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. Author manuscript; available in PMC: 2023 Mar 1.
Published in final edited form as: Addiction. 2021 Oct 1;117(3):637–645. doi: 10.1111/add.15654

Association between dynamic dose increases of buprenorphine for treatment of opioid use disorder and risk of relapse

Kara E Rudolph 1, Matisyahu Shulman 2, Marc Fishman 3,4, Iván Díaz 5, John Rotrosen 6, Edward V Nunes 2
PMCID: PMC9717480  NIHMSID: NIHMS1847273  PMID: 34338389

Abstract

Background and Aims:

Dynamic, adaptive pharmacologic treatment for opioid use disorder (OUD) has been previously recommended over static dosing to prevent relapse, and is aligned with personalized medicine. However, there has been no quantitative evidence demonstrating its advantage. Our objective was to estimate the extent to which a hypothetical intervention that increased buprenorphine dose in response to opioid use would affect risk of relapse over 24 weeks of follow-up.

Design:

A secondary analysis of the buprenorphine arm of an open-label randomized controlled 24-week comparative effectiveness trial, 2014–17.

Setting:

Eight community addiction treatment programs in the United States.

Participants:

English-speaking adults with DSM-5 OUD, recruited during inpatient admission (n = 270). Participants were mainly white (65%) and male (72%).

Intervention(s):

Participants were treated with daily sublingual buprenorphine–naloxone (BUP–NX), with dose based on clinical indication, determined by the provider. We examined a hypothetical intervention of increasing dose in response to opioid use.

Measurements:

Outcome was relapse to regular opioid use during the 24 weeks of outpatient treatment, assessed in a survival framework. We estimated the relapse-free survival curves of participants under a hypothetical (i.e. counterfactual) intervention in which their BUP–NX dosage would be increased following their own subject-specific opioid use during the first 12 weeks of treatment versus a hypothetical intervention in which dose would remain constant.

Findings:

We estimated that increasing BUP–NX dose in response to recent opioid use would lower risk of relapse by 19.17 percentage points [95% confidence interval (CI) = −32.17, −6.18) (additive risk)] and 32% (0.68, 95% CI = 0.49, 0.86) (relative risk). The number-needed-to-treat with this intervention to prevent a single relapse is 6.

Conclusions:

In people with opioid use disorder, a hypothetical intervention that increases sublingual buprenorphine–naloxone dose in response to opioid use during the first 12 weeks of treatment appears to reduce risk of relapse over 24 weeks, compared with holding the dose constant after week 2.

Keywords: Adaptive treatment, buprenorphine, dynamic dosing, dynamic treatment, opioid use disorder, personalized medicine

INTRODUCTION

Opioid-related overdose is a national health emergency in the United States [1], and people with opioid use disorder (OUD) are at more than 10 times higher risk of death [2, 3]. There are multiple effective pharmacological treatments for OUD (i.e. buprenorphine, methadone, extended-release naltrexone) [4], but they remain underutilized [5]. Buprenorphine, a partial opioid agonist [6], has the advantage of being widely available [7], but treatment dropout and relapse rates are high [8, 9].

Illicit use of opioids while being treated with buprenorphine, especially early in the process, is associated with risk of relapse [10]. There are a range of clinical practices in responding to opioid use. Many providers use low-dose buprenorphine (below 8 mg) due to concerns for diversion or sedation and may respond to opioid use by increasing the requirements for psychosocial treatment or the level of care (move to intensive outpatient or a residential treatment setting) rather than increasing the dose. Other providers respond to cravings or opioid use by increasing buprenorphine dose based on evidence that continued use may be due to inadequate saturation of the opioid receptors under lower doses [11]. Data suggest that higher doses (e.g. 32 mg) may be needed to achieve full or near-full receptor occupancy and clinical effect [12]. However, trials have not systematically tested this range, and typical doses in clinical practice are in the range of 10–18 mg [13]. Although some patients do well on low to medium dosages, persistently high dropout and relapse rates raise the question of whether dynamic dose increases–i.e. continuing to raise the dose in response to an individual’s continued opioid use—would saturate more receptors and lower the risk of dropout and relapse.

