Pharmacokinetic modeling is a crucial part of drug development. An important goal is to estimate patients' total and peak exposure to a drug over time, quantified by the area under the concentration--time curve (AUC) and the maximum concentration ($C_{\max}$) respectively. Such exposure assessment is essential to balance efficacy and safety in medications that offer therapeutic benefits but carry risks of toxicity, such as chemotherapy drugs. Uncertainty quantification for exposure quantities, however, remains challenging, since they are functionals of an often sparsely observed concentration--time curve with measurement errors. We propose a compartment-driven Gaussian process framework that propagates uncertainty in concentration--time curves to pharmacokinetic exposure functionals. Our approach uses pharmacokinetic compartmental models to specify a mechanistically informed prior and Gaussian processes to accommodate departures from the assumed pharmacokinetic dynamics. The framework can accommodate both individual-level and group-aggregated concentration--time data commonly seen in practice. We provide straightforward computational procedures for drawing posterior inference on AUC and $C_{\max}$. Simulations across a range of observation schemes demonstrate robustness to departures from the assumed compartmental dynamics. We apply the method to patient-level datasets on warfarin and theophylline, and aggregated data from a chemotherapy study of 5-fluorouracil and capecitabine in patients with normal or impaired hepatic function. The chemotherapy analysis quantifies drug-specific exposure differences between groups with differing liver function, with potential implications for informing dosing decisions.

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