# A methodological framework for constructing opioid agonist therapy episodes in administrative health data

## TL;DR

This paper introduces a new framework for accurately tracking opioid treatment episodes in health data by considering medication switches and dispensing patterns.

## Contribution

The novel contribution is a methodological framework combining Allen’s interval algebra, temporal margins, and drug-specific permissible gaps for OAT episode construction.

## Key findings

- The before relation was most common for methadone dispensations.
- Monotherapy episodes made up 93.53% of all identified OAT episodes.
- The framework is transferable to other populations with parameter adjustments.

## Abstract

Opioid Agonist Therapy (OAT) is the most effective intervention to reduce overdose risk, and administrative health data are now increasingly used to study OAT outcomes. However, current methods for constructing OAT episodes rely heavily on fixed permissible gaps and often overlook switches between medications, concurrent therapies, and the temporal complexity of dispensing patterns. We aimed to develop a robust episode-construction framework that more precisely reflects real-world OAT use within administrative health data.

We analyzed OAT dispensations from people living with HIV in British Columbia (2010–2020). Episodes were constructed using three components: Allen’s interval algebra, temporal margins (\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{E}$$\end{document}), and drug-specific permissible gaps. Allen’s algebra characterized the temporal relation between two dispensations as meets (one starts when another ends), before (a positive gap), overlaps (partial overlap), starts (same start, earlier end), finishes (later start, same end), contains (one fully encloses another), or equals (identical start and end). Temporal margins distinguished short from long overlaps within the same OAT medication and differentiated switches from concurrent therapy when different OATs overlapped. Permissible gaps defined the maximum interruption allowed before episode discontinuation and were mapped onto Allen’s before relation. Using this combined framework, we identified monotherapy (single-OAT use), transition (medication switches), multitherapy (concurrent OAT use), and transition-multitherapy episodes.

The before relation predominated across all OATs, particularly for methadone (99.43%). The equals relation was notably prevalent for buprenorphine (21.46%), slow-release oral morphine (20.87%), and injectable OAT (1.91%). To build monotherapy episodes, we applied \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{E}$$\end{document}=7 days, while \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{E}$$\end{document}=14 days differentiated transition from multitherapy episodes. We identified 10,386 episodes: 93.53% monotherapy, 3.72% transition, 2.27% multitherapy, and < 1% transition-multitherapy.

We propose an episode-building framework based on Allen’s relations, temporal margins, and permissible gaps that fine-tune OAT classification in administrative health data. The method is transferable to other settings and populations with suitable parameter adjustments.

The online version contains supplementary material available at 10.1186/s44330-026-00064-9.