A Single Compartment Quantal Response Model with an Inspection Process

✍ Scribed by Mr. Chia-Tsung Horng; Prof. Wen-Jang Huang; Prof. Mong-Na Lo Huang

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 736 KB
• Volume: 32
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710320813

✦ Synopsis

Abstract

In a single compartment quantal response model, besides the input and release processes, an inspection process, assumed to be independent of the input and release processes, is considered. Each time when a release occurs, we assume the amount of release is randomly proportional to the amount present and the proportional rates form a sequence of independent and identically distributed random variables with support on [0, 1]. The input policy we consider is a modification of (s, S) input policy in the inventory model. More precisely, let 0 ≦s~2~ ≦s~1~ ≦s ≦ S, if after a release, the amount of the drug in subject's body is less than a level s~2~ which is small enough, then there will be an input immediately with probability 1 — p and no more inputs thereafter with probability p, also there will be an input immediately if the dose level is in the interval [s~2~, s~1~). If the dose level is in the interval [s~1~, s) there will be no input unless the inspector arrives. On the other hand, if the dose level is greater than or equal to s, then there will be no input. We consider a stochastic model as described above, and obtain the expressions for some quantities of interest. A Monte Carlo study has also been carried out to demonstrate some behaviors of our quantal response process.