<p>Following oral administration of a drug, we observe an absorption delay before the drug enters systemic circulation. This delay is attributed to the time taken for disintegration of the drug delivery system, drug dissolution from the delivery system, migration of the drug to the absorption site, and transfer of the drug through absorption site tissue. Additionally, pharmacokinetic profiles of such drugs frequently exhibit substantial variability among individuals from different sub-populations. In this article, we present a hierarchical transit compartment model that systematically describes absorption delay in orally administered drugs, and explicitly accounts for between sub-population variations. Such a transit compartment model can be regarded as an accurate representation of the underlying physiology, that also accounts for the influence of drug formulation and the physicochemical properties of the drug on the absorption process. Here, we specify non-informative priors on the pharmacokinetic parameters of interest, and develop an efficient computational scheme based on Hamiltonian Monte Carlo algorithm to conduct inference. The proposed joint inferential procedure ensures valid uncertainty quantification, and enables us to conduct simultaneous inference on sub-population specific as well as population parameters. The utility of the methodology is demonstrated through simulation studies, and two case studies.</p>