A generalized additive model approach to time-to-event analysis

This tutorial article demonstrates how time-to-event data can be modelled in a very flexible way by taking advantage of advanced inference methods that have recently been developed for generalized additive mixed models. In particular, we describe the necessary pre-processing steps for transforming such data into a suitable format and show how a variety of effects, including a smooth nonlinear baseline hazard, and potentially nonlinear and nonlinearly time-varying effects, can be estimated and interpreted. We also present useful graphical tools for model evaluation and interpretation of the estimated effects. Throughout, we demonstrate this approach using various application examples. The article is accompanied by a new R-package called pammtools implementing all of the tools described here

A generalized Fellner-Schall method for smoothing parameter estimation with application to Tweedie location, scale and shape models

We consider the estimation of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall (1991). In particular: (i) we generalize the original method to the case of penalties that are linear in several smoothing parameters, thereby covering the important cases of tensor product and adaptive smoothers; (ii) we show why the method's steps increase the restricted marginal likelihood of the model, that it tends to converge faster than the EM algorithm, or obvious accelerations of this, and investigate its relation to Newton optimization; (iii) we generalize the method to any Fisher regular likelihood. The method represents a considerable simplification over existing methods of estimating smoothing parameters in the context of regular likelihoods, without sacrificing generality: for example, it is only necessary to compute with the same first and second derivatives of the log-likelihood required for coefficient estimation, and not with the third or fourth order derivatives required by alternative approaches. Examples are provided which would have been impossible or impractical with pre-existing Fellner-Schall methods, along with an example of a Tweedie location, scale and shape model which would be a challenge for alternative methods

A special case of reduced rank models for identification and modelling of time varying effects in survival analysis

Flexible survival models are in need when modelling data from long term follow-up studies. In many cases, the assumption of proportionality imposed by a Cox model will not be valid. Instead, a model that can identify time varying effects of fixed covariates can be used. Although there are several approaches that deal with this problem, it is not always straightforward how to choose which covariates should be modelled having time varying effects and which not. At the same time, it is up to the researcher to define appropriate time functions that describe the dynamic pattern of the effects. In this work, we suggest a model that can deal with both fixed and time varying effects and uses simple hypotheses tests to distinguish which covariates do have dynamic effects. The model is an extension of the parsimonious reduced rank model of rank 1. As such, the number of parameters is kept low, and thus, a flexible set of time functions, such as b-splines, can be used. The basic theory is illustrated along with an efficient fitting algorithm. The proposed method is applied to a dataset of breast cancer patients and compared with a multivariate fractional polynomials approach for modelling time-varying effects. Copyright © 2016 John Wiley & Sons, Ltd

Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation

Generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed models includes an L1-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets

Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation

Generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed models includes an L1-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets