Assessing Opioid Use Disorder Treatments in Trials Subject to Non-Adherence via a Functional Generalized Linear Mixed-Effects Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Generalized Linear Functional Mixed-Effects Model
2.2. Prior Specification
2.3. Data Augmentation and Posterior Sampling
3. Secondary Data Analysis of Buprenorphine Efficacy
3.1. Trial Data
3.2. Patient Characteristics
3.3. Functional General Linear Mixed Model
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Posterior Distributions
Appendix B. Efficacy and Safety Clinical Trials of Buprenorphine Maintenance Treatment
Division (Study ID) | Title | Investigators | Release Date |
---|---|---|---|
DTMC (CSP-999) | A Multicenter Clinical Trial of Buprenorphine in Treatment of Opiate Dependence | Walter Ling, M.D., Donald R. Wesson, M.D., C. James Klett, Ph.D. | 2 September 2015 |
DTMC (CSP-1008A) | A Multicenter Efficacy/Safety Trial of Buprenorphine/Naloxone for the Treatment of Opiate Dependence | Peter Bridge, M.D., Paul J. Fudala, Ph.D. | 4 December 2014 |
DTMC (CSP-1008B) | A Multicenter Safety Trial of Buprenorphine/Naloxone for the Treatment of Opiate Dependence | Peter Bridge, M.D. | 4 December 2014 |
DTMC (CSP-1018) | A Multicenter Safety Trial of Buprenorphine/Naloxone for the Treatment of Opiate Dependence | Walter Ling, M.D., Paul J. Fudala, Ph.D., Paul Casadonte, M.D. | 2 September 2015 |
CTN (CTN-0027) | Starting Treatment with Agonist Replacement Therapies (START) | Walter Ling, M.D. | 30 July 2009 |
CTN (CTN-0030) | A Two-Phase Randomized Controlled Clinical Trial of Buprenorphine/Naloxone Treatment Plus Individual Drug Counseling for Opioid Analgesic Dependence | Walter Ling, M.D., Roger Weiss, M.D. | 22 June 2011 |
Appendix C. Model Analysis for CSP-999 Trial
Appendix C.1. Patient Characteristics
Appendix C.2. Functional Generalized Linear Mixed Model
All Trials | CSP-999 | |||||
---|---|---|---|---|---|---|
Variable | Est | ESE | CI95 | Est | ESE | CI95 |
Intercept | 2.05 | 0.27 | (1.54, 2.61) | 1.49 | 0.77 | (−0.07, 2.96) |
Age | −0.02 | 0.01 | (−0.03, −0.01) | −0.02 | 0.02 | (−0.05, 0.03) |
Gender (Ref: Male) | ||||||
Female | 0.13 | 0.08 | (−0.03, 0.30) | 0.43 | 0.26 | (−0.03, 0.94) |
Race (Ref: White) | ||||||
Black | −0.16 | 0.14 | (−0.43, 0.12) | −1.27 | 0.32 | (−1.89, −0.64) |
American Indian | 0.14 | 0.27 | (−0.39, 0.68) | −0.62 | 0.88 | (−2.83, 0.83) |
Asian | −0.14 | 0.27 | (−0.72, 0.35) | −1.31 | 1.44 | (−4.83, 0.67) |
Hispanic | −0.22 | 0.12 | (−0.46, 0.02) | 0.02 | 0.24 | (−0.47, 0.52) |
Other | −0.32 | 0.67 | (−1.79, 0.93) | |||
Education (Ref: High School) | ||||||
Graduate School | −0.34 | 0.24 | (−0.81, 0.11) | −1.27 | 0.86 | (−2.98, 0.21) |
Standard College | 0.05 | 0.16 | (−0.25, 0.37) | −0.11 | 0.34 | (−0.79, 0.59) |
Partial College | −0.18 | 0.10 | (−0.39, 0.02) | −0.04 | 0.21 | (−0.47, 0.37) |
Partial High School | −0.27 | 0.15 | (−0.58, 0.01) | −0.03 | 0.27 | (−0.63, 0.44) |
