title: Estimation of the transition matrix of a discrete-time Markov chain.
abstract: Discrete-time Markov chains have been successfully used to investigate treatment programs and health care protocols for chronic diseases. In these situations, the transition matrix, which describes the natural progression of the disease, is often estimated from a cohort observed at common intervals. Estimation of the matrix, however, is often complicated by the complex relationship among transition probabilities. This paper summarizes methods to obtain the maximum likelihood estimate of the transition matrix when the cycle length of the model coincides with the observation interval, the cycle length does not coincide with the observation interval, and when the observation intervals are unequal in length. In addition, the bootstrap is discussed as a method to assess the uncertainty of the maximum likelihood estimate and to construct confidence intervals for functions of the transition matrix such as expected survival.
authors.affiliation: Department of Statistics, 1399 Mathematical Sciences, Purdue University, West Lafayette, IN 47907-1399, USA. bacraig@stat.purdue.edu
authors.forename: Bruce A
authors.initials: BA
authors.lastname: Craig
authors.forename: Peter P
authors.initials: PP
authors.lastname: Sendi
mesh_terms: D000465:Algorithms; D018791:CD4 Lymphocyte Count; D002908:Chronic Disease / Q000145:classification* / Q000191:economics; D015331:Cohort Studies; D016001:Confidence Intervals; D003362:Cost-Benefit Analysis / Q000706:statistics & numerical data; D003661:Decision Support Techniques; D018450:Disease Progression; D015658:HIV Infections / Q000276:immunology; D006302:Health Services Research / Q000379:methods*; D006305:Health Status Indicators; D006801:Humans; D008390:Markov Chains; D019370:Observation; D018570:Risk Assessment; D013997:Time Factors