title: An approach to the residence time distribution for stochastic multi-compartment models.
abstract: Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.
authors.affiliation: Department of Biostatistics, Roswell Park Cancer Institute, Elm & Carlton Streets, Buffalo, NY 14228, USA.
authors.forename: Jihnhee
authors.initials: J
authors.lastname: Yu
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Wehrly
mesh_terms: D000924:Anticholesteremic Agents / Q000008:administration & dosage / Q000494:pharmacology; D001825:Body Fluid Compartments; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D006937:Hypercholesterolemia / Q000188:drug therapy / Q000378:metabolism; D008390:Markov Chains; D008954:Models, Biological; D010599:Pharmacokinetics; D017035:Pravastatin / Q000008:administration & dosage / Q000493:pharmacokinetics; D013269:Stochastic Processes
chemical_list: D000924:Anticholesteremic Agents; D017035:Pravastatin