Numerous methods for joint analysis of longitudinal measures of a continuous outcome y and a time to event outcome T have recently been developed either to focus on the longitudinal data y while correcting for nonignorable dropout, to predict the survival outcome T using the longitudinal data y, or to examine the relationship between y and T. The motivating problem for our work is in joint modeling the serial measurements of pulmonary function (FEV1 % predicted) and survival in cystic fibrosis (CF) patients using registry data. Within the CF registry data, an additional complexity is that not all patients have been followed from birth; therefore, some patients have delayed entry into the study while others may have been missed completely, giving rise to a left truncated distribution. This paper shows in joint modeling situations where y and T are not independent, it is necessary to account for this left truncation in order to obtain valid parameter estimates related to both survival and the longitudinal marker. We assume a linear random effects model for FEV1 % predicted, where the random intercept and slope of FEV1 % predicted, along with a specified transformation of the age at death follow a trivariate normal distribution. We develop an EM algorithm for maximum likelihood estimation of parameters, which takes left truncation and right censoring of survival times into account. The methods are illustrated using simulation studies and using data from CF patients in a registry followed at Rainbow Babies and Children’s Hospital, Cleveland, OH.

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Previous reports of lung function in cystic fibrosis (CF) patients with liver disease have shown worse, similar, or even better forced expiratory volume in 1 second (FEV1), compared to CF patients without liver disease. Varying definitions of CF liver disease likely contribute to these inconsistent relationships reported between CF lung function and liver disease. We retrospectively evaluated spirometric data in 179 subjects (62% male; 58% Phe508del homozygous) with severe CF liver disease (CFLD; defined by presence of portal hypertension due to cirrhosis). FEV1 values were referenced to both a normal population (FEV1% predicted) and CF population (CF-specific FEV1 percentile). We utilized a linear mixed model with repeated measures to assess changes in lung function (before and after diagnosis of CFLD), relative to both the normal and CF populations. At diagnosis of CFLD, the mean FEV1 was 81% predicted, or at the 53rd percentile referenced to CF patients without CFLD. There was a significant difference in post-CFLD slope compared to pre-CFLD slope (post–pre) using FEV1% predicted (-1.94, p-value < 0.0001). However, there was insignificant evidence of this difference using the CF-specific FEV1 percentile measure (-0.99, p-value = 0.1268). Although FEV1% predicted values declined in patients following CFLD diagnosis, there was not significant evidence of lung function decline in CF-specific FEV1 percentiles. Thus, the observed study cohort indicates diagnosis of severe CFLD was not associated with worsened CF lung disease when compared to a large CF reference population.