Sensitivity analysis for missing outcomes

Outcome data can be missing for many reasons. The reason why outcomes are missing is important to understand, as naive analyses may give biased results. For example, if people in a study tend to not show up to follow-up appointments because they're not doing well, then an analysis of the data of the (healthier) people who did continue to participate will have some biases. In such situations, sensitivity analysis can be helpful. With sensitivity analysis, we try to understand what the outcome (such as: average improvement from start to end of study) could look like for the entire study population, not just for the people whose outcomes are known.

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Specifically, we study a Bayesian procedure introduced by Scharfstein and co-authors, where a prior distribution is placed on a sensitivity function. The sensitivity function indicates how likely it is that someone will drop out, depending on their eventual outcome. With the prior distribution, we express our ideas about this relationship. We investigated two ways to create a prior distribution. In the first, ideas about the probability of dropping out of the study remain the same, no matter what outcomes we end up observing. In the second, our ideas about the probability of drop-out as a function of the outcome can be updated after seeing the outcomes. For both situations, we proved Bernstein-von Mises theorems, which tell us what the posterior distributions look like (when sufficient people participated in a study). With that, we can understand the behavior of the estimators from this procedure.

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This research received financial support from the Dutch Research Foundation (NWO), under Veni 192.087 'What if you missed something?'.