Normalised Local Hazard Plots
Abstract
The purpose of this paper is to develop and illustrate certain classes of graphical plots that can be used for model verification in quite general survival data and life history data models. By suitably comparing nonparametric and parametric estimates of hazard rate functions over time a hazard comparison function can be constructed which under parametric model assumptions is approximately a zero-mean normal process. The test curves we propose are locally normalised versions of such hazard comparison functions. Under model conditions the test function is approximately a standard normal for each time point. This makes the normalised local hazard curves easy to interpret.We give explicit constructions for the most commonly used models of survival analysis, including the exponential, the Weibull, the Gompertz, the gamma, and for parametric Cox regression. Algorithms carrying this out have been developed in Splus. Various theoretical and practical issues are discussed, including detection power and extensions to time-discrete models. Illustrations are given on simulated and real data.
Cite
@article{arxiv.2603.22373,
title = {Normalised Local Hazard Plots},
author = {Nils Lid Hjort and Thomas Lumley},
journal= {arXiv preprint arXiv:2603.22373},
year = {2026}
}
Comments
41 pages, 15 figures. Statistical Research Report, Department of Mathematics, University of Oslo, from May 1993, but now arXiv'd March 2026. A Splus package for generating such plots is available from either of the authors