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OBJECTIVES: Randomisation can be used as an instrumental variable (IV) to account for unmeasured confounding when seeking to assess the impact of non-compliance with treatment allocation in a randomised trial. We present and compare different methods to calculate the treatment effect on a binary outcome as a rate ratio in a randomised surgical trial. STUDY DESIGN AND SETTING: The effectiveness of peeling versus not peeling the internal limiting membrane of the retina as part of the surgery for a full thickness macular hole. We compared IV based estimates (non-parametric causal bound, and two stage residual inclusion approach [2SRI] with standard treatment effect measures (intention to treat [ITT], per protocol [PP] and treatment received [TR]). Compliance was defined in two ways (initial and up to time point of interest). Poisson regression was used for the model based approaches with robust standard errors to calculate the risk ratio with 95% confidence intervals. RESULTS: Results were similar for 1-month macular hole status across methods. For 3- and 6-month macular hole status, non-parametric causal bounds provided a narrower range of uncertainty than other methods, though still had substantial imprecision. For 3-month macular hole status, the TR estimate was substantially different from the other point estimates. CONCLUSION: Non-parametric causal bound approaches are a useful addition to an IV estimation approach, which tend to have large levels of uncertainty. Methods which allow risk ratios to be calculated when addressing non-compliance in randomised trials exist and may be superior to standard estimates. Further research is needed to explore the properties of different IV methods in a broad range of RCT scenarios.

Original publication




Journal article


J Clin Epidemiol

Publication Date



Instrumental variable, RCT, binary, causal modelling, risk ratio, non-compliance