Bayesian Joint Modeling for Longitudinal Magnitude Data with Informative Dropout: an Application to Critical Care Data

In various biomedical studies, analysis often focuses on data magnitudes, particularly when algebraic signs are irrelevant or lost. For repeated measures studies involving magnitude outcomes, incorporating random effects is essential as they account for individual heterogeneity, thereby enhancing parameter estimation precision. However, established regression methods specifically designed for magnitude outcomes that incorporate random effects are currently lacking. This article bridges this gap by introducing Bayesian regression modeling approaches for analyzing magnitude data, with a key focus on incorporating random effects. The proposed method is further extended to address multiple causes of informative dropout, a common challenge in repeated measures studies. To tackle this missing data challenge, a joint modeling strategy is developed, building upon the introduced regression techniques. Two numerical simulation studies assess the validity of our method. The chosen simulation scenarios are designed to resemble the conditions of our motivating study. Results demonstrate that the proposed method for magnitude data performs well in terms of estimation accuracy, and the joint models effectively mitigate bias due to missing data. Finally, we apply these models to analyze magnitude data from the motivating study, investigating whether sex impacts the magnitude change in diaphragm thickness over time for ICU patients.