Model Selection and Inference in Variational Longitudinal Distributed Lag Models for Analyzing Post-flight Effects of In-flight Exposures

Flight-related health effects are a growing area of environmental health research with most work examining the concurrent impact of in-flight exposure on cardiac health. One understudied area is on the post-flight effects of in-flight exposures. Studies investigating the health effects of flight often collect a range of repeatedly sampled, time-varying exposure-related measurements under both crossover and longitudinal sampling designs. A natural choice to model the relationship between these lagged exposures and post-flight outcomes is the distributed lag model (DLM). However, longitudinal DLMs are a lightly studied area. Thus, we propose a class of models for analyzing longitudinal DLMs where the random effects can incorporate more general structures -- including random lags -- that arise from repeatedly sampling lagged exposures. We develop variational Bayesian algorithms to estimate model components under differing random effect structures, derive a novel variational AIC for model selection between these structures, and show the converged variational estimates can be used to test for the difference between two semiparametric curves under the crossover design. We then analyze the impact of in-flight, lagged exposure-related physiological effects on post-flight heart health. We also perform simulation studies to evaluate the operating characteristics of our models and inference procedures.