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

In many applications, the time to some event of interest (generically called "failure") is the end point of an underlying stochastic process. This article considers processes that can be characterized by multi-state models, specifically progressive semi-Markov processes. Under this framework, the authors examine estimation and prediction efficiencies of two approaches for making inference about the time-to-failure (TTF) distribution. The first is the traditional approach based on just TTF data. The second uses all the information in the multi-state data to estimate the underlying parameters and then makes inference about the TTF. The latter inference can be complex with panel data (involving interval and right censoring), so it is important to quantify the efficiency gains to determine if the additional complexity is worth the effort. The authors focus mostly on gamma distributions for state sojourn times because they are closed under convolution. Results for the inverse Gaussian case which shares this property are also briefly discussed. The Canadian Journal of Statistics 39: 537-555; 2011 (C) 2011 Statistical Society of Canada