  Not-at-random missingness presents a challenge in addressing missing data in
many health research applications. In this paper, we propose a new approach to
account for not-at-random missingness after multiple imputation through
weighted analysis of stacked multiple imputations. The weights are easily
calculated as a function of the imputed data and assumptions about the
not-at-random missingness. We demonstrate through simulation that the proposed
method has excellent performance when the missingness model is correctly
specified. In practice, the missingness mechanism will not be known. We show
how we can use our approach in a sensitivity analysis framework to evaluate the
robustness of model inference to different assumptions about the missingness
mechanism, and we provide R package StackImpute to facilitate implementation as
part of routine sensitivity analyses. We apply the proposed method to account
for not-at-random missingness in human papillomavirus test results in a study
of survival for patients diagnosed with oropharyngeal cancer.