Such a personalized, dynamic treatment strategy, sometimes referred to as ‘stepped care’ adaptive treatment, has been recommended previously for opioid addiction [14] and other substance use disorders [15], and is aligned with the broader goals of personalized medicine [16]. The general goal of dynamic treatment regimens [17, 18] is to use updated information on a participant’s history and/or ongoing course of treatment and response to make informed treatment decisions or modifications in real time to optimize outcomes. Although estimating the effects of dynamic treatment regimens is widespread in medical research, including to inform treatment of cancer [19, 20], mental illness [21, 22], HIV/AIDS [23, 24] and other chronic conditions [25, 26], to our knowledge there has been little evaluation of pharmacological dynamic treatment regimens in OUD (although adaptive, stepped-care counseling approaches have been studied in this group [27]). In particular, our hypothesis that increasing buprenorphine dose in response to illicit opioid use may reduce relapse risk has not been quantitatively evaluated.

The X:BOT comparative effectiveness trial that randomized OUD participants (1:1) to 24 weeks of treatment with extended-release naltrexone (XR–NTX) versus buprenorphine-naloxone (BUP-NX) [28] presents an opportunity to study the potential benefits of BUP–NX dynamic dosing, given its large sample and flexible dosing of BUP–NX (mainly in the 8–24 mg per day range) per clinical judgement. Specifically, we harnessed the naturalistic variation in BUP–NX dosing in relation to ongoing abstinence versus opioid use in a secondary analysis. We used a robust and efficient estimator of longitudinal, time-varying treatments [29] to estimate the difference in risk of relapse under a dynamic treatment regimen in which buprenorphine dose during the first 12 weeks of treatment is increased in response to participant-specific opioid use versus under a static regimen, where dose does not increase. We hypothesized that the risk of relapse would be lower under the dynamic treatment regimen.

METHODS

Data and sample

We used data from the subset of 270 participants who initiated BUP–NX treatment by receiving at least one dose in the X:BOT comparative effectiveness trial (ClinicalTrials.gov: NCT02032433), as described previously [28, 30, 31]. Briefly, the parent trial compared effectiveness of XR–NTX (n = 283) to BUP–NX (n = 287) in preventing opioid relapse, the trial’s end-point. X:BOT was conducted across eight sites of the National Drug Abuse Treatment Clinical Trials Network from 30 January to 31 January 2017. These sites were community-based addiction treatment programs with inpatient and outpatient medical management capabilities and frequent admissions with OUD. Participants were English-speaking adults with Diagnostic and Statistical Manual of Mental Disorders 5 (DSM-5) OUD who had used non-prescribed opioids during the previous 30 days. Additional exclusion criteria are shown in the Supporting information Appendix. The Institutional Review Board at the New York State Psychiatric Institute determined this secondary analysis of de-identified data to be non-human subject research.

Measures

BUP–NX dose

BUP–NX was dispensed at weeks 0 (t = 0,time at randomization), 1, 2, 3, 4, 6, 8, 10, 12, 14, 16 and 20 for sublingual daily self-administration. Although clinicians were encouraged by the lead study team to increase the dose of buprenorphine in response to cravings or opioid use, it was not part of the official protocol; there was variability in the application of this advice (see Results), and ultimately, dose and dose adjustment were based on the clinical judgement of the study medical staff. All ongoing treatment and dosing adjustments (or not) were performed at the addiction treatment site where the trial was conducted.

