Estimating disease progression using panel data

Continuous-time Markov processes are frequently used to describe the evolution of a disease over different phases. Such modeling can provide estimates for important parameters that are defined on the paths of the process. A simple example is the mean first hitting time to a set of states. However, more interesting events are defined by several time points such as the first time the process stays in state j for at least Δ time units. These kinds of events are very important in relapsing-remitting diseases such as in multiple sclerosis (MS) where the focus is on a sustained worsening that lasts 6 months or longer. The current paper considers data on independent continuous Markov processes that are only observed intermittently. It reviews modeling and estimation, presents a new general concept of hitting times, and provides point and interval estimates for it. The methodology is applied to data from a phase III clinical trial of Avonex-a drug given to MS patients.