Non-Markov Multistate Modeling Using Time-Varying Covariates

Bacchetti et al have a new paper in The International Journal of Biostatistics. This considers modelling progression of liver fibrosis due to hepatitis C following liver transplant using a 5-state progressive multi-state model. The data are panel observed at irregular time points, so it would be most natural to model the data in continuous time. In addition the observed states are subject to classification error. To avoid having to making either Markov or time homogeneity assumptions, the authors adopt a discrete time assumption: assuming 4 time periods per year. They then model the transition probabilities as linear on the log-odds scale, depending on covariates such as medical center, donor age, year of transplant as well as log time since entry into the current state (relaxing the Markov assumption). Potentially, time since transplant could also be included in the model (for non-homogeneity).

The main challenge in fitting the models is to enumerate all possible complete "paths" of true states at the discrete time points that could result in the observed data. Obviously an iterative algorithm is needed for this. The computational complexity will depend on the complexity of the state transition matrix, the misclassification probability matrix and the degree of discretization.

The main drawback of approximating a continuous time process by a discrete-time process is the restriction that only 1 transition may occur between time points. While this can be acceptable for progressive models such as the one considered here, it may be more problematic when backward transitions are allowable.

The authors have developed an R package called mspath, designed to complement the existing package for continuous-time Markov and hidden Markov model msm, to allow non-Markov models through the discrete-time approximation.