Outcome

The outcome was time to opioid relapse, occurring between 20 days post-randomization and prior to the end of the 24-week follow-up [the initial 20 days were excluded to preclude a relapse determination on the basis of opioids used for detoxification (methadone, buprenorphine) or early testing of blockade]. Consequently, relapse was possible during weeks 3–24; any participant who dropped out of the study prior to week 3 was considered to have relapsed in week 3. Our definition of relapse to regular opioid use (which we call ‘relapse’ for brevity) was operationalized slightly differently in this analysis than in the parent trial. A patient was classified as having relapsed if they used non-study opioids at least once per week for 4 consecutive weeks (relapse date defined as the start of week 4) or daily use for 7 consecutive days (relapse date defined as the end date), where missed visits or refused urine samples were considered as positive for opioid use, consistent with the parent trial [28].

Baseline Covariates

We considered numerous covariates that could potentially act as confounders and/or as moderators, many of which were used in previous analyses [28, 32]. Covariates included study site, gender, age, homeless status, race/ethnicity, level of education, marital status, primary drug cost, employment, age at onset of heroin use, history of intravenous (i.v.) drug use, duration of opioid use, history of amphetamine use, sedative use, cannabis use, alcohol use disorder, cocaine use disorder, whether or not living with someone with problematic alcohol use, whether or not living with someone who uses drugs, history of psychiatric disorder, prior opioid withdrawal discomfort level, whether or not this was the first treatment for OUD, baseline pain score, baseline depressive score, severity of opioid use and timing of randomization.

Time-varying covariates

We considered the time-varying covariates of (1) the most recently prescribed buprenorphine dose and (2) weekly illicit opioid use that was under the threshold of what was considered relapse (henceforth, ‘subthreshold’). Weekly illicit opioid use was assessed each week of the 24 weeks of follow-up, and was positive if the participant reported using opioids [methadone, morphine (heroin, codeine, morphine), oxycodone] from the time-line follow-back interview [33] or if a urine drug screen was positive for the above. Urine drug screens at weeks 1 and 2 could have been affected by medication used for detoxification, so for these weeks we excluded positives for opioid types used during detoxification (buprenorphine, possibly in combination with methadone, depending on the individual).

Statistical analysis

As a secondary analysis of a randomized trial, this study was exploratory. Our statistical approach can be summarized as follows. We used data throughout the duration of the 24-week trial, discretized into weeks. We used the observed data to model the longitudinal relationship between the time-varying exposure of buprenorphine dose increase on the outcome of time to first relapse, conditional on the time-varying covariates of previous-week opioid use and buprenorphine dose and baseline covariates. This longitudinal modeling approach uses sequential regression [,3436] such that BUP–NX dosage influences the likelihood of subsequent opioid use which, in turn, influences subsequent BUP–NX dosage in a dynamic/reciprocal manner [29, 37]. We then used this model to predict how risk of relapse would be affected if, every time there was opioid use, buprenorphine dose was subsequently increased versus remained constant regardless of use. Note that individuals were considered censored after their first relapse event.

Because missed visits or refused urine samples were considered positive for opioid use, the outcome has no missingness. Missingness of baseline covariates was minimal (<1%). The time-varying covariates of opioid use and buprenorphine dose were missing for between 4 and 11% of uncensored participants, depending on the time-point (where ‘uncensored’ at time t means those who had not yet relapsed and were still participating in the study at time t). If dose was missing at week t, we classified missing opioid use as negative for opioid use, because missing dose indicated that the provider did not have the opportunity to adjust the dose. If dose was not missing at week t,we classified missing opioid use as positive for opioid use, in alignment with the definition of relapse in the primary analysis of X:BOT [28]. For missing dose, we carried forward the previous dose, which we believe is more accurate than imputing, because the last prescribed dose is what the participant would have access to throughout the trial. We addressed missing data in the baseline covariates with multiple imputation by chained equations [38], which assumes that data are missing at random conditional on the variables in the imputation model. We generated five imputed data sets, executed the analysis on each and combined the resulting estimates using Rubin’s combining rules [39].

