An approach to the residence time distribution for stochastic multi-compartment models |
| |
Authors: | Yu Jihnhee Wehrly Thomas E |
| |
Institution: | Department of Biostatistics, Roswell Park Cancer Institute, Elm & Carlton Streets, Buffalo, NY 14228, USA. |
| |
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. |
| |
Keywords: | Stochastic compartment model Moment generating function Residence time Saddlepoint approximation Cofactor rule Semi-Markov process |
本文献已被 ScienceDirect PubMed 等数据库收录! |