A non-Markovian stochastic model for the Taichung medical IUD experiment

• Published in: Mathematical biosciences Vol. 34; no. 3; pp. 279 - 302
• Main Authors: Littman, Gary S., Mode, Charles J.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 1977
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/0025-5564(77)90106-7

A non-Markovian stochastic model is developed and validated within the context of data from the Taichung Medical IUD Study. The principles of the more traditionally used semi-Markov processes are first set down, along with the presentation of a computing algorithm to handle a key calculation arising in connection with these processes. Then, the set of data from the Taichung study is described, and an indication is given as to why a Markovian process is inappropriate for modeling the behavior reported in these data. Using semi-Markov processes to model various portions of the reproductive process, an overall non-Markovian model is developed with a view towards the contraceptive-pregnancy history of an individual as a sequential decision process. Some calculations based on this model are presented along with empirical determinations from the data reflecting what actually occurred. A comparison of these calculations and determinations shows that the model seems to describe the behavior reported quite well.