Let Lt = 1 denote subthreshold illicit opioid use and BUP-NX dose <32 mg at time t and Lt = 0 otherwise, and At = 1 denote increased BUP-NX dose at time t. We assessed the effect of a hypothetical dynamic regimen d(Lt − 1), in which treatment at time t would be assigned according to Lt −1. Specifically, d(Lt − 1) = 1 denotes increased BUP-NX dose at time t in response to illicit, subthreshold opioid use in the prior week (Lt −1), as long as dose in the prior week was <32 mg, for weeks 2, 3, 4, 8, 10 and 12 (week 6 was omitted because no participants had dose increases in response to opioid use that week). So, d(Lt − 1) = 1 if Lt − 1 = 1, else d(Lt − 1) = 0. We estimated the average treatment effect: P(Ydt) - P(Yd′t) for all t ∈ (3, ..., 24), where Yd denotes the counterfactual time-to-relapse in a hypothetical world where treatment would be assigned according to regimen d. This is the expected risk of relapse by time t contrasted under the longitudinal, counterfactual dynamic treatment regimen d versus d′. The regimen d′ represents a static regimen where d′(Lt − 1) = 0 for all t∈(2, 3,4,8,10,12) and represents no increase in dose during that time-frame, regardless of opioid use. In other words, we contrasted the relapse-free survival curve of participants under a hypothetical (i.e. counterfactual) intervention in which their BUP–NX dose was increased during the week following their own subject-specific, subthreshold opioid use versus a hypothetical intervention in which dose remained constant. We provide and discuss the assumptions under which this causal effect is identified from the observed data in the Supporting information Appendix.

We used a longitudinal targeted minimum loss-based estimator to estimate the above effect [29], which is a doubly robust and efficient substitution estimator, and incorporated an ensemble of machinelearning algorithms [40] to flexibly model relationships (detailed in the Supporting information Appendix). Variances were estimated using the sample variance of the influence curve [29]. In the results that follow, we present estimates of: (1) the predicted risk of relapse by time t had the dynamic treatment regimen of increasing dose in response to use been followed [P(Ydt)], (2) the predicted risk of relapse by time t had the static treatment regimen been followed [P(Ydt)], (3) the difference between these two predictions [P(Ydt) − P (Yd′t)], which is called the additive treatment effect (ATE) or the treatment effect on the additive scale, and (4) the ratio of these two predictions P(Ydt)P(Ydt), which is called the relative risk (RR) or the treatment effect on the relative scale.

We used R (version 4.0.4) for all analyses [41] and the ltmle [42] and SuperLearner packages [43]. The code to replicate the analyses is available at: https://github.com/kararudolph/code-for-papers/XBOT_BUPdosing.

RESULTS

Table 1 displays descriptive information on the participants randomized to BUP–NX and initiating treatment. Participants were mainly male, white, had a high school education or greater, reported current i.v. drug use and had history of a psychiatric disorder. The mean maximum buprenorphine dose was 16.36 mg and the median maximum dose was 16 mg, as has been reported previously [28]. The percentages of participants reaching various maximum dosing thresholds during the course of treatment were: 27% had a maximum dose <16 mg, 73% ≥16 mg; 71% had a maximum dose <20 mg, 29% ≥20 mg; 79% had a maximum dose <24 mg, 21% ≥ 24 mg. A total of 245 individuals had subthreshold opioid use while on a BUP–NX dose<32 mg, and of these, 25 had a dose increase during the week following use. As shown in Supporting information, Table S1, most of the participants who relapsed stopped medication early (74%, a retention-related outcome), approximately one-fifth met relapse criteria by using opioids for 4 consecutive weeks and none met relapse criteria by using opioids for 7 consecutive days.

TABLE 1.

