Sensitivity of estimands in clinical trials with imperfect compliance
-
Heng Chen
and
Daniel F. Heitjan
Abstract
In clinical trials that are subject to noncompliance, the commonly used intention-to-treat estimand is valid as a causal effect of treatment assignment but is sensitive to the level of compliance. An alternative estimand, the complier average causal effect (CACE), measures the average effect of treatment received in the latent subset of subjects who would comply with either assigned treatment. Because the principal stratum of compliers can vary with the circumstances of the trial, CACE too depends on the compliance fraction. We propose a model in which an underlying latent proto-compliance interacts with trial characteristics to determine a subject’s compliance behavior. When the latent compliance is independent of the individual treatment effect, the average causal effect is constant across compliance classes, and CACE is robust across trials and equal to the population average causal effect. We demonstrate the potential degree of sensitivity of CACE in a simulation study, an analysis of data from a trial of vitamin A supplementation in children, and a meta-analysis of trials of epidural analgesia in labor.
Acknowledgment
We thank the reviewers for many helpful comments and suggestions.
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
1. Efron, B, Feldman, D. Compliance as an explanatory variable in clinical trials. J Am Stat Assoc 1991;86:9–17. https://doi.org/10.1080/01621459.1991.10474996.Search in Google Scholar
2. Balke, A, Pearl, J. Bounds on treatment effects from studies with imperfect compliance. J Am Stat Assoc 1997;92:1171–6. https://doi.org/10.1080/01621459.1997.10474074.Search in Google Scholar
3. Swanson, SA, Hernán, MA, Miller, M, Robins, JM, Richardson, TS. Partial identification of the average treatment effect using instrumental variables: review of methods for binary instruments, treatments, and outcomes. J Am Stat Assoc 2018;113:933–47. https://doi.org/10.1080/01621459.2018.1434530.Search in Google Scholar PubMed PubMed Central
4. Hernán, M, Robins, J. Causal inference: what if. Boca Raton, FL: Chapman & Hall/CRC; 2020.Search in Google Scholar
5. Angrist, JD, Imbens, GW, Rubin, DB. Identification of causal effects using instrumental variables. J Am Stat Assoc 1996;91:444–55. https://doi.org/10.1080/01621459.1996.10476902.Search in Google Scholar
6. Mounier-Vehier, C, Bernaud, C, Carré, A, Lequeuche, B, Hotton, JM, Charpentier, JC. Compliance and antihypertensive efficacy of amlodipine compared with nifedipine slow-release. Am J Hypertens 1998;11:478–86. https://doi.org/10.1016/s0895-7061(97)00485-8.Search in Google Scholar PubMed
7. Claxton, AJ, Cramer, J, Pierce, C. A systematic review of the associations between dose regimens and medication compliance. Clin Therapeut 2001;23:1296–310. https://doi.org/10.1016/s0149-2918(01)80109-0.Search in Google Scholar PubMed
8. Ogedegbe, GO, Boutin-Foster, C, Wells, MT, Allegrante, JP, Isen, AM, Jobe, JB, et al.. A randomized controlled trial of positive-affect intervention and medication adherence in hypertensive African Americans. Arch Intern Med 2012;172:322–6. https://doi.org/10.1001/archinternmed.2011.1307.Search in Google Scholar PubMed PubMed Central
9. Zhou, J, Hodges, JS, Suri, MFK, Chu, H. A Bayesian hierarchical model estimating CACE in meta-analysis of randomized clinical trials with noncompliance. Biometrics 2019;75:978–87. https://doi.org/10.1111/biom.13028.Search in Google Scholar PubMed PubMed Central
10. Baker, SG. CACE and meta-analysis (letter to the editor). Biometrics 2020;76:1383–4. https://doi.org/10.1111/biom.13240.Search in Google Scholar PubMed
11. Bannister-Tyrrell, M, Miladinovic, B, Roberts, CL, Ford, JB. Adjustment for compliance behavior in trials of epidural analgesia in labor using instrumental variable meta-analysis. J Clin Epidemiol 2015;68:525–33. https://doi.org/10.1016/j.jclinepi.2014.11.005.Search in Google Scholar PubMed
12. Zhou, J, Hodges, JS, Chu, H. A Bayesian hierarchical CACE model accounting for incomplete noncompliance with application to a meta-analysis of epidural analgesia on cesarean section. J Am Stat Assoc 2021;116:1700–12. https://doi.org/10.1080/01621459.2021.1900859.Search in Google Scholar PubMed PubMed Central
13. Imbens, GW, Rubin, DB. Bayesian inference for causal effects in randomized experiments with noncompliance. Ann Stat 1997;25:305–27. https://doi.org/10.1214/aos/1034276631.Search in Google Scholar
14. Imbens, GW, Rubin, DB. Causal inference in statistics, social, and biomedical sciences. Cambridge: Cambridge University Press; 2015.10.1017/CBO9781139025751Search in Google Scholar
