### Abstract

Proportional hazards frailty models use a random effect, so called frailty, to construct association for clustered failure time data. It is customary to assume that the random frailty follows a gamma distribution. In this paper, we propose a graphical method for assessing adequacy of the proportional hazards frailty models. In particular, we focus on the assessment of the gamma distribution assumption for the frailties. We calculate the average of the posterior expected frailties at several followup time points and compare it at these time points to 1, the known mean frailty. Large discrepancies indicate lack of fit. To aid in assessing the goodness of fit, we derive and estimate the standard error of the mean of the posterior expected frailties at each time point examined. We give an example to illustrate the proposed methodology and perform sensitivity analysis by simulations.

Original language | English (US) |
---|---|

Pages (from-to) | 205-220 |

Number of pages | 16 |

Journal | Lifetime Data Analysis |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1995 |

Externally published | Yes |

### Fingerprint

### Keywords

- Clustered failure times
- gamma frailties
- posterior
- proportional hazards

### ASJC Scopus subject areas

- Medicine(all)
- Applied Mathematics

### Cite this

*Lifetime Data Analysis*,

*1*(2), 205-220. https://doi.org/10.1007/BF00985771

**Assessing gamma frailty models for clustered failure time data.** / Shih, Joanna H.; Louis, Thomas.

Research output: Contribution to journal › Article

*Lifetime Data Analysis*, vol. 1, no. 2, pp. 205-220. https://doi.org/10.1007/BF00985771

}

TY - JOUR

T1 - Assessing gamma frailty models for clustered failure time data

AU - Shih, Joanna H.

AU - Louis, Thomas

PY - 1995/6

Y1 - 1995/6

N2 - Proportional hazards frailty models use a random effect, so called frailty, to construct association for clustered failure time data. It is customary to assume that the random frailty follows a gamma distribution. In this paper, we propose a graphical method for assessing adequacy of the proportional hazards frailty models. In particular, we focus on the assessment of the gamma distribution assumption for the frailties. We calculate the average of the posterior expected frailties at several followup time points and compare it at these time points to 1, the known mean frailty. Large discrepancies indicate lack of fit. To aid in assessing the goodness of fit, we derive and estimate the standard error of the mean of the posterior expected frailties at each time point examined. We give an example to illustrate the proposed methodology and perform sensitivity analysis by simulations.

AB - Proportional hazards frailty models use a random effect, so called frailty, to construct association for clustered failure time data. It is customary to assume that the random frailty follows a gamma distribution. In this paper, we propose a graphical method for assessing adequacy of the proportional hazards frailty models. In particular, we focus on the assessment of the gamma distribution assumption for the frailties. We calculate the average of the posterior expected frailties at several followup time points and compare it at these time points to 1, the known mean frailty. Large discrepancies indicate lack of fit. To aid in assessing the goodness of fit, we derive and estimate the standard error of the mean of the posterior expected frailties at each time point examined. We give an example to illustrate the proposed methodology and perform sensitivity analysis by simulations.

KW - Clustered failure times

KW - gamma frailties

KW - posterior

KW - proportional hazards

UR - http://www.scopus.com/inward/record.url?scp=0029420414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029420414&partnerID=8YFLogxK

U2 - 10.1007/BF00985771

DO - 10.1007/BF00985771

M3 - Article

C2 - 9385102

AN - SCOPUS:0029420414

VL - 1

SP - 205

EP - 220

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

IS - 2

ER -