### Abstract

This paper concerns the regression analysis of discrete time survival data for heterogeneous populations by means of frailty models. We express the survival time for each individual as a sequence of binary variables that indicate if the individual survived at each time point. The main result is that the likelihood for these indicators can be factored into contributions that involve the conditional survival probabilities integrated over the frailty distribution of the risk set (population-averaged). We then model these population-averaged conditional probabilities as a function of covariates. The result justifies the practice of treating the failure indicators as independent Bernoulli trials and fitting binary regression models for the conditional failure probabilities at each time point. However, we must interpret the regression coefficients as population-averaged rather than subject-specific parameters. We apply the method to the Framingham Heart Study on risk factors for cardiovascular disease.

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

Pages (from-to) | 1983-1993 |

Number of pages | 11 |

Journal | Statistics in Medicine |

Volume | 16 |

Issue number | 17 |

DOIs | |

State | Published - Sep 15 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*16*(17), 1983-1993. https://doi.org/10.1002/(SICI)1097-0258(19970915)16:17<1983::AID-SIM628>3.0.CO;2-3

**Regression analysis of discrete time survival data under heterogeneity.** / Xue, Xiaonan (Nan); Brookmeyer, Ron.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 16, no. 17, pp. 1983-1993. https://doi.org/10.1002/(SICI)1097-0258(19970915)16:17<1983::AID-SIM628>3.0.CO;2-3

}

TY - JOUR

T1 - Regression analysis of discrete time survival data under heterogeneity

AU - Xue, Xiaonan (Nan)

AU - Brookmeyer, Ron

PY - 1997/9/15

Y1 - 1997/9/15

N2 - This paper concerns the regression analysis of discrete time survival data for heterogeneous populations by means of frailty models. We express the survival time for each individual as a sequence of binary variables that indicate if the individual survived at each time point. The main result is that the likelihood for these indicators can be factored into contributions that involve the conditional survival probabilities integrated over the frailty distribution of the risk set (population-averaged). We then model these population-averaged conditional probabilities as a function of covariates. The result justifies the practice of treating the failure indicators as independent Bernoulli trials and fitting binary regression models for the conditional failure probabilities at each time point. However, we must interpret the regression coefficients as population-averaged rather than subject-specific parameters. We apply the method to the Framingham Heart Study on risk factors for cardiovascular disease.

AB - This paper concerns the regression analysis of discrete time survival data for heterogeneous populations by means of frailty models. We express the survival time for each individual as a sequence of binary variables that indicate if the individual survived at each time point. The main result is that the likelihood for these indicators can be factored into contributions that involve the conditional survival probabilities integrated over the frailty distribution of the risk set (population-averaged). We then model these population-averaged conditional probabilities as a function of covariates. The result justifies the practice of treating the failure indicators as independent Bernoulli trials and fitting binary regression models for the conditional failure probabilities at each time point. However, we must interpret the regression coefficients as population-averaged rather than subject-specific parameters. We apply the method to the Framingham Heart Study on risk factors for cardiovascular disease.

UR - http://www.scopus.com/inward/record.url?scp=0030827927&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030827927&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0258(19970915)16:17<1983::AID-SIM628>3.0.CO;2-3

DO - 10.1002/(SICI)1097-0258(19970915)16:17<1983::AID-SIM628>3.0.CO;2-3

M3 - Article

VL - 16

SP - 1983

EP - 1993

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 17

ER -