  We consider estimating the "de facto" or effectiveness estimand 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. Carpenter et al (2013) 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 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. Results from simulation
studies are presented. 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.