Junior High School | −0.20 | 0.21 | (−0.63, 0.18) | −0.18 | 0.34 | (−0.98, 0.44) |
Less than 7th Grade | −0.35 | 0.47 | (−1.39, 0.47) | −0.48 | 0.84 | (−2.53, 0.88) |
Emp. History (Ref: Skilled) | ||||||
Never Gainfully | 0.07 | 0.14 | (−0.20, 0.34) | 0.02 | 0.32 | (−0.62, 0.70) |
Unskilled | −0.20 | 0.16 | (−0.52, 0.09) | −0.22 | 0.36 | (−0.97, 0.44) |
Machine Operator | −0.01 | 0.13 | (−0.26, 0.24) | −0.18 | 0.28 | (−0.76, 0.34) |
Clerical/Sales | 0.11 | 0.12 | (−0.14, 0.35) | 0.07 | 0.28 | (−0.51, 0.64) |
Administrative | −0.04 | 0.15 | (−0.35, 0.24) | 0.04 | 0.32 | (−0.55, 0.73) |
Business Manager | −0.24 | 0.24 | (−0.72, 0.22) | −0.93 | 0.93 | (−3.03, 0.48) |
Executive | −0.18 | 0.26 | (−0.71, 0.29) | 0.05 | 1.04 | (−2.03, 2.47) |
Work Type (Ref: Full time) | ||||||
Regular PT | −0.10 | 0.15 | (−0.39, 0.18) | −0.42 | 0.34 | (−1.13, 0.21) |
Irregular PT | 0.07 | 0.13 | (−0.19, 0.35) | 0.29 | 0.30 | (−0.25, 0.91) |
Student | 0.06 | 0.26 | (−0.44, 0.61) | 0.17 | 0.72 | (−1.38, 1.67) |
Military | −0.28 | 1.22 | (−3.25, 2.02) | |||
Retired | 0.23 | 0.24 | (−0.19, 0.71) | 0.21 | 0.79 | (−1.13, 2.08) |
Unemployed | 0.33 | 0.14 | (0.05, 0.59) | 0.35 | 0.34 | (−0.27, 1.05) |
Controlled | 0.84 | 0.59 | (−0.2, 2.11) | 1.18 | 0.97 | (−0.30, 3.30) |
Income | 0.00 | 0.00 | (0.00, 0.00) | 0.00 | 0.00 | (0.00, 0.00) |
Marital Status (Ref: Married) | ||||||
Remarried | −0.17 | 0.39 | (−1.01, 0.59) | 0.56 | 0.93 | (−1.07, 2.67) |
Widowed | 0.19 | 0.25 | (−0.25, 0.73) | 0.30 | 0.52 | (−0.61, 1.38) |
Separated | 0.19 | 0.17 | (−0.10, 0.55) | 0.15 | 0.33 | (−0.46, 0.81) |
Divorced | 0.04 | 0.12 | (−0.20, 0.28) | 0.09 | 0.28 | (−0.44, 0.66) |
Never Married | 0.19 | 0.12 | (−0.05, 0.42) | 0.35 | 0.26 | (−0.08, 0.89) |
Living Arr (Ref: Partner and Child) | ||||||
Partner Only | 0.24 | 0.13 | (−0.02, 0.49) | 0.79 | 0.30 | (0.17, 1.38) |
Child Only | −0.03 | 0.16 | (−0.36, 0.29) | −0.19 | 0.31 | (−0.82, 0.42) |
Parents | 0.21 | 0.17 | (−0.10, 0.53) | 0.28 | 0.29 | (−0.23, 0.87) |
Family | 0.05 | 0.16 | (−0.27, 0.36) | −0.22 | 0.34 | (−0.96, 0.38) |
Friends | −0.14 | 0.16 | (−0.44, 0.17) | −0.07 | 0.30 | (−0.74, 0.50) |
Alone | −0.03 | 0.18 | (−0.42, 0.31) | 0.10 | 0.70 | (−1.40, 1.60) |
Controlled | −0.01 | 0.37 | (−0.77, 0.75) | 0.98 | 1.02 | (−0.63, 3.24) |
No Stable | −0.15 | 0.36 | (−0.93, 0.52) |
All Trials | CSP−999 | |||||
---|---|---|---|---|---|---|
Variable | Est | ESE | CI95 | Est | ESE | CI95 |
Heroine Use (Ref: YES) | ||||||
NO | −0.57 | 0.21 | (−1.00, −0.16) | |||
Years of Opiate Use | 0.01 | 0.01 | (−0.01, 0.02) | 0.01 | 0.02 | (−0.02, 0.04) |
Mode of Opioid Abuse (Ref: IV) | ||||||
Oral | −1.32 | 0.23 | (−1.78, −0.88) | −1.21 | 0.48 | (−2.11, −0.21) |
Snorting | −0.14 | 0.10 | (−0.35, 0.06) | −0.15 | 0.23 | (−0.60, 0.29) |
Smoking | −0.40 | 0.28 | (−0.94, 0.09) | −0.57 | 0.78 | (−2.37, 0.69) |
Sublingual | −1.34 | 0.97 | (−3.42, 0.16) | |||
