A causal modelling framework for reference-based imputation and tipping point analysis in clinical trials with quantitative outcome

We consider estimation in a randomised placebo-controlled or standard-of-care-controlled drug trial with quantitative outcome, where participants who discontinue an investigational treatment are not followed up thereafter, and the estimand follows a treatment policy strategy for handling treatment discontinuation. Our approach is also useful in situations where participants take rescue medication or a subsequent line of therapy and the estimand follows a hypothetical strategy to estimate the effect of initially randomised treatment in the absence of rescue or other active treatment. Carpenter et al proposed reference-based imputation methods which use a reference arm to inform the distribution of post-discontinuation outcomes and hence to inform an imputation model. However, the reference-based imputation methods were not formally justified. We present a causal model which makes an explicit assumption in a potential outcomes framework about the maintained causal effect of treatment after discontinuation. We use mathematical argument and a simulation study to show that the "jump to reference", "copy reference" and "copy increments in reference" reference-based imputation methods, with the control arm as the reference arm, are special cases of the causal model with specific assumptions about the causal treatment effect. We also show that the causal model provides a flexible and transparent framework for a tipping point sensitivity analysis in which we vary the assumptions made about the causal effect of discontinued treatment. We illustrate the approach with data from two longitudinal clinical trials.