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A Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized Clinical Trials Subject to Noncompliance
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Summary We consider the analysis of clinical trials that involve randomization to an active treatment (T = 1) or a control treatment (T = 0), when the active treatment is subject to all‐or‐nothing compliance. We compare three approaches to estimating treatment efficacy in this situation: as‐treated analysis, per‐protocol analysis, and instrumental variable (IV) estimation, where the treatment effect is estimated using the randomization indicator as an IV. Both model‐ and method‐of‐moment based IV estimators are considered. The assumptions underlying these estimators are assessed, standard errors and mean squared errors of the estimates are compared, and design implications of the three methods are examined. Extensions of the methods to include observed covariates are then discussed, emphasizing the role of compliance propensity methods and the contrasting role of covariates in these extensions. Methods are illustrated on data from the Women Take Pride study, an assessment of behavioral treatments for women with heart disease.
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“The impact of non-adherence (i.e. non-uptake of ACT in the intervention group) and contamination (i.e. delivery of psychological therapy in the control group) will be assessed using complier-average causal effect analysis and a per-protocol analysis. Average Causal Response analysis will be used to assess any incremental impacts of the number of ACT sessions received [65].”
From A randomised controlled trial of acceptance and commitment therapy plus usual care compared to usual care alone for improving psychological health in people with motor neuron disease (COMMEND): study protocol. (2022) · cites this paper as [65]
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Causal inference in randomized clinical trials
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“In addition, authors may use a per-protocol analysis to handle non-compliance [103] but an ITT analysis is the standard analysis and should be presented as well [104].”
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Medical Scribes as an Input in Health-Care Production: Evidence from a Randomized Experiment
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“Evaluable patient analysis has been criticized for the bias that results from imperfect randomization.(36,37) An empirical study found that run-in designs disproportionately exclude participants who are less educated and identify as Black, leading to selection bias.”
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“The main problem with this approach is that the group who actually received the treatment is unlikely to be comparable to the group who did not, making this approach prone to selection bias.(56) AT analysis is less commonly used in practice compared with ITT and PP conventional methods.”
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“As an alternative to ITT, PP or AT analysis, instrumental variable (IV) methods have been proposed [6,9].”
MethodNon-Compliance and Instrumental Variables in Behavioural Medicine: a Commentary on van Dongen et al.
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“The adjusted PP methods offer consistently excellent performance under the scenarios without unmeasured confounding [14].”
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“However, an ITT analysis provides estimates of treatment effectiveness, rather than efficacy (Little et al., 2009).”
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The Phantom Menace of Omitted Variables
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“…variable of interest, but are relevant determinants of the dependent variable, a circumstance that is not uncommon in natural experiments (e.g. Galiani et al., 2005; Little et al., 2009), then their inclusion can serve to increase the precision of the coefficient estimates without imparting bias.”
McGuire, A., Porter‐Steele, J., McDonald, N., Burgess, S., Anderson, D. J., & Seib, C. A. (2021) · Collegian Journal of the Royal College of Nursing Australia · doi:10.1016/j.colegn.2021.09.003 · Cited by 4
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“Besides, the 2SLS and 2SRI have a higher SE than other methods, which is consistent with the literature.(35) The wide bounds of the NPCB are consistent with the results of our recent simulation study(96) and a previous study.”
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“Although per-protocol and as-treated analysis are the most commonly used methods to supplement ITT in evaluating efficacy [4, 5], these post hoc analyses are bereft of the benefits of randomization.”
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Intention to Treat and Alternative Approaches
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Adaptive Mobile Health Intervention to Reduce Excess Gestational Weight Gain
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“PSM is used to improve the comparability of the differently treated groups (Little et al., 2009; Ten Have et al., 2008; Joffe et al., 2003).”
