Hazard function estimators: a simulation study

Kernel-based methods for the smooth, non-parametric estimation of the hazard function have received considerable attention in the statistical literature. Although the mathematical properties of the kernel-based hazard estimators have been carefully studied, their statistical properties have not. We reviewed various kernel-based methods for hazard function estimation from right-censored data and compared the statistical properties of these estimators through computer simulations. Our simulations covered seven distributions, three levels of random censoring, four types of bandwidth functions, two sample sizes and three types of boundary correction. We conducted a total of 504 simulation experiments with 500 independent samples each. Our results confirmed the advantages of two recent innovations in kernel estimation - boundary correction and locally optimal bandwidths. The median relative improvement (decrease) in mean square error over fixed-bandwidth estimators without boundary correction was 3 per cent for fixed-bandwidth estimators with left boundary correction, 52 per cent locally optimal bandwidths without boundary correction, and 66 per cent for locally optimal bandwidths with left boundary correction. The locally optimal bandwidth estimators with left boundary correction also outperformed three previously published and publicly available algorithms, with median relative improvements in mean square error of 31 per cent, 77 per cent and 80 per cent.