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**Gamma and inverse Gaussian frailty models with time-varying co-variates based on some parametric baseline hazards functions.**
*(English.
French summary)*
Zbl 1445.62044

Summary: Ignoring the existence of frailty term in the analysis of survival time data, when heterogeneity is present will produce a less accurate estimated parameters with higher standard errors. In survival analysis, Cox proportional hazards model is frequently used to measure the effects of covariates. The covariates may fail to fully account for the true differences in hazard. This may be due to an existence of another response variable that is disregarded in the model but can be explained by the term known as frailty. The incorporation of frailty in the model thereby avoid underestimation and overestimation of parameters and also correctly measure the effects of the covariates on the response variable. This paper presents a parametric non-proportional hazard models with Weibull, Loglogistic and Gompertz as baseline distributions and Gamma and Inverse Gaussian as frailty distribution. A maximum likelihood method is used and is illustrated with a numerical example in which the fit is compared using Akaike Information Criterion (AIC).

### MSC:

62F10 | Point estimation |

62B10 | Statistical aspects of information-theoretic topics |

62N05 | Reliability and life testing |

### Keywords:

time-varying covariate; unobserved covariates; non-proportional hazard model; inverse cumulative hazard; survival time; frailty models; Akaike information criterion
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\textit{A. W. Oyekunle} et al., Afr. Stat. 15, No. 1, 2199--2224 (2020; Zbl 1445.62044)

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