Open Access
March, 1982 Piecewise Exponential Models for Survival Data with Covariates
Michael Friedman
Ann. Statist. 10(1): 101-113 (March, 1982). DOI: 10.1214/aos/1176345693


A general class of models for analysis of censored survival data with covariates is considered. If $n$ individuals are observed over a time period divided into $I(n)$ intervals, it is assumed that $\lambda_j(t)$, the hazard rate function of the time to failure of the individual $j$, is constant and equal to $\lambda_{ij} > 0$ on the $i$th interval, and that the vector $\ell = \{\log \lambda_{ij}: j = 1, \ldots, n; i = 1, \ldots, I(n)\}$ lies in a linear subspace. The maximum likelihood estimate $\hat{\ell}$ of $\ell$ provides a simultaneous estimate of the underlying hazard rate function, and of the effects of the covariates. Maximum likelihood equations and conditions for existence of $\hat{\ell}$ are given. The asymptotic properties of linear functionals of $\hat{\ell}$ are studied in the general case where the true hazard rate function $\lambda_0(t)$ is not a step function, and $I(n)$ increases without bound as the maximum interval length decreases. In comparison with recent work on regression analysis of survival data, the asymptotic results are obtained under more relaxed conditions on the regression variables.


Download Citation

Michael Friedman. "Piecewise Exponential Models for Survival Data with Covariates." Ann. Statist. 10 (1) 101 - 113, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0483.62086
MathSciNet: MR642722
Digital Object Identifier: 10.1214/aos/1176345693

Primary: 62E20
Secondary: 62F10

Keywords: Asymptotic theory , Censored data , Log-linear model , maximum likelihood estimation , piecewise exponential model , survival data

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
Back to Top