Normalised Local Hazard Plots

TL;DR

This paper introduces normalized local hazard plots for model verification in survival analysis, enabling easy interpretation by comparing nonparametric and parametric hazard estimates, with algorithms implemented in Splus.

Contribution

It develops a new graphical method for model checking in survival data, applicable to various models including Cox regression, with explicit constructions and practical algorithms.

Findings

Plots are approximately standard normal under correct models.

Method effectively detects model misspecification.

Algorithms are demonstrated on simulated and real data.

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.