Longitudinal Hierarchical Bayesian models of covariate effects on airway and alveolar nitric oxide

Biomarkers such as exhaled nitric oxide (FeNO), a marker of airway inflammation, have applications in the study of chronic respiratory disease where longitudinal studies of within-participant changes in the biomarker are particularly relevant. A cutting-edge approach to assessing FeNO, called multiple flow FeNO, repeatedly assesses FeNO across a range of expiratory flow rates at a single visit and combines these data with a deterministic model of lower respiratory tract NO to estimate parameters quantifying airway wall and alveolar NO sources. Previous methodological work for multiple flow FeNO has focused on methods for data from a single participant or from cross-sectional studies. Performance of existing ad hoc two-stage methods for longitudinal multiple flow FeNO in cohort or panel studies has not been evaluated. In this paper, we present a novel longitudinal extension to a unified hierarchical Bayesian (L_U_HB) model relating longitudinally assessed multiple flow FeNO to covariates. In several simulation study scenarios, we compare the L_U_HB method to other unified and two-stage frequentist methods. In general, L_U_HB produced unbiased estimates, had good power, and its performance was not sensitive to the magnitude of the association with a covariate and correlations between NO parameters. In an application relating height to longitudinal multiple flow FeNO in schoolchildren without asthma, unified analysis methods estimated positive, statistically significant associations of height with airway and alveolar NO concentrations and negative associations with airway wall diffusivity while estimates from two-stage methods were smaller in magnitude and sometimes non-significant.