Combining growth curves when a longitudinal study switches measurement tools

When longitudinal studies are performed to investigate the growth of traits in children, the measurement tool being used to quantify the trait may need to change as the subjects' age throughout the study. Changing the measurement tool at some point in the longitudinal study makes the analysis of that growth challenging which, in turn, makes it difficult to determine what other factors influence the growth rate. We developed a Bayesian hierarchical modeling framework that relates the growth curves per individual for each of the different measurement tools and allows for covariates to influence the shapes of the curves by borrowing strength across curves. The method is motivated by and demonstrated by speech perception outcome measurements of children who were implanted with cochlear implants. Researchers are interested in assessing the impact of age at implantation and comparing the growth rates of children who are implanted under the age of two versus those implanted between the ages of two and four.