Web-based Supplementary Materials for “A Bayesian Semi-parametric Survival Model with Longitudinal Markers”
نویسندگان
چکیده
From Lvi0 with censored observations the two values taken by ωvi lead to two models of different dimensions. If ωvi = 0, we have a model with Tvi being a random parameter. In contrast, Tvi is fixed at Tvi = tc if ωvi = 1. Such a change in dimension complicates posterior simulation (Green, 1995). We use the pseudo prior approach by Carlin and Chib (1995) to avoid this complication. In other words, we augment the smaller probability model under ωvi = 1 by defining a prior probability model for a hypothetical Tvi (but keep tc in the regression for yvi). The new variable Tvi has no meaningful interpretation under ωvi = 1. It is only introduced to match the model dimensions. The augmented likelihood factor under the new model is
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