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Maximum Likelihood Estimation for Cox's Regression Model Under Case–Cohort Sampling

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  • Thomas H. Scheike
  • Torben Martinussen

Abstract

. Case–cohort sampling aims at reducing the data sampling and costs of large cohort studies. It is therefore important to estimate the parameters of interest as efficiently as possible. We present a maximum likelihood estimator (MLE) for a case–cohort study based on the proportional hazards assumption. The estimator shows finite sample properties that improve on those by the Self & Prentice [Ann. Statist. 16 (1988)] estimator. The size of the gain by the MLE varies with the level of the disease incidence and the variability of the relative risk over the considered population. The gain tends to be small when the disease incidence is low. The MLE is found by a simple EM algorithm that is easy to implement. Standard errors are estimated by a profile likelihood approach based on EM‐aided differentiation.

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  • Thomas H. Scheike & Torben Martinussen, 2004. "Maximum Likelihood Estimation for Cox's Regression Model Under Case–Cohort Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 283-293, June.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:2:p:283-293
    DOI: 10.1111/j.1467-9469.2004.02-064.x
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    Cited by:

    1. Ørnulf Borgan & Ruth H. Keogh & Aleksander Njøs, 2023. "Use of multiple imputation in supersampled nested case‐control and case‐cohort studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 13-37, March.
    2. Ying Yan & Haibo Zhou & Jianwen Cai, 2017. "Improving efficiency of parameter estimation in case-cohort studies with multivariate failure time data," Biometrics, The International Biometric Society, vol. 73(3), pages 1042-1052, September.
    3. Yei Eun Shin & Ruth M. Pfeiffer & Barry I. Graubard & Mitchell H. Gail, 2020. "Weight calibration to improve the efficiency of pure risk estimates from case‐control samples nested in a cohort," Biometrics, The International Biometric Society, vol. 76(4), pages 1087-1097, December.
    4. Suhyun Kang & Wenbin Lu & Mengling Liu, 2017. "Efficient estimation for accelerated failure time model under case-cohort and nested case-control sampling," Biometrics, The International Biometric Society, vol. 73(1), pages 114-123, March.
    5. Cécile Chauvel & John O'Quigley, 2017. "Survival model construction guided by fit and predictive strength," Biometrics, The International Biometric Society, vol. 73(2), pages 483-494, June.
    6. Lu, Zudi & Zhang, Wenyang, 2012. "Semiparametric likelihood estimation in survival models with informative censoring," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 187-211.
    7. Lu Mao & D. Y. Lin, 2017. "Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 573-587, March.
    8. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Feature screening for case‐cohort studies with failure time outcome," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 349-370, March.
    9. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    10. Yu, Qiqing, 2007. "A note on the proportional hazards model with discontinuous data," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 735-739, April.
    11. Jie-Huei Wang & Chun-Hao Pan & I-Shou Chang & Chao Agnes Hsiung, 2020. "Penalized full likelihood approach to variable selection for Cox’s regression model under nested case–control sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 292-314, April.
    12. Han, Bo & Wang, Xiaoguang, 2020. "Semiparametric estimation for the non-mixture cure model in case-cohort and nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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