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

In various biomedical studies, the focus of analysis centers on the magnitudes of data, particularly when algebraic signs are irrelevant or lost. To analyze the magnitude outcomes in repeated measures studies, using models with random effects is essential. This is because random effects can account for individual heterogeneity, enhancing parameter estimation precision. However, there are currently no established regression methods that incorporate random effects and are specifically designed for magnitude outcomes. This article bridges this gap by introducing Bayesian regression modeling approaches for analyzing magnitude data, with a key focus on the incorporation of random effects. Additionally, the proposed method is extended to address multiple causes of informative dropout, commonly encountered in repeated measures studies. To tackle the missing data challenge arising from dropout, a joint modeling strategy is developed, building upon the previously introduced regression techniques. Two numerical simulation studies are conducted to assess the validity of our method. The chosen simulation scenarios aim to resemble the conditions of our motivating study. The results demonstrate that the proposed method for magnitude data exhibits good performance in terms of both estimation accuracy and precision, and the joint models effectively mitigate bias due to missing data. Finally, we apply proposed models to analyze the magnitude data from the motivating study, investigating if sex impacts the magnitude change in diaphragm thickness over time for ICU patients.