### 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 language | English |
---|---|

Pages (from-to) | 227-241 |

Number of pages | 15 |

Journal | Stat |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

Externally published | Yes |

### Fingerprint

### 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

*Stat*,

*2*(1), 227-241. https://doi.org/10.1002/sta4.31

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

Research output: Contribution to journal › Article

*Stat*, vol. 2, no. 1, pp. 227-241. https://doi.org/10.1002/sta4.31

}

TY - JOUR

T1 - A new class of semiparametric transformation models based on first hitting times by latent degradation processes

AU - Choi, Sangbum

AU - Doksum, Kjell A.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - Birnbaum-Saunders

KW - First hitting time

KW - Inverse Gaussian

KW - Non-parametric likelihood

KW - Survival analysis

KW - Transformation model

UR - http://www.scopus.com/inward/record.url?scp=84942610402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942610402&partnerID=8YFLogxK

U2 - 10.1002/sta4.31

DO - 10.1002/sta4.31

M3 - Article

VL - 2

SP - 227

EP - 241

JO - Stat

JF - Stat

SN - 2049-1573

IS - 1

ER -