Get Bayesian Analysis of Failure Time Data Using P-Splines PDF

By Matthias Kaeding

ISBN-10: 3658083921

ISBN-13: 9783658083922

ISBN-10: 365808393X

ISBN-13: 9783658083939

Matthias Kaeding discusses Bayesian equipment for interpreting discrete and non-stop failure occasions the place the influence of time and/or covariates is modeled through P-splines and extra easy functionality expansions, permitting the alternative of linear results via extra normal capabilities. The MCMC technique for those types is gifted in a unified framework and utilized on information units. between others, latest algorithms for the grouped Cox and the piecewise exponential version below period censoring are mixed with a knowledge augmentation step for the purposes. the writer exhibits that the ensuing Gibbs sampler works good for the grouped Cox and is only enough for the piecewise exponential model.

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Extra resources for Bayesian Analysis of Failure Time Data Using P-Splines

Sample text

Blj (x) = x − k j−l l−1 k j+1 − x B j−1 (x) + Bl−1 (x). k j − k j−l k j+1 − k j+1−l j Due to the recursive definition, the inner knot sequence k1 < ... < km , must be expanded to k1−l < ... < km+l . , m + l, with interval width s = (max(x) − min(x))/(m − 1). Here, knots are always taken as equidistant knots for reasons that will be made clear in the following. B-spline functions exhibit the following properties from which their numerical stability follows: • Nonnegativity: B(y) ≥ 0, for all y and every degree l.

The corresponding Bayes estimators can be obtained from MCMC output as empirical counterpart. To communicate estimation uncertainty the interval containing 100(1 − α)% of the posterior density is often reported. This interval can be directly obtained from MCMC output, invariant to one-to-one transformations of the parameter, and is directly interpretable. An alternative is the set of highest posterior density, for a given α defined as the set C = {θ ∈ Θ : f (θ |D) ≥ k(α)}, where k(α) is the largest constant satisfying f (C|D) ≥ 1 − α (Carlin and Louis 2011, p.

As η is unchanged by the discretization of the time scale, regression coefficients and estimated effects can be directly interpreted in terms of T (Fahrmeir and Tutz 2001, p. 140). Independent of the connection to the relative risk model, the complementary log-log link provides a good fit for binary models if one of the categories is more frequent than the other, due to the asymmetry of the response function (Cameron and Trivedi 2005, p. 466). This holds obviously for most data sets for failure time.

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Bayesian Analysis of Failure Time Data Using P-Splines by Matthias Kaeding

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