A discrete-state discrete-time model using indirect observation.

This research was motivated by a desire to model the progression of a chronic disease through various disease stages when data are not available to directly estimate all the transition parameters in the model. This is a common occurrence when time and expense make it unfeasible to follow a single cohort to estimate all the transition parameters. One difficulty of developing a model of chronic disease progression from such data is that the available studies often do not include the transitions of interest. For example, in our model of diabetic nephropathy, many clinical studies did not differentiate between patients without nephropathy and those who had microalbuminuria (a pre-clinical stage of nephropathy). Another difficulty was a lack of data to directly estimate parameters of interest. We consider models which can accommodate such difficulties. In this paper we consider the problem of estimating parameters of a discrete-time Markov process when longitudinal data describing the entire process are not available. First, we present a likelihood approach to estimate parameters of a discrete-time Markov model. Next, we use simulation to investigate the finite-sample behaviour of our approach. Finally, we present two examples: a model of diabetic nephropathy and a model of cardiovascular disease in diabetes.