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Scaled Fisher consistency for the partial likelihood estimation in various extensions of the Cox model

100%

Bednarski T., Nowak P. B., Skolimowska-Kulig M.

Statistics in Transition new series

2022

vol. 23

issue 2

185-196

The Cox proportional hazards model has become the most widely used procedure in survival analysis. The theoretical basis of the original model has been developed in various extensions. In the recent years, vital research has been undertaken involving the incorporation of random effects to survival models. In this setting, the random effect is a variable (frailty) which embraces a variation among individuals or groups of individuals which cannot be explained by observable covariates. The right choice of the frailty distribution is essential for an accurate description of the dependence structure present in the data. In this paper, we aim to investigate the accuracy of inference based on the primer Cox model in the existence of unobserved heterogeneity, that is, when the data generating mechanism is more complex than presumed and described by the kind of an extension of the Cox model with undefined frailty. We show that the conventional partial likelihood estimator under the considered extension is Fisher-consistent up to a scaling factor, provided symmetry-type distributional assumptions on covariates. We also present the results of simulation experiments that reveal an exemplary behaviour of the estimators.

Scaled Consistent Estimation of Regression Parameters in Frailty Models

63%

Bednarski T., Skolimowska-Kulig M.

Acta Universitatis Lodziensis. Folia Oeconomica

2018

vol. 5

issue 338

133-142

W artykule omówiono atrakcyjną obliczeniowo metodę estymacji parametrów dla klasy modeli regresyjnych z nieobserwowaną zmienną „frailty”. Dowiedziono, że estymator największej wiarygodności stosowany w klasycznym wykładniczym modelu regresji jest Fisherowsko zgodny z dokładnością do skali w rozważanym modelu „frailty”. Przeprowadzone badania symulacyjne oraz analiza rzeczywistych danych wskazują na dobre własności asymptotyczne prezentowanej metody estymacji.

A computationally attractive method of estimation of parameters for a class of frailty regression models is discussed. The method uses maximum likelihood estimation for the classical exponential regression model. Scaled Fisher consistency is shown to hold and a simulation study indicating good asymptotic properties of the method, as well as real data case analysis, are presented.

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1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Statistics in Transition new series

2 Bednarski T.

2 Skolimowska-Kulig M.

1 Nowak P. B.

1 2022

1 2018

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Scaled Fisher consistency for the partial likelihood estimation in various extensions of the Cox model

Scaled Consistent Estimation of Regression Parameters in Frailty Models