Statistical methods for the analysis of the association between bronchial responsiveness and pulmonary function changes.

An autoregressive model for the analysis of longitudinal data was applied in the context of investigating the effect of bronchial responsiveness on the growth of pulmonary function in children. In the model used, the correlation between pulmonary function values within an individual decreases exponentially as the time between visits increases. The model incorporates both fixed and time-dependent covariates in a unified fashion and does not require complete data in all visits for each individual. Furthermore, the change in pulmonary function is not assumed to be linear over time. Using response to cold air data as a measure of bronchial responsiveness, we found that children who responded to cold air have a slower rate of growth in pulmonary function. In addition, the data suggested that the effect of cigarette smoking may be greater as the response to cold air increases. Extensions of the autoregressive approach to other correlation structures and to the case of unequidistant observations are discussed.