ORDMKV - A COMPUTER-PROGRAM FITTING PROPORTIONAL ODDS MODEL FOR MULTISTATE MARKOV PROCESS

ORDMKV is a computer program designed to fit a multi-state discrete-ti me Markov model for k-stages disease processes having an ordinal struc ture. The model consists of k transient states representing the increa sing severity of the disease process, and the final state can be optio nally chosen to be an absorbing state in cases such as death. The ordi nal structure of the stages of the disease is modelled by using ordina l response models. Each row of the one-step transition probability mat rix is modelled using a proportional odds model based on the cumulativ e transition probabilities. By using these ordinal response models, th e number of parameters used to model the disease process can be reduce d significantly not only with respect to a general discrete-time model , but also compared with a parsimonuos continuous-time model. A restri cted model can be fitted by assuming that the effect of the covariable s in the cumulative probability has common regression coefficients in all stages of the disease process. This assumption, if it holds, reduc es the number of regression coefficients associated with each covariat e to only one. The regression coefficients of this model are estimated via the method of maximum likelihood, using a quasi-Newton optimizati on algorithm. When the last state is considered as an absorbing state, it is possible to compute survival curves from the transient states o f the process. The program was written in standard FORTRAN 77 and is i llustrated using a four-state model to determine factors influencing d iabetic retinopathy in young subjects with insulin-dependent diabetes mellitus.