Decomposing differences in multistate indices.- The problem of decomposing differences in synthetic indices derived from sets of transition probabilities needs a closer look. For this class of model, we can choose from any of the three generalized decomposition approaches that I’m aware of (Caswell (1989), Andreev et al. (2002), Horiuchi et al. (2008)), and there is no acute need to develop a new decomposition approach per se. The crux of the problem is in how to parameterize the multistate model. Specifically, we can calculate the exact same index given arbitrary subsets of the transition probabilities available to us, and each of these arbitrary sets yields a qualitatively and irreconcilably different decomposition result. Each decomposition result is additive and valid in the same way. This situation is both outrageous and easy not to notice, and it is due to the compositional nature of transition probabilities. I propose a new decomposition property: symmetry, whereby we transform transition probabilities in such as way as to yield consistent decomposition results no matter which subset we chose. I suggest a specific example parameterization for a common multistate health model. Decomposition results retain all other properties we think are essential. Now you can explain differences in discrete-time multistate indices in terms of their constituent transitions and structure.

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Code: 363807