Regression analysis of mean lifetime: Exploring nonlinear relationship with heteroscedasticity

Zhiping Sun*, Wenxin Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

As a generalization of the accelerated failure time models, we consider parametric models of lifetime Y, where the conditional mean E(Y X;beta) can depend nonlinearly on the covariates X and some parameters beta. The error distribution can be heteroscedastic and dependent on X. With observed data subject to right censoring, we propose regression analysis for beta based on Kaplan-Meier estimates of the means over several regions of X. Consistency and asymptotic distributional properties of the estimators are established under general conditions. A resulting estimator of beta is shown to be the sum of two possibly dependent asymptotic normal quantities, based on which conservative confidence intervals and tests are derived. Simulation studies are conducted to investigate the performance of the proposed estimator and to compare it with Buckley-Jame's method. To illustrate the methodology, we study an example with kidney transplant data, where a nonlinear relationship called "mixtures-of-experts", proposed in the neural networks literature, is used to model the relationship between the survival time and the age of the patients.

Original languageEnglish (US)
Article number5
JournalInternational Journal of Biostatistics
Volume3
Issue number1
DOIs
StatePublished - 2007

Keywords

  • Accelerated failure time model
  • Asymptotic normality
  • Heteroscedasticity
  • Kaplan-Meier estimate
  • Mixtures of experts
  • Nonlinear regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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