Estimating disease progression using panel data

Micha Mandel has a new paper in Biostatistics. This considers estimation for panel observed data relating to MS progression. The underlying process can have backward transitions, so reaching a higher state is not in itself considered as evidence of progression. Instead, the patient is required to have stayed in the higher state for some period of time (e.g. 6 months). The quantities of interest in the study is therefore the time taken to first have stayed in state 3 for 6 months. For a continuous time, time-homogeneous Markov process expressions for the mean time and the distribution function are obtained.

As noted by Mandel, the estimates obtained are strongly dependent on the Markov assumption and time homogeneity. This is demonstrated in a simulation study. Mandel notes that more methods for semi-Markov models are required, the recent paper on phase-type semi-Markov models may be of use. Indeed, in the simulations Mandel actually uses phase-type distributions to create a semi-Markov process. However, the MS dataset may be too small to reliably estimate a semi-Markov model.

Informative observation times are a potential problem in the MS study. Mandel shows that observations that occur away from the scheduled 26-week gap time, are more likely to involve a transition, suggesting these observation times are informative. As a result, only observations within a 4 week period of the scheduled visit time are included in the analysis.

A comparison with a discrete-time Markov model approach showed that estimates based on assuming a discrete-time process gave larger estimates of the hitting times.