Flexible semiparametric joint modeling: an application to estimate individual lung function decline and risk of pulmonary exacerbations in cystic fibrosis

Background: Epidemiologic surveillance of lung function is key to clinical care of individuals with cystic fibrosis, but lung function decline is nonlinear and often impacted by acute respiratory events known as pulmonary exacerbations. Statistical models are needed to simultaneously estimate lung function decline while providing risk estimates for the onset of pulmonary exacerbations, in order to identify relevant predictors of declining lung function and understand how these associations could be used to predict the onset of pulmonary exacerbations. Methods: Using longitudinal lung function (FEV1) measurements and time-to-event data on pulmonary exacerbations from individuals in the United States Cystic Fibrosis Registry, we implemented a flexible semiparametric joint model consisting of a mixed-effects submodel with regression splines to fit repeated FEV1 measurements and a time-to-event submodel for possibly censored data on pulmonary exacerbations. We contrasted this approach with methods currently used in epidemiological studies and highlight clinical implications. Results: The semiparametric joint model had the best fit of all models examined based on deviance information criterion. Higher starting FEV1 implied more rapid lung function decline in both separate and joint models; however, individualized risk estimates for pulmonary exacerbation differed depending upon model type. Based on shared parameter estimates from the joint model, which accounts for the nonlinear FEV1 trajectory, patients with more positive rates of change were less likely to experience a pulmonary exacerbation (HR per one standard deviation increase in FEV1 rate of change = 0.566,95% CI 0.516-0.619), and having higher absolute FEV1 also corresponded to lower risk of having a pulmonary exacerbation (HR per one standard deviation increase in FEV1 = 0.856, 95% CI 0.781-0.937). At the population level, both submodels indicated significant effects of birth cohort, socioeconomic status and respiratory infections on FEV1 decline, as well as significant effects of gender, socioeconomic status and birth cohort on pulmonary exacerbation risk. Conclusions: Through a flexible joint-modeling approach, we provide a means to simultaneously estimate lung function trajectories and the risk of pulmonary exacerbations for individual patients; we demonstrate how this approach offers additional insights into the clinical course of cystic fibrosis that were not possible using conventional approaches.