Descriptive statistics for those randomized to BUP–NX and initiating treatment (n = 270)

Never use
Use
All Never increase Non-responsive increase Never increasea Non-responsive increase Responsive increase
n 270 9 16 106 114 25

Baseline covariates
Women 28.5 22.2 37.5 24.5 30.7 32.0
Age (years) 33.67 (9.81) 34.44 (8.05) 32.5 (10.14) 34.06 (10.56) 33.92 (9.6) 31.32 (7.93)
Homeless 23.7 11.1 37.5 20.8 25.4 24.0
White 65.2 100.0 68.8 66.0 61.4 64.0
Black
Hispanic/Latino 19.6 0.0 25.0 17.9 22.8 16.0
Other race 6.3 0.0 0.0 7.5 6.1 8.0
<High school (HS) 41.5 33.3 43.8 38.7 43.9 44.0
HS/GED 34.4 55.6 43.8 35.8 30.7 32.0
>HS
Married 7.8 0.0 6.2 10.4 7.0 4.0
Primary opioid consumption cost ($/day) 94.12 (73.78) 148.33 (120.52) 105.31 (84.43) 95.42 (62.6) 82.21 (68.16) 116.2 (101.65)
Employed 36.3 66.7 18.8 34.0 38.6 36.0
Age first started using heroin (years) 21.8 (10.63) 22.11(11.11) 20.25 (12.27) 23.94 (9.84) 19.86 (11) 22.44 (9.93)
Duration of opioid use (years) 12.23 (9.09) 10.89 (5.4) 12.62 (9.48) 12.12 (10.02) 12.71 (8.79) 10.72 (7.19)
Current i.v. drug use 68.1 55.6 62.5 70.8 67.5 68.0
History amphetamine use 25.2 22.2 31.2 20.8 23.7 48.0
History sedative use 38.1 33.3 37.5 34.0 43.9 32.0
History cannabis use 55.2 55.6 56.2 50.9 54.4 76.0
Moderate/extreme self-reported pain (versus none) 37.8 44.4 43.8 34.9 38.6 40.0
Depressive symptom score 9.45 (6.71) 7.78 (7.9) 7.81 (5.46) 7.99 (6.35) 10.25 (6.76) 13.64 (6.26)
Alcohol use disorder 30 11.1 31.2 22.6 36.8 36.0
Cocaine use disorder 34.4 22.2 50.0 35.8 31.6 36.0
Living with someone with an alcohol use disorder 11.9 0.0 6.2 13.2 10.5 20.0
Living with someone who uses drugs 19.6 22.2 37.5 15.1 21.1 20.0
Severe opioid useb 40 55.6 12.5 50.0 34.2 36.0
Late randomization timing (versus early) 60 44.4 81.2 46.2 70.2 64.0
History of psychiatric disorder 67.8 33.3 62.5 59.4 76.3 80.0
Not previously treated for OUD 38.9 66.7 50.0 42.5 29.8 48.0
Past opioid withdrawal discomfort (0–10) 6.61 (3.12) 7.89 (1.83) 6.69 (2.85) 6.97 (2.95) 6.13 (3.46) 6.8 (2.5)
Time-varying covariates Maximum dose 16.56 (5.63) 14.67 (4.9) 17.62 (4.8) 13.89 (5.01) 18.19 (5.03) 20.48 (6.46)
Number dose increases 0.87 (0.93) 0(0) 1.5 (0.63) 0(0) 1.49 (0.74) 1.68 (0.69)
Outcomes Week of relapse 15.25 (8.03) 21.67 (4) 22.38 (2.5) 12.22 (8.35) 17.44 (6.95) 11.28 (7.23)
Relapse by week 24 55.6 11.1 6.2 69.8 46.5 84.0
a

Non-responsive static dose;

b

≥6 bags of i.v. heroin per day in the 7 days prior to admission. BUP–NX = buprenorphine–naltrexone; OUD = opioid use disorder; GED = general educational development; i.v. = intravenous.

