Flexible boosting of accelerated failure time models

Matthias Schmid,Torsten Hothorn

doi:10.1186/1471-2105-9-269

Abstract

BackgroundWhen boosting algorithms are used for building survival models from high-dimensional data, it is common to fit a Cox proportional hazards model or to use least squares techniques for fitting semiparametric accelerated failure time models. There are cases, however, where fitting a fully parametric accelerated failure time model is a good alternative to these methods, especially when the proportional hazards assumption is not justified. Boosting algorithms for the estimation of parametric accelerated failure time models have not been developed so far, since these models require the estimation of a model-specific scale parameter which traditional boosting algorithms are not able to deal with.ResultsWe introduce a new boosting algorithm for censored time-to-event data which is suitable for fitting parametric accelerated failure time models. Estimation of the predictor function is carried out simultaneously with the estimation of the scale parameter, so that the negative log likelihood of the survival distribution can be used as a loss function for the boosting algorithm. The estimation of the scale parameter does not affect the favorable properties of boosting with respect to variable selection.ConclusionThe analysis of a high-dimensional set of microarray data demonstrates that the new algorithm is able to outperform boosting with the Cox partial likelihood when the proportional hazards assumption is questionable. In low-dimensional settings, i.e., when classical likelihood estimation of a parametric accelerated failure time model is possible, simulations show that the new boosting algorithm closely approximates the estimates obtained from the maximum likelihood method.

Highlights

When boosting algorithms are used for building survival models from highdimensional data, it is common to fit a Cox proportional hazards model or to use least squares techniques for fitting semiparametric accelerated failure time models
In low-dimensional settings, i.e., when classical likelihood estimation of a parametric accelerated failure time model is possible, simulations show that the new boosting algorithm closely approximates the estimates obtained from the maximum likelihood method
Prediction error curves obtained from boosting with the negative log-logistic log likelihood, boosting with the negative Weibull log likelihood, and boosting with the negative lognormal log likelihood

Summary

Introduction

When boosting algorithms are used for building survival models from highdimensional data, it is common to fit a Cox proportional hazards model or to use least squares techniques for fitting semiparametric accelerated failure time models. A interesting problem in this context is the analysis of studies relating patients' genotypes, for example measured via gene expression levels, to a clinical outcome such as "disease free survival" or "time to progression" Survival models of this type share the common problems that are typical for the analysis of gene expression data: Sample sizes are small while the number of potential predictors (i.e., gene expression levels) is extremely large. For these reasons, a variety of new methods for obtaining survival predictions from high-dimensional data have been suggested in the literature. A variety of new methods for obtaining survival predictions from high-dimensional data have been suggested in the literature Most of these methods are focused on the Cox proportional hazards model [1], while some other methods have been developed for fitting semiparametric accelerated failure time (AFT) models [2] in high-dimensional settings. In addition to penalized estimation techniques, there are various strategies for reducing the dimensionality of microarray data before building an unpenalized survival model, see Schumacher et al [13], Bovelstad et al [14], and van Wieringen et al [15] for overviews of this topic

Methods

Results

Conclusion