Table 3. Proposed subgroup and sensitivity analysis.

Proposed sensitivity analysis	Rationale
Sample restriction
Stratified analysis for individuals who interrupted at a higher dose (≥80 mg/day for methadone; ≥16 mg/day for buprenorphine/naloxone)	A higher dose (≥80 mg/day for methadone; ≥16 mg/day for buprenorphine/naloxone) is associated with increased treatment retention and reduced unregulated opioid use.18 We will stratify the cohort based on the aforementioned dose at treatment interruption and conduct a stratified analysis to assess the impact on our primary results
Stratified analysis for the duration of treatment retention before time zero (1 to <3, 3 to <6, 6 to <12 and ≥12 months for methadone and buprenorphine/naloxone)	Cumulative incidence of treatment interruption (5 days for methadone or 6 days for buprenorphine/naloxone) increases with the duration from OAT initiation.82 We will stratify individuals based on the treatment retention and conduct a stratified analysis.
People who completed induction	The induction phase for treatment with methadone and buprenorphine/naloxone occurs while individuals receive their initial dose and gradually titrate up to their maintenance dose. Individuals are closely monitored during the induction phase to assess withdrawal symptoms, cravings and other adverse effects.3 18 Individuals are more unstable during induction phase compared with the maintenance phase.83 We will restrict the study population to individuals who completed induction, that is, individual reaches the end of a 2-week period with no dose increases.20 We will re-run the analysis to assess the impact of induction phase on our results.
Individuals with OUD with >1 year of cumulative OAT experience	To access the impact of dose adjustment strategies on treatment discontinuation among individuals with OAT experience
Evaluation of alternate exposure thresholds according to different clinical guidelines	Given that the 2017 BC guidelines3 provided dose adjustment strategies after missed methadone doses of 1–2, 3–4 or ≥5 days, and missed buprenorphine/naloxone doses of 1–5, 6–7 and ≥8 days, we will redefine the methadone trial to account for interruptions of 1–2, 3–4, 5–7 and 8–14 days, and the buprenorphine/naloxone trial to account for interruptions of 1–5, 6–7 and 8–14 days. Other components of trial emulation protocol will remain unchanged. This alternative trial definition will help assess the robustness of the results across different interruption lengths.
Excluding individuals who reinitiated from 1 October 2022 to 31 December 2022.	To address potential bias due to inadequate follow-up time near the study end date, we will exclude individuals reinitiating OAT in the final 3 months. This allows assessment of robustness to administrative censoring.
People with OUD in regions with highest fentanyl concentrations*	To access the treatment association among those who primarily misuse fentanyl.
Timeline restriction
The date of the first death for which fentanyl was detected in the province (1 April 2012)	Fentanyl, which is 50–100 times more potent than morphine, has significantly contributed to the overdose epidemic in North America and is implicated in 84% of drug-related toxicity cases in Canada from January to June 2023.84 Fentanyl was first detected in overdose deaths in BC on 1 April 2012. We will redefine the study population to the fentanyl era (1 April 2012 to 31 December 2022) and conduct the analysis. This will control for the impact of fentanyl’s emergence on treatment strategies and discontinuation.
Exposure classification
Treatment categories of each trial are redefined as of figure 1.	The treatment categories in the primary analysis are not explicitly defined but are empirically derived from the linked data set. This reclassification of treatment categories will assess the impact of alternative dose adjustment strategies on the primary results.
Alternative time zero: reinitiation dates after any (ie, first, second, and subsequent) treatment interruptions within episode	While we considered the first reinitiation date as the time zero in primary analyses, incorporating repeated eligibility and subsequent time zero increases statistical efficiency of the estimate.85 An individual may meet eligibility criteria repeatedly (such as following the first, second and subsequent interruptions) within an OAT episode in incident user and prevalent new-user designs. Following each interruption, we will mark the reinitiation date as a new time zero to emulate the trials. All covariates measured at each time zero will be included in the propensity score models of IPTW along with one additional confounder.† Other components of the emulation protocols will remain the same.
Outcome definition
Episode discontinuation: 30 days	Alternative discontinuation thresholds have been defined in other studies.86
Secondary outcome: all-cause acute care visits	In 2023, opioid-related poisonings resulted in 17 hospitalisations and 78 ED visits per day in Canada, marking a 16% increase compared with 2022.2 Repeat ED visits (two or more) for OUDs within a year rose from 26% to 34% between 2018 and 2022 in Alberta, Ontario and the Yukon.87 Time to all-cause acute care visits will be considered secondary outcomes. We will repeat the statistical analysis for this outcome to evaluate the impact of secondary outcome on our results. Other components of the target trial and emulation process will remain the same.
No truncation at 12 months of follow-up	While this redefining follow-up may cause instability in the weights of statistical analysis, the non-truncation at 12 months is to confirm the results.
Alternative definition of prevalent new users: no OAT dispensation in past 30 days	To account impact of alternative definition of prevalent new users on our results.
Composite outcome: Overdose-related acute care visits or OAT discontinuation	Instead of considering separate outcomes of overdose-related acute care visits and OAT discontinuation, we will consider the composite outcome of any of the two events. The other components of emulation will remain the same.
Model specification
Machine learning algorithms in hdPS analysis67 88	Potential interactions and non-linear terms may not have been fully captured in the hdPS analysis due to the large number of investigator-selected and top-ranked 200 empirical covariates, potentially leading to model misspecification bias. To address this potential bias, we will apply cross-fitted doubly-robust estimator to compare the treatment.88 We will model the binary exposure‡ using SuperLearner89 with a library consisting of generalised linear models, generalised additive models, multivariate adaptive regression splines, random forests and extreme gradient boosting. The conditional survival and censoring models will be estimated using the survSuperLearner90 with a library consisting of the treatment group-specific Kaplan-Meier estimators, parametric survival models, Cox proportional hazard models, generalised additive models and piecewise constant hazard models.88 A fivefold cross-validation will be applied to estimate each of the models using the same selected covariates specific to each trial. We will then estimate the risk difference at 1 year of post reinitiation date and cumulative incidence curves to compare the dose adjustment strategy (see detailed in online supplemental eMethods 4).

^*Restricted to the lower mainland Vancouver area after 1 April 2016 (declaration of public health emergency).

^†number of treatment interruptions prior to time zero.

^‡Binary exposure (which are the same as constructed for IV analysis): 1 for specific dose adjustment strategy and 0 for no dose change group.

BC, British Columbia; ED, emergency department; hdPS, high dimensional propensity score estimation; IPTW, inverse probability of treatment weighting estimation; IV, instrumental variable; OAT, opioid agonist treatment; OUD, opioid use disorder.