Scaled Consistent Estimation of Regression Parameters in Frailty Models

Tadeusz Bednarski; Magdalena Skolimowska-Kulig

doi:10.18778/0208-6018.338.08

Authors

Tadeusz Bednarski University of Wrocław, Faculty of Law, Administration and Economics, Institute of Economic Sciences
Magdalena Skolimowska-Kulig University of Wrocław, Faculty of Law, Administration and Economics, Institute of Economic Sciences

DOI:

https://doi.org/10.18778/0208-6018.338.08

Keywords:

frailty models, maximum likelihood estimation, Fisher consistency

Abstract

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.

Downloads

Download data is not yet available.

References

Aalen O.O. (1992), Modelling heterogeneity in survival analysis by the compound Poisson distribution, “Annals of Applied Probability”, vol. 2, no. 4, pp. 951–972.
Google Scholar

Aalen O.O., Borgan O., Gjessing H.K. (2008), Survival and Event History Analysis. A Process Point of View, Springer, New York.
Google Scholar

Bednarski T. (1993), Robust estimation in Cox regression model, “Scandinavian Journal of Statistics”, vol. 20, no. 3, pp. 213–225.
Google Scholar

Cox D.R. (1972), Regression models and life‑tables (with discussion), “Journal of the Royal Statistical Society B”, vol. 34, no. 2, pp. 187–220.
Google Scholar

Henderson R., Oman P. (1999), Effect of frailty on marginal regression estimates in survival analysis, “Journal of the Royal Statistical Society B”, vol. 61, no. 2, pp. 367–379.
Google Scholar

Kalbfleisch J.D., Prentice R.L. (1980), The Statistical Analysis of Failure Time Data, Wiley, New York.
Google Scholar

Minder C.E., Bednarski T. (1996), A robust method for proportional hazard regression, “Statistics in Medicine”, vol. 15, pp. 1033–1047.
Google Scholar

Murphy S.A. (1994), Consistency in a proportional hazard model incorporating a random effect, “The Annals of Statistics”, vol. 22, no. 2, pp. 712–734.
Google Scholar

Ruud P. (1983), Sufficient conditions for the consistency of maximum likelihood estimation despite misspecification of distribution in multinomial discrete choice models, “Econometrica”, vol. 51, no. 1, pp. 225–228.
Google Scholar

Sasieni P.D. (1993), Maximum weighted partial likelihood estimates for the Cox model, “Journal of the American Statistical Association”, vol. 88, pp. 144–152.
Google Scholar

Stoker T. (1986), Consistent estimation of scaled coefficients, “Econometrica”, vol. 54, no. 6, pp. 1461–1481.
Google Scholar

Vaupel J.W., Manton K.G., Stallard E. (1979), The impact of heterogeneity in individual frailty on the dynamics of mortality, “Demography”, vol. 16, pp. 439–454.
Google Scholar