Dirichlet process mixture models for the analysis of repeated attempt designs

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.

Automated summary

In longitudinal studies, multiple attempts to collect a measurement after baseline are common. Recording whether these attempts are successful is important for assessing missing data assumptions. Previous models were limited in their ability to perform sensitivity analysis, but we propose a new approach that uses Bayesian nonparametrics and introduces a novel method for identification and sensitivity analysis. We applied this approach to a clinical trial dataset and conducted simulations to evaluate its properties.