On stochastic models for linear compartmental systems [microform]
- Bib ID:
- 3282903
- Format:
- Book and Microform
- Author:
- Simpson, Pippa Margaret
- Description:
- 162 p.
- Summary:
-
The most common approach to the study of pharmacokinetics is to represent a body as a series of compartments, which may only loosely correspond to the physical actuality. Often, in studying the transfer of drugs from compartment to compartment and the elimination of the drugs from the body, a linear system of differential equations results, which will be called a linear compartmental system. In this thesis a particular linear three compartmental system is studied in detail. Unlike the traditional deterministic model, where a measurement error is assumed to take care of variation, a particular stochastic model, called a particle model, is used. With a stochastic model, a non-diagonal variance-covariance structure is given, which seems preferable in that the compartments' contents are likely to be correlated over time.
For the particular system, the two models are examined in chapter II. This study differs from previous work since it is assumed that only one compartment is observed and this complicates estimation procedures considerably. In chapter III, it is shown that, under this restriction, a deterministic model will not give identifiability, but a stochastic model will, for the system studied. Estimation of the vector of parameters is done using a maximum likelihood approach. It is necessary to take a diffusion approximation and this is compared to the other two models in chapter I. In chapter IV, it is established that the resulting estimate is consistent and asymptotically normal. To achieve a practical model as well as a theoretically sound one, a program has been written in Pascal, which can be run on an IBM clone.
The logic is described in chapter V and a listing is provided in the Appendix. A result of Jennrich and Moore (1975), relating weighted least squares and maximum likelihood estimates is adjusted to be used in this new situation and an algorithm by Fletcher (1980) is modified to achieve convergence of the algorithm.
- Notes:
-
- (UnM)AAI8821132
- Source: Dissertation Abstracts International, Volume: 49-08, Section: B, page: 3286.
- Directors: David M. Allen; Constance L. Wood.
- Thesis (Ph.D.)--University of Kentucky, 1988.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Statistics
- Other authors/contributors:
- University of Kentucky
- Copyright:
-
In Copyright
Contact us for information about copying.
Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 1988
Copyright status may not be correct if data in the record is incomplete or inaccurate. Other access conditions may also apply. For more information please see: Copyright in library collections.
Request this item
Request this item to view in the Library’s reading room.