Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

 

The article featured today is from the Canadian Journal of Statistics, with the full article now available to read here.

 

Brunel, E. and Comte, F. (2021), Hazard regression with noncompactly supported bases. Can J Statistics. https://doi.org/10.1002/cjs.11619

 

Survival modelling is devoted to analysis of random duration of time until one event of interest occurs, such as death in biological organisms or failure in reliability. In this context, the hazard rate, also called force of mortality in actuarial sciences, is usually more informative about the underlying behaviour of failure than the other functions characterizing  a lifetime distribution, such as the density probability function or the cumulative distribution function. Thus, the hazard rate estimation is of great importance in real data studies. In addition, censoring often appears in lifetime data. In that case, time to event cannot directly be observed because the study ends before all subjects have shown the event of interest or the subject has left the study before its event of interest has happened. The paper deals with the nonparametric estimation of hazard rate for censored data. A least squares estimator on Laguerre bases is defined which can be seen as a combination of gamma-type functions. Such bases with non compact support are particularly well-suited to the hazard rate estimation under right-censoring. In fact, it interestingly avoids to make a prior choice of the set of estimation, which is very sensitive to the high proportion of censored data at the end of the interval. Besides, It might capture the good shape of the hazard rate when usual parametric models fail.   A new penalized criterion is proposed to  automatically choose the number of gamma functions in the combination defining the estimator. This data-driven strategy comes out from the very general results obtained on the risk bound. The new estimator is shown to perform better than previous kernel or wavelet methods on simulated data.