Estimation of the Cox model with grouped lifetimes

• Authors: Piotr Bolesław Nowak

Abstracts

EN

This paper presents how random numbers can be used to transform grouped lifetimes into a pseudo-complete sample. The aim of the study is to investigate the Fisher consistency of the partial likelihood estimator of the regression parameters in the Cox model based on the restored sample. It has been proven that for elliptical-type distributional assumptions about explanatory variables the estimators of the regression parameters in the Cox model based on the pseudo-complete sample are consistent up to a scaling factor. A simulation study illustrates the asymptotic properties of the estimates. In addition, real data case analysis is presented.

Keywords

EN

Cox model; grouped data; Fisher consistency; elliptical distribution

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2024
• Volume: 25
• Issue: 4
• Pages: 179-189

Dates

published

2024

Contributors

author

Piotr Bolesław Nowak

• University of Wrocław, Institute of Economic Sciences

• https://orcid.org/0000000274042946

References

• Agresti, A., (2010). Analysis of Ordinal Categorical Data, 2nd Edition, John Wiley and Sons.
• Arias, E., (2007). United States life tables, 2004. National Vital Statistics Reports, 56(9), pp. 1-40.
• Bednarski, T., (1993). Robust estimation in Cox's regression model. Scandinavian Journal of Statistics, 20(3), pp. 213-225.
• Bednarski, T., Nowak, P. B., (2021). Scaled Fisher consistency of partial likelihood estimator in the Cox model with arbitrary frailty. Probability and Mathematical Statistics, 41(1), pp. 77-87.
• Bednarski, T., Nowak, P. B., Skolimowska-Kulig, M., (2022). Scaled Fisher consistency for the partial likelihood estimation in various extensions of the Cox model. Statistics in Transition new series, 23(2), pp. 185-196.
• Bednarski, T., Skolimowska-Kulig, M., (2018). Scaled consistent estimation of regression parameters in frailty models. Acta Universitatis Lodziensis. Folia Oeconomica, 5(338), 133-142.
• Breslow, N., (1974). Covariance analysis of censored survival data. Biometrics, 30(1), pp. 89-99.
• Cox, D. R., (1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society B, 34(2), pp. 187-220.
• Efron, B., (1977). The efficiency of Cox's likelihood function for censored data. Journal of the American Statistical Association, 71(359), pp. 557-565.
• Fahrmeir, L., Tutz, G., (2001). Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd Edition, Springer-Verlag, New York.
• Haitovsky, Y., 1982. Grouped data, in Encyclopedia of Statistical Sciences 3, John Wiley and Sons, pp. 527-536.
• Hosmer, D., Jr, Lemeshow, S., (1999). Applied Survival Analysis. Regression Modeling of Time to Event Data, John Wiley and Sons.
• Huber, P. J., Ronchetti, E. M., (2009). Robust Statistics, 2nd Edition, John Wiley and Sons.
• Kalbfleich, J. D., Prentice, R. L., (1973). Marginal likelihoods based on Cox's regression and life model. Biometrika, 60(2), pp. 267-278.
• Kalbfleich, J. D., Prentice, R. L., (1980). John Wiley and Sons.
• The Statistical Analysis of Failure Time Data, Kestenbaum, B., Ferguson, R., (2010). Supercentenarians in the United States, in H. Maier et al. (eds.), Demographic Research Monographs, Springer, Berlin, Heidelberg, pp. 43-58.
• McKeague, I. W., Zhang, M. J., (1996). Fitting Cox's Proportional Hazards Model Using Grouped Survival Data, in N.P. Jewell et al. (eds.), Lifetime Data: Models in Reliability and Survival Analysis, Kluwer, Boston, pp. 227-232.
• Prentice, R. L., Gloeckler, L. A., (1978). Regression analysis of grouped survival data with application to breast cancer data. Biometrics, 34(1), pp. 57-67.
• Ruud, P., (1983). Sufficient conditions for the consistency of maximum likelihood estimation despite misspecification of distribution in multinomial discrete choice models. Econometrica, 51(1), pp. 225-228.
• Stoker, T., (1986). Consistent estimation of scaled coefficients. pp. 1461-1481.
• Econometrica, 54(6), Thompson, W. A., (1977). On the treatment of grouped observations in live studies. Biometrics, 33(3), pp. 463-470.
• Whitten, B. J., Cohen, A. C., Sundaraiyer, V., (1988). A pseudo-complete sample technique for estimation from censored samples. Communications in Statistics - Theory and Methods, 17(7), pp. 2239-2258.

Identifiers

DOI

10.59139/stattrans-2024-009

Biblioteka Nauki

59193274