A hierarchical Bayesian approach for combining pharmacokinetic/pharmacodynamic modeling and Phase IIa trial design in orphan drugs: Treating adrenoleukodystrophy with Lorenzo's oil

X-linked adrenoleukodystrophy (X-ALD) is a rare, progressive, and typically fatal neurodegenerative disease. Lorenzo's oil (LO) is one of the few X-ALD treatments available, but little has been done to establish its clinical efficacy or indications for its use. In this article, we analyze data on 116 male asymptomatic pediatric patients who were administered LO. We offer a hierarchical Bayesian statistical approach to understand LO pharmacokinetics (PK) and pharmacodynamics (PD) resulting from an accumulation of very long-chain fatty acids. We experiment with individual- and observational-level errors and various choices of prior distributions and deal with the limitation of having just one observation per administration of the drug, as opposed to the more usual multiple observations per administration. We link LO dose to the plasma erucic acid concentrations by PK modeling, and then link this concentration to a biomarker (C26, a very long-chain fatty acid) by PD modeling. Next, we design a Bayesian Phase IIa study to estimate precisely what improvements in the biomarker can arise from various LO doses while simultaneously modeling a binary toxicity endpoint. Our Bayesian adaptive algorithm emerges as reasonably robust and efficient while still retaining good classical (frequentist) operating characteristics. Future work looks toward using the results of this trial to design a Phase III study linking LO dose to actual improvements in health status, as measured by the appearance of brain lesions observed via magnetic resonance imaging.