove clinically meaningful safety and liveness properties of the protocol before incorporating it into a trial, and then as an on-line decision support system while the trial is underway. Our RC specification also readily accommodates certain pragmatic modifications to trial enrollment which severely strain traditionally imperative formulations. The features of modern Prolog systems let us describe the 3 + 3 protocol with a short and general program that has desirable algebraic properties and can therefore be used, tested and reasoned about in several different ways.
Paper Structure (18 sections, 2 figures)

This paper contains 18 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Prolog prerequisites and compatibility considerations
  3. Dose-escalation trials
  4. The traditional rules of 3 + 3 dose-escalation
  5. Indeterminacies in dose escalation
  6. Regret-constrained specification of $\mathbf{3 + 3}$ designs
  7. Specific, clinically-motivated regrets
  8. Reification of regret
  9. Anticipatory regret
  10. Algebraic properties of our formulation
  11. Relation of our specification to natural-language descriptions
  12. Verification of safety properties
  13. Verification of liveness properties
  14. Generality and versatility of the specification
  15. Flexibly accommodating protocol variations
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Natural-language description of the 3 + 3 dose-escalation protocol, from korn_comparison_1994. Our specification implements the "more common requirement" described here.
  • Figure 2: Natural-language description of the 3 + 3 dose-escalation protocol, from skolnik_shortening_2008. The "more common" variant of korn_comparison_1994 appears to be taken for granted here.