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

## TL;DR

The paper introduces a new statistical method to analyze variable relationships in single-person observational studies, showing how stress and exercise can be linked differently at individual and population levels.

## Contribution

The novel additive Bayesian network method improves modeling of observational N-of-1 study relationships using generalized linear mixed-effects models.

## Key findings

- The additive Bayesian network outperforms traditional methods in recovering network structures from simulated data.
- Stress and physical activity show population-level associations but individual-level differences in an empirical N-of-1 study.
- The method is validated through simulation and applied to a real-world 12-month observational study.

## Abstract

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.