15. Reiersøl, O. Confluence analysis by means of instrumental sets of variables. Stockholm: Almqvist & Wiksell; 1945.Search in Google Scholar
16. Epstein, RJ. The fall of OLS in structural estimation. Oxf Econ Pap 1989;41:94–107. https://doi.org/10.1093/oxfordjournals.oep.a041930.Search in Google Scholar
17. Angrist, J, Imbens, G. Identification and estimation of local average treatment effects. Econometrica 1994;62:467–75. https://doi.org/10.2307/2951620.Search in Google Scholar
18. Stock, JH, Trebbi, F. Retrospectives: who invented instrumental variable regression? J Econ Perspect 2003;17:177–94. https://doi.org/10.1257/089533003769204416.Search in Google Scholar
19. Hernán, MA, Robins, JM. Instruments for causal inference: an epidemiologist’s dream? Epidemiology 2006;17:360–72. https://doi.org/10.1097/01.ede.0000222409.00878.37.Search in Google Scholar PubMed
20. Wang, L, Tchetgen, ET. Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables. J Roy Stat Soc B 2018;80:531–50. https://doi.org/10.1111/rssb.12262.Search in Google Scholar PubMed PubMed Central
21. Ding, P, Lu, J. Principal stratification analysis using principal scores. J Roy Stat Soc B 2017;79:757–77. https://doi.org/10.1111/rssb.12191.Search in Google Scholar
22. Greenland, S. Response and follow-up bias in cohort studies. Am J Epidemiol 1977;106:184–7. https://doi.org/10.1093/oxfordjournals.aje.a112451.Search in Google Scholar PubMed
23. Hernán, MA. Invited commentary: selection bias without colliders. Am J Epidemiol 2017;185:1048–50. https://doi.org/10.1093/aje/kwx077.Search in Google Scholar PubMed PubMed Central
24. Frangakis, CE, Rubin, DB. Principal stratification in causal inference. Biometrics 2002;58:21–9. https://doi.org/10.1111/j.0006-341x.2002.00021.x.Search in Google Scholar PubMed PubMed Central
25. Sommer, A, Zeger, SL. On estimating efficacy from clinical trials. Stat Med 1991;10:45–52. https://doi.org/10.1002/sim.4780100110.Search in Google Scholar PubMed
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- Survival analysis using deep learning with medical imaging
- Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions
- Approximate reciprocal relationship between two cause-specific hazard ratios in COVID-19 data with mutually exclusive events
- Sensitivity of estimands in clinical trials with imperfect compliance
- Highly robust causal semiparametric U-statistic with applications in biomedical studies
- Hierarchical Bayesian bootstrap for heterogeneous treatment effect estimation
- Penalized logistic regression with prior information for microarray gene expression classification
- Bayesian learners in gradient boosting for linear mixed models
- Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates
- HiPerMAb: a tool for judging the potential of small sample size biomarker pilot studies
- Heterogeneity in meta-analysis: a comprehensive overview
- On stochastic dynamic modeling of incidence data
- Power of testing for exposure effects under incomplete mediation
- Exact correction factor for estimating the OR in the presence of sparse data with a zero cell in 2 × 2 tables
- Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset
- Assessing HIV-infected patient retention in a program of differentiated care in sub-Saharan Africa: a G-estimation approach
- Prediction-based variable selection for component-wise gradient boosting
Articles in the same Issue
- Frontmatter
- Research Articles
- Survival analysis using deep learning with medical imaging
- Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions
- Approximate reciprocal relationship between two cause-specific hazard ratios in COVID-19 data with mutually exclusive events
- Sensitivity of estimands in clinical trials with imperfect compliance
- Highly robust causal semiparametric U-statistic with applications in biomedical studies
- Hierarchical Bayesian bootstrap for heterogeneous treatment effect estimation
- Penalized logistic regression with prior information for microarray gene expression classification
- Bayesian learners in gradient boosting for linear mixed models
- Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates
- HiPerMAb: a tool for judging the potential of small sample size biomarker pilot studies
- Heterogeneity in meta-analysis: a comprehensive overview
- On stochastic dynamic modeling of incidence data
- Power of testing for exposure effects under incomplete mediation
- Exact correction factor for estimating the OR in the presence of sparse data with a zero cell in 2 × 2 tables
- Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset
- Assessing HIV-infected patient retention in a program of differentiated care in sub-Saharan Africa: a G-estimation approach
- Prediction-based variable selection for component-wise gradient boosting