Other | 0.02 | 0.41 | (−0.82, 0.89) | −0.42 | 0.72 | (−2.08, 0.74) |
Cocaine Use (Ref: YES) | ||||||
NO | −0.04 | 0.09 | (−0.22, 0.12) | −0.17 | 0.28 | (−0.69, 0.37) |
Meth Use (Ref: NO) | ||||||
YES | 0.13 | 0.09 | (−0.05, 0.31) | 0.77 | 0.28 | (0.24, 1.31) |
Alcohol Use (Ref: YES) | ||||||
NO | −0.12 | 0.10 | (−0.33, 0.07) | −0.49 | 0.23 | (−0.97, −0.04) |
Tranquilizer Use (Ref: NO) | ||||||
YES | 0.07 | 0.10 | (−0.14, 0.25) | 0.38 | 0.24 | (−0.06, 0.85) |
Marijuana Use (Ref: YES) | ||||||
NO | 0.05 | 0.10 | (−0.16, 0.25) | 0.20 | 0.23 | (−0.27, 0.64) |
PCP Use (Ref: NO) | ||||||
YES | −0.01 | 0.11 | (−0.22, 0.21) | −0.07 | 0.28 | (−0.60, 0.54) |
Mean | Median | Range | |
---|---|---|---|
Daily Dose | 7.49 | 4 | 0–64 |
Time in Trial | 148.76 | 133 | 3–527 |
Urinalysis (Yes = 1) | 0.51 | 1 | 0–1 |
Demographics | Sociodemographics | ||||
---|---|---|---|---|---|
Age | Mean | SD | Income | Mean | SD |
36.16 | 7.78 | 19,454 | 21,365 | ||
Gender | N | % | Employment History | N | % |
Male | 453 | 69 | Skilled Manual | 151 | 23 |
Female | 201 | 31 | Never Gainfully | 168 | 26 |
Race | N | % | Machine Operator | 83 | 13 |
White | 309 | 47 | Clerical/Sales | 124 | 19 |
Hispanic | 184 | 28 | Administrative | 54 | 8 |
Black | 152 | 23 | Unskilled | 64 | 10 |
American Indian | 5 | 1 | Business Manager | 7 | 1 |
Asian | 4 | 1 | Executive | 3 | <1 |
Other | 0 | 0 | Work Type | N | % |
Full time | 294 | 45 | |||
Drug Use History | Unemployed | 198 | 30 | ||
Years of Opiate Abuse | Mean | SD | Irregular PT | 81 | 12 |
11.56 | 8.70 | Regular PT | 58 | 9 | |
Heroin Use | N | % | Retired | 7 | 1 |
YES | 654 | 100 | Student | 7 | 1 |
NO | 0 | 0 | Controlled | 9 | 1 |
Mode of Opiate Abuse | N | % | Military | 0 | 0 |
IV | 406 | 62 | Education | N | % |
Snort | 194 | 30 | High School | 213 | 33 |
Oral | 37 | 6 | Partial College | 201 | 31 |
Smoking | 9 | 1 | Partial High School | 119 | 18 |
Other | 8 | 1 | Standard College | 48 | 7 |
Sublingual | 0 | 0 | Junior High School | 56 | 8 |
Cocaine Use | N | % | Complete Graduate School | 11 | 2 |
YES | 540 | 83 | Less than 7th Grade | 6 | 1 |
NO | 114 | 17 | Marital Status | N | % |
Meth Use | N | % | Married | 170 | 26 |
NO | 436 | 67 | Never Married | 256 | 39 |
YES | 218 | 33 | Divorced | 142 | 22 |
Alcohol Use | N | % | Separated | 64 | 10 |
YES | 446 | 68 | Widowed | 18 | 3 |
NO | 208 | 32 | Remarried | 4 | <1 |
Tranquilizer Use | N | % | Living Arr | N | % |
NO | 353 | 54 | Partner and Child | 163 | 25 |
YES | 301 | 46 | Partner Only | 126 | 19 |
Marijuana Use | N | % | Parents | 116 | 18 |
YES | 482 | 74 | Family | 55 | 8 |
NO | 172 | 26 | Friends | 97 | 15 |
PCP Use | N | % | Alone | 8 | 1 |
NO | 533 | 82 | Child Only | 82 | 13 |
YES | 121 | 18 | Controlled | 7 | 1 |
No Stable | 0 | 0 |
Variable | Est | ESE | CI95 |
---|---|---|---|
Race (Ref: White) | |||
Black | −11.27 | 0.32 | (−11.89, −10.64) |
Living Arr (Ref: Partner and Child) | |||
Partner Only | 0.79 | 0.30 | (0.17, 1.38) |
