Fast tipping point sensitivity analyses in clinical trials with missing continuous outcomes under multiple imputation

When dealing with missing data in clinical trials, it is often convenient to work under simplifying assumptions, such as missing at random (MAR), and follow up with sensitivity analyses to address unverifiable missing data assumptions. One such sensitivity analysis, routinely requested by regulatory agencies, is the so-called tipping point analysis, in which the treatment effect is re-evaluated after adding a successively more extreme shift parameter to the predicted values among subjects with missing data. If the shift parameter needed to overturn the conclusion is so extreme that it is considered clinically implausible, then this indicates robustness to missing data assumptions. Tipping point analyses are frequently used in the context of continuous outcome data under multiple imputation. While simple to implement, computation can be cumbersome in the two-way setting where both comparator and active arms are shifted, essentially requiring the evaluation of a two-dimensional grid of models. We describe a computationally efficient approach to performing two-way tipping point analysis in the setting of continuous outcome data with multiple imputation. We show how geometric properties can lead to further simplification when exploring the impact of missing data. Lastly, we propose a novel extension to a multi-way setting which yields simple and general sufficient conditions for robustness to missing data assumptions.