Pharmacokinetic/pharmacodynamic data extrapolation models for improved pediatric efficacy and toxicity estimation, with application to secondary hyperparathyroidism

In most drug development settings, the regulatory approval process is accompanied by extensive studies performed to understand the drug's pharmacokinetic (PK) and pharmacodynamic (PD) properties. In this article, we attempt to utilize the rich PK/PD data to inform the borrowing of information from adults during pediatric drug development. In pediatric settings, it is especially crucial that we are parsimonious with the patients recruited for experimentation. We illustrate our approaches in the context of clinical trials of cinacalcet for treating secondary hyperparathyroidism in pediatric and adult patients with chronic kidney disease, where we model both parathyroid hormone (efficacy endpoint) and corrected calcium levels (safety endpoint). We use population PK/PD modeling of the cinacalcet data to quantitatively assess the similarity between adults and children, and use this information in various hierarchical Bayesian adult borrowing rules whose statistical properties can then be evaluated. In particular, we simulate the bias and mean square error performance of our approaches in settings where borrowing is and is not warranted to inform guidelines for the future use of our methods.