Mode of Opioid Abuse (Ref: IV) | |||
Oral | −11.21 | 0.48 | (−12.11, −10.21) |
Meth Use (Ref: NO) | |||
YES | 0.77 | 0.28 | (0.24, 1.31) |
Alcohol Use (Ref: YES) | |||
NO | −10.49 | 0.23 | (−10.97, −10.04) |
References
- Kuehn, B.M. Massive Costs of the US Opioid Epidemic in Lives and Dollars. JAMA 2021, 325, 2040. [Google Scholar] [CrossRef] [PubMed]
- Kampman, K.; Jarvis, M. American Society of Addiction Medicine (ASAM) National Practice Guideline for the Use of Medications in the Treatment of Addiction Involving Opioid Use. J. Addict. Med. 2015, 9, 358–367. [Google Scholar] [CrossRef] [PubMed]
- Ling, W.; Jacobs, P.; Hillhouse, M.; Hasson, A.; Thomas, C.; Freese, T.; Sparenborg, S.; McCarty, D.; Weiss, R.; Saxon, A.; et al. From research to the real world: Buprenorphine in the decade of the Clinical Trials Network. J. Subst. Abuse Treat. 2010, 38 (Suppl. 1), S53–S60. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Mattick, R.P.; Breen, C.; Kimber, J.; Davoli, M. Buprenorphine maintenance versus placebo or methadone maintenance for opioid dependence. Cochrane Database Syst. Rev. 2014, 2, CD002207. [Google Scholar] [CrossRef] [PubMed]
- Fiellin, D.A.; Pantalon, M.V.; Chawarski, M.C.; Moore, B.A.; Sullivan, L.E.; O’Connor, P.G.; Schottenfeld, R.S. Counseling plus buprenorphine-naloxone maintenance therapy for opioid dependence. N. Engl. J. Med. 2006, 355, 365–374. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Bergen, A.W.; Baurley, J.W.; Ervin, C.M.; McMahan, C.S.; Bible, J.; Stafford, R.S.; Mudumbai, S.C.; Saxon, A.J. Effects of buprenorphine dose and therapeutic engagement on illicit opiate use in opioid use disorder treatment trials. Int. J. Environ. Res. Public Health 2022, 19, 4106. [Google Scholar] [CrossRef] [PubMed]
- Ramsay, J.; Silverman, B. Functional Data Analysis, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
- Hastie, T.; Tibshirani, R.; Friedman, J. The Elemnts of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Armagan, A.; Dunson, D.; Lee, J. Generalized double Pareto shrinkage. Stat. Sin. 2013, 23, 119–143. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Browne, W.J.; Draper, D. A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Anal. 2006, 1, 473–514. [Google Scholar] [CrossRef]
- Gelman, A.; Carlin, J.B.; Stern, H.S.; Dunson, D.B.; Vehtari, A.; Rubin, D.B. Bayesian Data Analysis, 3rd ed.; Chapman and Hall/CRC: London, UK, 2013. [Google Scholar]
- Polson, N.; Scott, J.; Windle, J. Bayesian inference for logistic models using Pólya-Gamma latent variables. J. Am. Stat. Assoc. 2012, 108, 1339–1349. [Google Scholar] [CrossRef] [Green Version]
- Audigier, V.; Husson, F.; Josse, J. A principal component method to impute missing values for mixed data. Adv. Data Anal. Classif. 2016, 10, 5–26. [Google Scholar] [CrossRef]
