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I discuss the assumptions needed for identification of average treatment effects and local average treatment effects in instrumented difference-in-differences (IDID), and the possible trade-offs between assumptions of standard IV and those needed for the new proposal IDID, in one- and two-sample settings. I also discuss the interpretation of the estimands identified under monotonicity. I conclude by suggesting possible extensions to the estimation method, by outlining a strategy to use data-adaptive estimation of the nuisance parameters, based on recent developments.

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Non-adherence to assigned treatment is a common issue in cluster randomised trials. In these settings, the efficacy estimand may also be of interest. Many methodological contributions in recent years have advocated using instrumental variables to identify and estimate the local average treatment effect. However, the clustered nature of randomisation in cluster randomised trials adds to the complexity of such analyses. In this paper, we show that the local average treatment effect can be estimated via two-stage least squares regression using cluster-level summaries of the outcome and treatment received under certain assumptions. We propose the use of baseline variables to adjust the cluster-level summaries before performing two-stage least squares in order to improve efficiency. Implementation needs to account for the reduced sample size, as well as the possible heteroscedasticity, to obtain valid inferences. Simulations are used to assess the performance of two-stage least squares of cluster-level summaries under cluster-level or individual-level non-adherence, with and without weighting and robust standard errors. The impact of adjusting for baseline covariates and of appropriate degrees of freedom correction for inference is also explored. The methods are then illustrated by re-analysing a cluster randomised trial carried out in a specific UK primary care setting. Two-stage least squares estimation using cluster-level summaries provides estimates with small to negligible bias and coverage close to nominal level, provided the appropriate small sample degrees of freedom correction and robust standard errors are used for inference.

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Nonadherence to assigned treatment is common in randomized controlled trials (RCTs). Recently, there has been increased interest in estimating causal effects of treatment received, for example, the so-called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two-stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of their perceived complexity and need for specialist software. Here, we propose using multiple imputation (MI) to impute the latent compliance class appearing in the mixture models. Since such models include an interaction term between the latent compliance class and randomized treatment, we use "substantive model compatible" MI (SMC MIC), which can additionally handle missing data in outcomes and other variables in the model, before fitting the mixture models via maximum likelihood to the MI data sets and combining results via Rubin's rules. We use simulations to compare the performance of SMC MIC to existing approaches and also illustrate the methods by reanalyzing an RCT in UK primary health. We show that SMC MIC can be more efficient than full Bayesian estimation when auxiliary variables are incorporated, and is superior to two-stage methods, especially for binary outcomes.

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BACKGROUND: Treatment non-adherence in randomised trials refers to situations where some participants do not receive their allocated treatment as intended. For cluster randomised trials, where the unit of randomisation is a group of participants, non-adherence may occur at the cluster or individual level. When non-adherence occurs, randomisation no longer guarantees that the relationship between treatment receipt and outcome is unconfounded, and the power to detect the treatment effects in intention-to-treat analysis may be reduced. Thus, recording adherence and estimating the causal treatment effect adequately are of interest for clinical trials. OBJECTIVES: To assess the extent of reporting of non-adherence issues in published cluster trials and to establish which methods are currently being used for addressing non-adherence, if any, and whether clustering is accounted for in these. METHODS: We systematically reviewed 132 cluster trials published in English in 2011 previously identified through a search in PubMed. RESULTS: One-hundred and twenty three cluster trials were included in this systematic review. Non-adherence was reported in 56 cluster trials. Among these, 19 reported a treatment efficacy estimate: per protocol in 15 and as treated in 4. No study discussed the assumptions made by these methods, their plausibility or the sensitivity of the results to deviations from these assumptions. LIMITATIONS: The year of publication of the cluster trials included in this review (2011) could be considered a limitation of this study; however, no new guidelines regarding the reporting and the handling of non-adherence for cluster trials have been published since. In addition, a single reviewer undertook the data extraction. To mitigate this, a second reviewer conducted a validation of the extraction process on 15 randomly selected reports. Agreement was satisfactory (93%). CONCLUSION: Despite the recommendations of the Consolidated Standards of Reporting Trials statement extension to cluster randomised trials, treatment adherence is under-reported. Among the trials providing adherence information, there was substantial variation in how adherence was defined, handled and reported. Researchers should discuss the assumptions required for the results to be interpreted causally and whether these are scientifically plausible in their studies. Sensitivity analyses to study the robustness of the results to departures from these assumptions should be performed.

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Missing outcomes are a commonly occurring problem for cluster randomised trials, which can lead to biased and inefficient inference if ignored or handled inappropriately. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. In this study, we assessed the performance of unadjusted cluster-level analysis, baseline covariate-adjusted cluster-level analysis, random effects logistic regression and generalised estimating equations when binary outcomes are missing under a baseline covariate-dependent missingness mechanism. Missing outcomes were handled using complete records analysis and multilevel multiple imputation. We analytically show that cluster-level analyses for estimating risk ratio using complete records are valid if the true data generating model has log link and the intervention groups have the same missingness mechanism and the same covariate effect in the outcome model. We performed a simulation study considering four different scenarios, depending on whether the missingness mechanisms are the same or different between the intervention groups and whether there is an interaction between intervention group and baseline covariate in the outcome model. On the basis of the simulation study and analytical results, we give guidance on the conditions under which each approach is valid. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

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OBJECTIVE: To assess the quality of reported consent processes of cluster-randomised trials conducted in residential facilities for older people and to explore whether the focus on improving the general conduct and reporting of cluster-randomised trials influenced the quality of conduct and reporting of ethical processes in these trials. DESIGN: Systematic review of cluster-randomised trials reports, published up to the end of 2010. DATA SOURCES: National Library of Medicine (Medline) via PubMed, hand-searches of BMJ, Journal of the American Medical Association, BMC Health Services Research, Age and Ageing and Journal of the American Geriatrics Society, reference search in Web of Knowledge and consultation with experts. ELIGIBILITY FOR SELECTING STUDIES: Published cluster-randomised trials where the unit of randomisation is a part or the whole of a residential facility for older people, without language or year of publication restrictions. RESULTS: We included 73 trials. Authors reported ethical approval in 59, obtaining individual consent in 51, and using proxies for this consent in 37, but the process to assess residents' capacity to consent was clearly reported in only eight. We rated only six trials high for the quality of consent processes. We considered that individual informed consent could have been waived legitimately in 14  of 22 trials not reporting obtaining consent. The proportions reporting ethical approval and quality of consent processes were higher in recent trials. CONCLUSIONS: Recently published international recommendations regarding ethical conduct in cluster-randomised trials are much needed. In relation to consent processes when cognitively impaired individuals are included in these trials, we provide a six-point checklist and recommend the minimum information to be reported. Those who lack capacity in trials with complex designs should be afforded the same care in relation to consent as competent adults in trials with simpler designs.