Nonlinear trajectories of lung function recovery in patients with pulmonary disease: empirical evaluation of longitudinal modeling approaches

Abstract

Introduction: Longitudinal lung function recovery after pulmonary disease commonly follows nonlinear trajectories, and failure to adequately model these trajectories can lead to biased or misleading estimates of treatment effects. However, an important methodological gap remains as there is limited assessment of statistical methods for modeling nonlinear lung function trajectories. Methods: We compared several longitudinal modeling approaches for characterizing recovery in percent predicted forced expiratory volume in one second (FEV1p) using data from a phase 2 randomized trial for pulmonary tuberculosis (TB). We estimate the differences in repeated mean FEV1p between each treatment arm and control arm over a 180-days follow-up period. We compared 6 different statistical models: (1) linear mixed-effects model, (2) a piecewise linear mixed-effects model, (3) quadratic and (4) natural cubic spline mixed-effects models, (5) a nonlinear mixed-effects model with exponential recovery function, and (6) a generalized additive mixed model. We discussed the assumptions, clinical interpretations, and resulting treatment-effect estimates across these approaches. Results: The results from the TB trial analyses showed that the conventional linear mixed-effects model provided limited evidence of treatment differences over follow-up, whereas several flexible models identified significant differences during specific periods of recovery. Conclusion: Flexible longitudinal models can complement conventional linear mixed-effects models by revealing treatment differences at certain periods of follow-up that may be obscured by assuming a single linear trend. The choice of nonlinear modeling strategy should be guided by the scientific objective, available data, and the desired balance between clinical interpretability and flexibility.