A latent class based imputation method under Bayesian quantile regression framework using asymmetric Laplace distribution for longitudinal medication usage data with intermittent missing values.

Evaluating the association between diseases and the longitudinal pattern of pharmacological therapy has become increasingly important. However, in many longitudinal studies, self-reported medication usage data collected at patients' follow-up visits could be missing for various reasons. These pieces of missing or inaccurate/untenable information complicate determining the trajectory of medication use and its complete effects for patients. Although longitudinal models can deal with specific types of missing data, inappropriate handling of this issue can lead to a biased estimation of regression parameters especially when missing data mechanisms are complex and depend upon multiple sources of variation. We propose a latent class-based multiple imputation (MI) approach using a Bayesian quantile regression (BQR) that incorporates cluster of unobserved heterogeneity for medication usage data with intermittent missing values. Findings from our simulation study indicate that the proposed method performs better than traditional MI methods under certain scenarios of data distribution. We also demonstrate applications of the proposed method to data from the Prospective Study of Outcomes in Ankylosing Spondylitis (AS) cohort when assessing an association between longitudinal nonsteroidal anti-inflammatory drugs (NSAIDs) usage and radiographic damage in AS, while the longitudinal NSAID index data are intermittently missing.