MARKOV: a computer program for multi-state Markov models with covariables

This paper discusses a computer program, called MARKOV, designed to fit a multi-state Markov model with covariables, with a particular emphasis on the analysis of survival data. The Markov model consists of k-1 transient disease states and one absorbing state. The exact transition times are not observed, except in situations such as death. Baseline transition intensities and regression coefficients are estimated via the method of maximum likelihood using a quasi-Newton optimization algorithm. The program's output includes the parameter estimates, the standard error of the estimates, the matrix of the correlation of the estimates and minus two times the log-likelihood function, evaluated at the initial values and at the maximum likelihood estimates. Optionally, survival curves can be generated from each transient state, for one or more combination of covariable values and simple tests about the parameters. The program is illustrated by using a four-state model to determine factors influencing diabetic retinopathy in young subjects with insulin-dependent diabetes mellitus.