A new class of semiparametric transformation models based on first hitting times by latent degradation processes

Sangbum Choi, Kjell A. Doksum

Research output: Contribution to journalArticle

Abstract

In many failure mechanisms, most subjects under study deteriorate physically over time, and thus a depreciation in health may precede failure. A latent stochastic process, called degradation process, may be assumed for modeling such depreciation whereby an event occurs when the process first crosses a threshold. A class of survival regression models can be constructed from the first hitting time of a latent accelerating degradation process, which turns out to be a transformation model in the literature. To characterize these models, we propose to use first-hitting-time models for the baseline distribution, specifically inverse Gaussian, Birnbaum-Saunders and gamma distributions, among others. The proposed models have many desirable features, such as a wide variety of shapes of hazard rates, analytical tractability and, most of all, its motivation from a plausible stochastic setting for failure. We estimate the model parameters by the non-parametric maximum likelihood approach. The estimators are shown to be consistent, asymptotically normal and asymptotically efficient. Simple and stable numerical algorithms are provided to calculate the parameter estimators and estimate their variances. Simulation studies show that the proposed approach is appropriate for practical use. The methodology is illustrated with two real examples.

Original languageEnglish
Pages (from-to)227-241
Number of pages15
JournalStat
Volume2
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Fingerprint

First Hitting Time
Transformation Model
Semiparametric Model
Degradation
Model-based
Birnbaum-Saunders Distribution
Nonparametric Maximum Likelihood
Latent Process
Inverse Gaussian Distribution
Estimator
Survival Model
Failure Mechanism
Hazard Rate
Tractability
Gamma distribution
Numerical Algorithms
Model
Estimate
Stochastic Processes
Baseline

Keywords

  • Birnbaum-Saunders
  • First hitting time
  • Inverse Gaussian
  • Non-parametric likelihood
  • Survival analysis
  • Transformation model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

A new class of semiparametric transformation models based on first hitting times by latent degradation processes. / Choi, Sangbum; Doksum, Kjell A.

In: Stat, Vol. 2, No. 1, 01.01.2013, p. 227-241.

Research output: Contribution to journalArticle

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