Hazard function estimators: A simulation study

Kernel-based methods for the smooth, non-parametric estimation of the hazar d function have received considerable attention in the statistical literatu re. Although the mathematical properties of the kernel-based hazard estimat ors have been carefully studied, their statistical properties have not. We reviewed various kernel-based methods for hazard function estimation from r ight-censored data and compared the statistical properties of these estimat ors through computer simulations. Our simulations covered seven distributio ns, three levels of random censoring, four types of bandwidth functions, tw o sample sizes and three types of boundary correction. We conducted a total of 504 simulation experiments with 500 independent samples each. Our resul ts confirmed the advantages of two recent innovations in kernel estimation - boundary correction and locally optimal bandwidths. The median relative i mprovement (decrease) in mean square error over fixed-bandwidth estimators without boundary correction was 3 per cent for fixed-bandwidth estimators w ith left boundary correction, 52 per cent locally optimal bandwidths withou t boundary correction, and 66 per cent for locally optimal bandwidths with left boundary correction. The locally optimal bandwidth estimators with lef t boundary correction also outperformed three previously published and publ icly available algorithms, with median relative improvements in mean square error of 31 per cent, 77 per cent and 80 per cent. Copyright (C) 1999 John Wiley & Sons, Ltd.