Parametric inference for time-to-failure in multi-state semi-Markov models: A comparison of marginal and process approaches

Yang Yang and Vijayan Nair have a new paper in Canadian Journal of Statistics as part of the Kalbfleisch and Lawless special issue. The paper considers inference for progressive semi-Markov processes for complete, right-censored and interval-censored data for parametric models with Gamma or inverse Gamma sojourn distributions. The advantage of considering Gamma or inverse Gamma distributions is that their convolutions have a closed form meaning the overall failure (absorption) time distribution is available in closed form. Inference using only the time-to-failure data is therefore relatively straightforward. The main focus of the paper is investigating the loss in efficiency of only using time-to-failure data when additional data on intermediate states (either through continuous observation or panel data) are available. The authors show that the loss in efficiency can be rather substantial, particularly if interest lies in making predictions about time to failure given an existing process history rather than just mean or median survival. It is therefore suggested that information on intermediate states should be incorporated where possible despite this presenting computationally difficulties in the case of panel data.