×

Maximum likelihood estimation for Cox’s regression model under case-cohort sampling. (English) Zbl 1060.62111

In the Prentice case-cohort design right censored survival times and censoring indicators are observed for all samples (cohorts) whence the covariate values are known only in cases for which the survival time was not censored and for a random sub-sample (sub-cohort) from cases with censored survival times. A typical example is an epidemiological study at which the covariates are observed for all ill persons and for a control group of healthy persons.
Cox’s regression model is considered for the effect of covariates. A maximum likelihood estimator for the regression coefficients is described and an EM-type algorithm is proposed for the computation of this estimator. The obtained estimator is compared with the estimators proposed by S. G. Self and R. L. Prentice [Ann. Stat. 16, No. 1, 64–81 (1988; Zbl 0666.62108)] and K. Chen and S.-H. Lo [Biometrika 86, No. 4, 755–764 (1999; Zbl 0940.62108)]. Simulation results are presented.

MSC:

62N02 Estimation in survival analysis and censored data
65C60 Computational problems in statistics (MSC2010)
62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Andersen P. K., Statistical models based on counting processes (1993) · Zbl 0769.62061
[2] Barlow W. E., Biometrics 50 pp 1064– (1994)
[3] DOI: 10.1198/016214502760047096 · Zbl 1073.62526
[4] Chen H., J. Amer. Statist. Assoc. 94 pp 896– (1999)
[5] Chen K., Biometrika 86 pp 755– (1999)
[6] Cox D. R., J. Roy. Statist. Soc. Ser. B 34 pp 406– (1972)
[7] Dempster A. P., J. Roy. Statist. Soc. Ser. B 39 pp 1– (1977)
[8] Lin D. Y., J. Amer. Statist. Assoc. 88 pp 1341– (1993)
[9] Louis T., J. Roy. Statist. Soc. Ser. B 44 pp 226– (1982)
[10] DOI: 10.1111/1467-9469.00163 · Zbl 0939.62033
[11] Murphy S. A., J. Amer. Statist. Assoc. 92 pp 968– (1997)
[12] Nielsen G. G., Scand. J. Statist. 19 pp 25– (1992)
[13] Prentice R. L., Biometrika 73 pp 1– (1986)
[14] Self S. G., Ann. Statist. 16 pp 64– (1988)
[15] DOI: 10.1023/A:1009691327335 · Zbl 0968.62071
[16] Turnbull B. W., J. Amer. Statist. Assoc. 69 pp 169– (1976)
[17] Wellner J. A., J. Amer. Statist. Assoc. 92 pp 945– (1997)
[18] DOI: 10.1016/S0047-259X(02)00047-7 · Zbl 1023.62055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.