Use of natural cubic splines for modeling pulmonary function in longitudinal epidemiological studies

Abstract

We present an application of natural cubic regression splines for the clinical practice in respiratory medicine. We derive reference equations for one pulmonary function index - the forced expiratory volume in one second (FEV1) - as a function of age, height, and body mass index (i.e. weight/height - squared), separately by gender. The non linear dependence of FEV1 on age is modeled by means of natural cubic splines with two breakpoints. They represent a simple and flexible parametric method that provides smooth curves that are continuous up to the second derivative over the whole age range, and are constrained to be linear in the extreme intervals. Data arise from the normal and healthy participants of a large longitudinal study on respiratory chronic obstructive diseases. Owing to serial dependence of the repeated observations, inferences are performed by means of random effects models. we graphically compare the prediction curves derived by applying natural cubic splines with those previously obtained by means of stratified linear regression.