- Crist, R.C.; Vickers-Smith, R.; Kember, R.L.; Rentsch, C.T.; Xu, H.; Edelman, E.J.; Hartwell, E.E.; Kampman, K.M.; Kranzler, H.R. Analysis of genetic and clinical factors associated with buprenorphine response. Drug Alcohol Depend. 2021, 227, 109013. [Google Scholar] [CrossRef] [PubMed]
- Hser, Y.I.; Evans, E.; Grella, C.; Ling, W.; Anglin, D. Long-term course of opioid addiction. Harv. Rev. Psychiatry 2015, 23, 76–89. [Google Scholar] [CrossRef] [PubMed]
- Weiss, R.D.; Potter, J.S.; Provost, S.E.; Huang, Z.; Jacobs, P.; Hasson, A.; Lindblad, R.; Connery, H.S.; Prather, K.; Ling, W. A multi-site, two-phase, Prescription Opioid Addiction Treatment Study (POATS): Rationale, design, and methodology. Contemp. Clin. Trials 2010, 31, 189–199. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Dreifuss, J.A.; Griffin, M.L.; Frost, K.; Fitzmaurice, G.M.; Potter, J.S.; Fiellin, D.A.; Selzer, J.; Hatch-Maillette, M.; Sonne, S.C.; Weiss, R.D. Patient characteristics associated with buprenorphine/naloxone treatment outcome for prescription opioid dependence: Results from a multisite study. Drug Alcohol Depend. 2013, 131, 112–118. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Stefanski, L.A. Measurement Error Models. J. Am. Stat. Assoc. 2000, 95, 1353–1358. [Google Scholar] [CrossRef]
- Center for Disease Control and Prevention. Drug Overdose Deaths in the U.S. Top 100,000 Annually. 2021. Available online: https://www.cdc.gov/nchs/pressroom/nchs_press_releases/2021/20211117.htm (accessed on 19 April 2022).
- Lapham, G.; Boudreau, D.M.; Johnson, E.A.; Bobb, J.F.; Matthews, A.G.; McCormack, J.; Liu, D.; Samet, J.H.; Saxon, A.J.; Campbell, C.I.; et al. Prevalence and treatment of opioid use disorders among primary care patients in six health systems. Drug Alcohol Depend. 2020, 207, 107732. [Google Scholar] [CrossRef] [PubMed]
- Ma, J.; Bao, Y.P.; Wang, R.J.; Su, M.F.; Liu, M.X.; Li, J.Q.; Degenhardt, L.; Farrell, M.; Blow, F.C.; Ilgen, M.; et al. Effects of medication-assisted treatment on mortality among opioids users: A systematic review and meta-analysis. Mol. Psychiatry 2019, 24, 1868–1883. [Google Scholar] [CrossRef] [PubMed]
- Park, T.; Casella, G. The Bayesian Lasso. J. Am. Stat. Assoc. 2008, 103, 681–686. [Google Scholar] [CrossRef]
Demographics | Sociodemographics | ||||
---|---|---|---|---|---|
Age | Mean | SD | Income | Mean | SD |
36.14 | 9.85 | 20,834 | 30,025 | ||
Gender | N | % | Employment History | N | % |
Male | 2017 | 67 | Skilled Manual | 889 | 29 |
Female | 1005 | 33 | Never Gainfully | 653 | 22 |
Race | N | % | Machine Operator | 445 | 15 |
White | 2001 | 66 | Clerical/Sales | 407 | 13 |
Hispanic | 495 | 16 | Administrative | 239 | 8 |
Black | 422 | 14 | Unskilled | 235 | 8 |
American Indian | 50 | 2 | Business Manager | 101 | 3 |
Asian | 48 | 2 | Executive | 53 | 2 |
Other | 6 | <1 | Work Type | N | % |
Full time | 1758 | 58 | |||
Drug Use History | Unemployed | 582 | 19 | ||
Years of Opiate Abuse | Mean | SD | Irregular PT | 284 | 9 |
