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

Abstract

Summary 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.

Bayesian Complex Innovative Trial Designs (CIDs) and Their Use in Drug Development for Rare Disease

“…In the previous illustration, Bayesian methods were used to borrow cautiously from auxiliary data, with adult‐child PK and PK/PD data similarity used to confirm the appropriateness of this borrowing. Basu et al 50 take this idea a step further by using the degree of adult‐child PK/PD data similarity to help select the appropriate amount of adult‐child clinical data borrowing. The need for such borrowing arose in clinical trials of the drug cinacalcet, used for treating secondary hyperparathyroidism (HPT) in patients with chronic kidney disease.…”

“…Basu et al 50 begin with a population nonlinear mixed‐effects model that describes the concentration‐time and effect‐time data for pediatric and adult patients. The conceptual PK/PD model is based on a multicompartmental model 51 and contains separate parameters for adults and children that can be shared between the 2 groups if appropriate.…”

“…Note that this P value corresponds to a valid statistical test, but not one that the PD experiment was designed to run. As such, Basu et al 50 simply use the P ‐value as a summary measure of similarity (or lack thereof) that can then inform the decision as to the proper amount of adult‐child extrapolation.…”

“…Basu et al 50 suggest using some scale multiple of this P ‐value (eg, $$Kp\ $$ for some $$K > 0$$) as a sensible power in a power prior model for the clinical data. Specifically, K might be chosen to produce an EHSS (adult) that regulatory authorities do not find unacceptably large (eg, many times larger than the actual pediatric sample sizes involved).…”

“…Posterior Estimates for the Estimated Effect of the Drug in Basu et al50 Using a Power Prior for Varying Values of λ = K p Bayesian credible interval; EHSS, effective historical sample size; SD, standard deviation.…”