Abstract
This paper highlights the estimation and test procedures for multi-state Markov models with covariate dependences in higher orders. Logistic link functions are used to analyze the transition probabilities of three or more states of a Markov model emerging from a longitudinal study. For illustration purpose the models are used for analysis of panel data on Health and Retirement Study conducted in USA during 1992-2002. The applications use self reported data on perceived emotional health at each round of the nationwide survey conducted among the elderly people. Useful and detailed results on the change in the perceived emotional health status among the elderly people are obtained.
Highlights
In a longitudinal study, we observe correlated outcomes over time which may pose difficulty in modelling such data
A popular choice is the use of generalized estimating equations (GEE) which is a marginal model with specification of underlying correlation structure
The model is used for analysis of panel data on Health and Retirement Study conducted in USA during 1992-2002
Summary
We observe correlated outcomes over time which may pose difficulty in modelling such data. A popular choice is the use of generalized estimating equations (GEE) which is a marginal model with specification of underlying correlation structure. It is noteworthy that Regier (1968) introduced a two state transition matrix for estimating odds ratio, Prentice and Gloeckler (1978) proposed a grouped data version of the proportional hazards regression model for estimating computationally feasible estimators of the relative risk function, Korn and Whittemore (1979) proposed a model for incorporating the role of previous state as a covariate to analyze the probability of occupying the current state, and Muenz and Rubinstein (1985) introduced a discrete time Markov chain for expressing the transition probabilities in terms of function of covariates for a binary sequence of presence or absence of a disease. A Markov chain model for three or more intercommunicating states is proposed for analysis of covariate dependences of the transition probabilities. The risk factors that contribute to specific transitions can be identified from the proposed model
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