戒菸期的傾向---一個馬可夫的方法

Abstract

在戒菸實驗中，我們常會觀察到參與者有多重離散型的階段。過去已有一些關於此的長期資料分析，我們也可假設這些資料具有馬可夫的性質。參與實驗者常會有驅向某一階段的傾向，我們用對數轉換傾向參數模型，提出別於二元的新的模型與方法，做出估計與檢定的問題。這些新的模型與方法將用於戒菸實驗的數據。我們也會做模擬實驗。

Intervention trials such as studies on smoking cessation may observe multiple, discrete outcomes over time. Participant observations may alternate states over the course of a study. Approaches exist which are commonly used to analyze binary, longitudinal data in the context of independent variables. However, the sequence of observations may be assumed to follow a Markov chain with stationary transition probabilities when observations are made at fixed time points. Participants favoring the transition to one particular state over the others would evidence a trend in the observations. Using a log-transformed trend parameter, the determinants of a trend in a binary, longitudinal study may be evaluated by maximizing the likelihood function. New methodology on extension to discrete time Markov chain model and continuous time Markov chain model is proposed here to test for the presence and determinants of a trend in multiple state, rather than binary, longitudinal observations. Practical application of the proposed method is made to data available from an intervention study on smoking cessation. Simulation studies will also be taken.