8.23 | 8.41 | Regular PT | 232 | 8 | |
Heroin Use | N | % | Retired | 84 | 3 |
YES | 2354 | 78 | Student | 64 | 2 |
NO | 668 | 22 | Controlled | 17 | <1 |
Mode of Opiate Abuse | N | % | Military | 1 | <1 |
IV | 1710 | 57 | Education | N | % |
Snort | 1089 | 36 | High School | 1456 | 48 |
Oral | 122 | 4 | Partial College | 829 | 27 |
Smoking | 74 | 2 | Partial High School | 304 | 10 |
Other | 22 | 1 | Standard College | 213 | 7 |
Sublingual | 5 | <1 | Junior High School | 116 | 4 |
Cocaine Use | N | % | Complete Graduate School | 89 | 3 |
YES | 1837 | 61 | Less than 7th Grade | 15 | 1 |
NO | 1185 | 39 | Marital Status | N | % |
Meth Use | N | % | Married | 1038 | 34 |
NO | 2304 | 76 | Never Married | 1014 | 33 |
YES | 718 | 24 | Divorced | 602 | 20 |
Alcohol Use | N | % | Separated | 261 | 9 |
YES | 1891 | 63 | Widowed | 87 | 3 |
NO | 1131 | 37 | Remarried | 20 | 1 |
Tranquilizer Use | N | % | Living Arr | N | % |
NO | 1997 | 66 | Partner and Child | 1251 | 41 |
YES | 1025 | 34 | Partner Only | 537 | 18 |
Marijuana Use | N | % | Parents | 294 | 10 |
YES | 1953 | 65 | Family | 263 | 9 |
NO | 1069 | 35 | Friends | 255 | 8 |
PCP Use | N | % | Alone | 190 | 6 |
NO | 2545 | 84 | Child Only | 183 | 6 |
YES | 477 | 16 | Controlled | 25 | 1 |
No Stable | 24 | 1 |
Mean | Median | Range | |
---|---|---|---|
Daily Dose | 12.65 | 14 | 0–90 |
Days in Trial | 112.70 | 87 | 1–527 |
Urinalysis | 0.41 | 0 | 0–1 |
Variable | Est | ESE | CI95 |
---|---|---|---|
Intercept | 2.05 | 0.27 | (1.54, 2.61) |
Age | −0.02 | 0.01 | (−0.03, −0.01) |
Work Type (Ref: Full time) | |||
Unemployed | 0.33 | 0.14 | (0.05, 0.59) |
Heroine Use (Ref: YES) | |||
No Heroine Use | −0.57 | 0.21 | (−1.00, −0.16) |
Mode of Opioid Abuse (Ref: IV) | |||
Oral | −1.32 | 0.23 | (−1.78, −0.88) |
Est | ESE | CI95 | |
---|---|---|---|
All Trials | −0.09 | <0.01 | (−0.09, −0.08) |
CSP-999 | −0.11 | 0.01 | (−0.12, −0.10) |
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St. Ville, M.; Bergen, A.W.; Baurley, J.W.; Bible, J.D.; McMahan, C.S. Assessing Opioid Use Disorder Treatments in Trials Subject to Non-Adherence via a Functional Generalized Linear Mixed-Effects Model. Int. J. Environ. Res. Public Health 2022, 19, 5456. https://doi.org/10.3390/ijerph19095456
St. Ville M, Bergen AW, Baurley JW, Bible JD, McMahan CS. Assessing Opioid Use Disorder Treatments in Trials Subject to Non-Adherence via a Functional Generalized Linear Mixed-Effects Model. International Journal of Environmental Research and Public Health. 2022; 19(9):5456. https://doi.org/10.3390/ijerph19095456
Chicago/Turabian StyleSt. Ville, Madeleine, Andrew W. Bergen, James W. Baurley, Joe D. Bible, and Christopher S. McMahan. 2022. "Assessing Opioid Use Disorder Treatments in Trials Subject to Non-Adherence via a Functional Generalized Linear Mixed-Effects Model" International Journal of Environmental Research and Public Health 19, no. 9: 5456. https://doi.org/10.3390/ijerph19095456