Following the long arc of history
Hébert, J. R., & Hofseth, L. J. (2022) · Elsevier eBooks · doi:10.1016/b978-0-12-822130-3.00007-7 · Cited by 2
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Conflicting Cues: Item Nonresponse and Experimental Mortality
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van den Bergh, J. C. J. M., Hoekstra, J., Imeson, R., Nunes, P. A. L. D., & de Blaeij, A. T. (2006) · Kluwer Academic Publishers eBooks · doi:10.1007/1-4020-4059-8_1 · Cited by 1
A note about the identifiability of causal effect estimates in randomized trials with non-compliance
Chan, K. C. G. (2013) · Statistical Methodology · doi:10.1016/j.stamet.2013.07.003 · Cited by 1
Causal inference methods to assess safety upper bounds in randomized trials with noncompliance
Wang, Y., Berlin, J. A., Pinheiro, J. C., & Wilcox, M. (2015) · Clinical Trials · doi:10.1177/1740774515572352 · Cited by 1
“Although we did not consider covariate adjustment (not yet implemented in the C-PROPHET or SNAFT STATA modules), it can reduce bias and improve precision for both causal and alternative methods.(36) We took the principal stratification approach(22) to noncompliance in clinical trials because our focus was potential ha…”
MethodResultBreslau, J. A., Leckman‐Westin, E., Han, B., Guarasi, D., Yu, H., Horvitz-Lennon, M. V., Pritam, R., & Finnerty, M. T. (2020) · Administration and Policy in Mental Health and Mental Health Services Research · doi:10.1007/s10488-020-01071-w · Cited by 1
Sun, X., Shin, Y., Lafata, J. E., & Raudenbush, S. W. (2024) · Statistics in Medicine · doi:10.1002/sim.10229 · Cited by 1
Liu, W., Qin, J., & Liu, Y. (2025) · Statistics in Medicine · doi:10.1002/sim.70153 · Cited by 1
Causal inference with complex sampling designs
Brumback, B., & He, Z. (2012) · Cited by 1
Yang, Z., Brentnall, A. R., Cuzick, J. M., & Sasieni, P. D. (2012) · International Journal of Statistics in Medical Research · doi:10.6000/1929-6029.2012.01.02.01
Odondi, L. (2013) · International Journal of Statistics and Probability · doi:10.5539/ijsp.v2n4p93
“However, these post-hoc analyses are devoid of the tenets of randomization and are likely to produce biased estimates due to selective choices arising from the underlying nature/pattern of arm-specific compliance (White, 2005; Little et al., 2009).”
The Phantom Menace of Omitted Variables – a CommentPreprint
Ritter, N., & Vance, C. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1927267
Ferguson, E. (2013) · RICERCHE DI PSICOLOGIA · doi:10.3280/rip2012-004009
Statistical causality in participant-unblinded randomised community trials
Pierse, N. (2011) · Otago University Research Archive (University of Otago)
BROWNE, G. B., & Thabane, L. (2014)
Randomization Inference and Principal Stratification in HIV Prevention Studies
Nolen, T. L. (2019) · ProQuest Demo Repository · doi:10.17615/g4wd-fb92
EVALUATING A BYSTANDER INTERVENTION PROGRAM ON REPRODUCTIVE COERCION
Starnes, C. P. (2016) · UKnowledge (University of Kentucky) · doi:10.13023/etd.2016.507
“The ITT analysis preserves and utilizes the benefits of random intervention assignment.(73,82) However, trials do not always go as planned.”
BackgroundMethodInfluentialAssessing Emergency Surgical Procedures for Life-Threatening Illness in Randomized Clinical Trials
Fujita, T. (2018) · Journal of the American College of Surgeons · doi:10.1016/j.jamcollsurg.2017.12.007
Out (2018) · Research Publications (Maastricht University) · doi:10.26481/dis.20180709mo
Ng, S., Byrnes, J., & Scuffham, P. (2019) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2019.07.013
“5% ) With adjustment for non-compliance using the IV method [10,12], the adjusted ITT estim ate for intervention efficacy is a saving of”
BackgroundMethodInfluentialSynthetic estimation for the complier average causal effect
Agniel, D. M., Cefalu, M. S., & Han, B. (2021) · Canadian Journal of Statistics · doi:10.1002/cjs.11634
Metadata
- Authors
- Little, R. J., Long, Q., & Lin, X.
- Affiliations
- University of Michigan (US)
- Emory University (US)
- Harvard University (US)
- Corresponding author
- Little, Roderick J.
- Long, Qi
- Lin, Xihong
- Venue
- Biometrics
- Publisher
- Oxford University Press (OUP)
- Published
- 2009-05-28
- Volume
- 65
- Issue
- 2
- Pages
- 640-649
- ISSN
- 0006-341X (ISSN-L)
- 1541-0420
- OpenAlex
- W2144385713
- Cited by
- 111
- References
- 34
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 3 · 2023: 4 · 2022: 6 · 2021: 4 · 2020: 8 · 2019: 11 · 2018: 6 · 2017: 3 · 2016: 5 · 2015: 9 · 2014: 6 · 2013: 8 · 2012: 8
- FWCI
- 5.95
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- Biometrics (publishedVersion)
- PubMed (publishedVersion)
- Deep Blue (University of Michigan) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Collection of Biostatistics Research Archive (submittedVersion)
- Funders
- National Cancer Institute (R01CA076404)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- treatment non-adherence, causal effect estimation, randomized controlled trials, as-treated analysis, per-protocol analysis, instrumental variable estimation
- MeSH terms
- Algorithms, Biometry, Computer Simulation, Data Interpretation, Statistical, Patient Compliance, Models, Statistical, Epidemiologic Research Design, Causality, Proportional Hazards Models, Randomized Controlled Trials as Topic, Outcome Assessment, Health Care
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