1,884 research outputs found
Parametrization and penalties in spline models with an application to survival analysis
In this paper we show how a simple parametrization, built from the definition of cubic
splines, can aid in the implementation and interpretation of penalized spline models, whatever
configuration of knots we choose to use. We call this parametrization value-first derivative
parametrization. We perform Bayesian inference by exploring the natural link between quadratic
penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some
penalty functionals. Alternatives include empirical Bayes methods involving model selection
type criteria. The proposed methodology is illustrated by an application to survival analysis
where the usual Cox model is extended to allow for time-varying regression coefficients
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