Jointly modelling the relationship between survival and pulmonary function in cystic fibrosis patients

Modelling the relationship between pulmonary function and survival in cystic fibrosis (CF) is complicated by the fact that measures of pulmonary function commonly used such as the forced expiratory volume in one second (FEV(1)) are measured with error, and patients with the poorest lung function are increasingly censored by death, that is, data are available only for the patients who have survived to the current age. We assume a linear random effects model for FEV1 per cent predicted, where the random intercept and slope of FEV(1) per cent predicted, along with a specified transformation of the age at death follow a trivariate normal distribution. We illustrate how this model can be used to describe the relationship between age at death and parameters of the individual patient's regression of FEV(1) per cent predicted versus age, such as the slope and the intercept or true value of FEV(1) per cent predicted at a given age. We also illustrate how the model provides empirical Bayes estimates of these individual parameters. In particular, we explore how the predicted value of the age at death might be used as a prognostic or severity index. The model and methods are illustrated on a cohort of 188 cystic fibrosis patients with a common genotype (homozygous for the DeltaF508 mutation), born on or after 1965 and followed at the CF Center at the Rainbow Babies and Children's Hospital, Cleveland, OH, U.S.A.