Implementing response-adaptive designs when responses are missing: Impute or ignore?

Missing data is a widespread issue in clinical trials, but is particularly problematic for digital health interventions where disengagement is common and outcomes are likely to be missing not at random (MNAR). Trials that use response-adaptive designs need to handle missingness online and not simply at the end of the trial. We propose a novel online imputation strategy which allows previous imputations to be re-imputed given updated estimates of success probabilities. We additionally consider: (i) truncation of deterministic algorithms to prevent extreme realised treatment imbalance and (ii) changing the random component of semi-randomised algorithms. Through a simulation study based on a trial for a digital smoking cessation intervention, we illustrate how the strategy for handling missing responses can affect the exploration-exploitation tradeoff and the bias of the estimated success probabilities at the end of the trial. In the settings explored, we found that the exploration-exploitation tradeoff is affected particularly when arms have very different rates of missingness and we identified combinations of response-adaptive designs and missingness strategies that are particularly problematic. Further, we show that estimated success probabilities at the end of the trial can be biased not only due to optimistic sampling, but potentially also due to an MNAR missingness mechanism.