We estimated the predicted effect of a hypothetical dynamic BUP–NX treatment regimen in which dose was increased in weeks 2, 3, 4, 8, 10 and 12 in response to subrelapse opioid use during the previous week compared to a static regimen where the dose remained constant during this time-period, on risk of relapse. By the end of the 24 weeks, such a dynamic dosing strategy was estimated to reduce cumulative risk of relapse by 19.17 percentage points [95% confidence interval (CI) = −32.17, −6.18, additive scale], with a relative risk reduction of 0.68 (95% CI = 0.49, 0.86, relative scale). These results translate to a number needed to treat of six, meaning that treating six individuals with a dynamic BUP–NX regimen in which dosage is increased in response to opioid use would be expected to prevent one relapse.

Figure 1a shows the estimated cumulative risk of relapse at each week of the trial comparing the hypothetical dynamic dose increase regimen with static dosing. Smoothed lines (loess) are fitted over these point estimates. Figure 1b shows the average treatment effect, taking the difference between the two curves in Figure 1a and associated 95% CIs at each time-point. In Fig. 1b we see the advantage of the dynamic dosing regimen over the duration of the trial, with slight differences in the point estimates by treatment week but overlapping CIs.

FIGURE 1.

FIGURE 1

Cumulative predicted risk of relapse by week comparing dynamic dose increase of buprenorphine–naloxone in response to subrelapse opioid use to constant/static dose. Secondary analysis of the buprenorphine–-naloxone arm of the X:BOT trial (n = 270)

DISCUSSION

Using data from a large comparative effectiveness trial for the treatment of OUD, we estimated that a hypothetical intervention in which the BUP–NX dose would be increased in response to recent opioid use during the first 12 weeks of treatment would lower the absolute risk of relapse over 24 weeks by 19 percentage points (additive risk) and 32% (relative risk) compared to static dosing. This translates to a number-needed-to-treat of six, which is within the range of other useful interventions for substance and mental health problems [44].

Previous studies compared flexible dosing of different pharmacotherapies to each other (e.g. buprenorphine versus methadone) but not within medication type, where ‘flexible’ dosing was based on patient and provider preference and, notably, was not standardized via dynamic treatment rules such as the one we examine here [6]. Flexible dosing in trials for substance use disorder treatment is abundant, whereas adaptive randomized trials in which dynamic treatment rules are part of the design are rare [26]. An example of such a trial was one in which patients not responding to buprenorphine were transferred to methadone, resulting in improved outcomes [45]. Given that flexible dosing and treatment within trials is much more common, some have advocated using these data to estimate the effects of clinically relevant dynamic treatments, a recent example being dynamic buprenorphine dosing for chronic pain patients [26]. Estimation of the effects of dynamic treatment regimens is a cornerstone of precision medicine and critical for understanding when and how treatments should be tailored, such that they are responsive to a patient’s changing health and behavior [46].

The maintenance dosage recommended for buprenorphine is between 12 and 24 mg, with evidence suggesting that higher doses (perhaps over a particular threshold, e.g.≥16 mg, or perhaps incrementally along a continuum) are protective against dropping out of treatment and relapse [6, 47]. In addition, evidence suggests an association between inadequate buprenorphine dosages and drug use while on treatment [11]. Such findings are consistent with buprenorphine’s pharmacological mechanism; studies have shown that buprenorphine dose needs to be high enough to result in full or near-full opioid-receptor occupancy (although individuals probably differ in terms of the dose required to achieve this) [12, 48]. While withdrawal and craving may be reduced at lower doses, higher doses have been shown to be important for blocking the positive reinforcing effects of opioids that are a key driver of drug use [49, 50].

The effects we estimated controlled for possible confounding effects of dose while allowing for the effect of increasing dose on subsequent risk of relapse to operate through higher doses. However, the effect of coupling a dynamic regimen with a minimum dose requirement remains an open question.

A related question is how a strategy in which buprenorphine dose would be increased regardless of opioid use would affect relapse risk compared to the two strategies we examined here (increased dose in response to use and constant dose). Too few participants had dose increases in the absence of opioid use to allow us to estimate the predicted effect of such a hypothetical strategy. Another open question is to determine an optimal rule by which participants would be assigned to the dynamic versus static dosing strategy as a function of their baseline covariates. Using the approach of Luedtke & van der Laan (2016) [51], we found that the optimal rule (such that risk of relapse was minimized) was to assign everyone to receive dynamic dose increases versus constant doses.

