Schmid, Matthias; Hothorn, Torsten
Flexible Boosting of Accelerated Failure Time Models.
Department of Statistics: Technical Reports, Nr. 18
When boosting algorithms are used for building survival models from high-dimensional data, it is common to fit a Cox proportional hazards model or to apply semiparametric least squares techniques. However, there are cases where a fully parametric accelerated failure time model might be 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. In this paper we 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. It is demonstrated that the performance of the new algorithm is competitive with the performance of boosting with the Cox partial likelihood. In particular, the estimation of the scale parameter does not affect the favorable properties of boosting with respect to variable
selection. In low-dimensional settings, i.e., when classical likelihood estimation of a parametric accelerated failure time model is possible, the new boosting algorithm closely approximates the maximum likelihood method.