ORDMKV: a computer program fitting proportional odds model for multi-state Markov process

Abstract

ORDMKV is a computer program designed to fit a multi-state discrete-time Markov model for k-stages disease processes having an ordinal structure. The model consists of k transient states representing the increasing severity of the disease process, and the final state can be optionally chosen to be an absorbing state in cases such as death. The ordinal structure of the stages of the disease is modelled by using ordinal response models. Each row of the one-step transition probability matrix is modelled using a proportional odds model based on the cumulative transition probabilities. By using these ordinal response models, the number of parameters used to model the disease process can be reduced significantly not only with respect to a general discrete-time model, but also compared with a parsimonuos continuous-time model. A restricted model can be fitted by assuming that the effect of the covariables in the cumulative probability has common regression coefficients in all stages of the disease process. This assumption, if it holds, reduces the number of regression coefficients associated with each covariate to only one. The regression coefficients of this model are estimated via the method of maximum likelihood, using a quasi-Newton optimization algorithm. When the last state is considered as an absorbing state, it is possible to compute survival curves from the transient states of the process. The program was written in standard FORTRAN 77 and is illustrated using a four-state model to determine factors influencing diabetic retinopathy in young subjects with insulin-dependent diabetes mellitus.