Limitations

Although our results suggested an advantage to increasing the BUP–NX dose in response to illicit opioid use, it is important to consider the limitations of this study. It was a secondary analysis of trial data—the X:BOT trial was neither designed nor powered to test the effect of dynamic BUP–NX treatment on relapse to OUD. Indeed, only 25 participants had a dose increase following use, resulting in limited power and wide CIs, although related analyses have relied upon similar sample sizes. As discussed above, precision medicine experts have argued that trial data with flexible dosing is well suited for such secondary analyses of dynamic treatment regimens, resulting in more fully utilizing available data to understand heterogeneities both in treatment and during the course of this chronic, relapsing disorder [26, 46].

In addition, in this trial, all patients were hospitalized and abstinent prior to treatment initiation. Our conclusions may not generalize to the more common clinical situation where outpatients are started on buprenorphine while they are still actively using opioids. It is possible that dynamic dosing may have more of an impact in this outpatient setting where abstinence has not yet been achieved.

Our outcome of ‘relapse’ did not distinguish between dropping out of treatment or the study early and relapse to regular opioid use, as missed visits or refused urine samples were considered positive for opioid use [28]. While such an operationalization introduces misclassification, research suggests that assuming relapse from study dropout may be reasonable [5255]. As shown in the Supporting information, Table S1, the majority of participants met ‘relapse’ criteria by discontinuing treatment or dropping out of the study early, suggesting that increasing the dose in response to use may be effective largely through improving retention.

Another limitation was that this was an observational analysis, so our results may have been biased due to residual confounding. For example, patient motivation may have confounded our estimated associations, and was unmeasured. Although we were unable to control this and other sources of residual confounding, we took several steps to address confounding due to measured variables. We incorporated more than two dozen baseline covariates hypothesized to act as potential confounders. We used a doubly robust estimator of longitudinal effects [29], which means that our estimates are expected to be unbiased even if either our treatment models or outcome models are misspecified. Additionally, the estimator we used appropriately incorporates the time-varying confounders of illicit opioid use and buprenorphine dose and time-varying exposures [29]. We also used an ensemble of machine learning algorithms to flexibly fit each model and incorporated 10-fold cross-validation to mitigate risk of overfitting [40].

Strengths and conclusions

We found evidence that increasing BUP–NX dose in response to opioid use would reduce risk of relapse compared to holding the BUP– NX dose constant after week 2. Our utilization of weekly data up to 24 weeks of treatment from a large, multi-site clinical trial that has been influential in informing clinical practice are strengths. Future research could utilize prospective, randomized designs to further explore our hypothesis that dynamic dosing is a superior strategy, perhaps by building-in standardized approaches via dynamic treatment rules as part of an adaptive trial design.

Supplementary Material

Appendix

ACKNOWLEDGEMENTS

This work was supported by the National Institute on Drug Abuse (R00DA042127, R01DA053243; Principal Investigator: K.E.R.).

Funding information

Columbia University: Data Science Institute; National Institute on Drug Abuse, Grant/Award Number: R00DA042127, R01DA053243.

Footnotes

CLINICAL TRIAL REGISTRATION

ClinicalTrials.gov, NCT02032433. However, this is a secondary analysis of one of the trial arms.

DECLARATION OF INTERESTS

J.R. has received medication and/or other support for research studies from Alkermes, Reckitt-Benckiser, Indivior and Braeburn. E.V.N. has received medication for research studies from Alkermes/Cephalon, Duramed Pharmaceuticals and Reckitt-Benckiser. The other authors have no conflicts of interest to report.

SUPPORTING INFORMATION

Additional supporting information may be found in the online version of the article at the publisher’s website.

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