  In longitudinal studies, it is not uncommon to make multiple attempts to
collect a measurement after baseline. Recording whether these attempts are
successful provides useful information for the purposes of assessing missing
data assumptions. This is because measurements from subjects who provide the
data after numerous failed attempts may differ from those who provide the
measurement after fewer attempts. Previous models for these designs were
parametric and/or did not allow sensitivity analysis. For the former, there are
always concerns about model misspecification and for the latter, sensitivity
analysis is essential when conducting inference in the presence of missing
data. Here, we propose a new approach which minimizes issues with model
misspecification by using Bayesian nonparametrics for the observed data
distribution. We also introduce a novel approach for identification and
sensitivity analysis. We re-analyze the repeated attempts data from a clinical
trial involving patients with severe mental illness and conduct simulations to
better understand the properties of our approach.
