Multivariate variable selection in N-of-1 observational studies via additive Bayesian networks

An N-of-1 observational design characterizes associations among several variables over time in a single individual. Traditional statistical models recommended for experimental N-of-1 trials may not adequately model these observational relationships. We propose an additive Bayesian network using a generalized linear mixed-effects model for the local mean as a novel method for modeling each of these relationships in a data-driven manner. We validate our approach via simulation studies and apply it to a 12-month observational N-of-1 study exploring the impact of stress on daily exercise engagement. We demonstrate the improved performance of the additive Bayesian network to recover the underlying network structure. From the empirical study, we found statistically discernible associations between reports of stress and physical activity on a population level, but these associations may differ at an individual level.