Penalized spline smoothing in multivariable survival models with varying coefficients

Penalized spline (P-spline) smoothing is discussed for hazard regression of multivariable survival data. Non-proportional hazard functions are fitted in a numerically handy manner by employing Poisson regression which results from numerical integration of the cumulative hazard function. Multivariate smoothing parameters are selected by utilizing the connection between P-spline smoothing and generalized linear mixed models. A hybrid routine is suggested which combines the mixed model idea with a classical Akaike information criteria. The model is evaluated with simulations and applied to data on the success and failure of newly founded companies.