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Analysis of two-phase sampling data with semiparametric additive hazards models

Author

Listed:
  • Yanqing Sun

    (University of North Carolina at Charlotte)

  • Xiyuan Qian

    (East China University of Science and Technology)

  • Qiong Shou

    (Merck China & Co., Inc.)

  • Peter B. Gilbert

    (University of Washington and Fred Hutchinson Cancer Research Center)

Abstract

Under the case-cohort design introduced by Prentice (Biometrica 73:1–11, 1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.

Suggested Citation

  • Yanqing Sun & Xiyuan Qian & Qiong Shou & Peter B. Gilbert, 2017. "Analysis of two-phase sampling data with semiparametric additive hazards models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 377-399, July.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:3:d:10.1007_s10985-016-9363-2
    DOI: 10.1007/s10985-016-9363-2
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    References listed on IDEAS

    as
    1. Zhiguo Li & Peter Gilbert & Bin Nan, 2008. "Weighted Likelihood Method for Grouped Survival Data in Case–Cohort Studies with Application to HIV Vaccine Trials," Biometrics, The International Biometric Society, vol. 64(4), pages 1247-1255, December.
    2. Yanqing Sun & Peter B. Gilbert, 2012. "Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 34-52, March.
    3. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    4. Kani Chen, 2001. "Generalized case–cohort sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 791-809.
    5. Lan Kong & Jianwen Cai, 2009. "Case–Cohort Analysis with Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(1), pages 135-142, March.
    6. Norman E. Breslow & Jon A. Wellner, 2007. "Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 86-102, March.
    7. Michal Kulich & D.Y. Lin, 2004. "Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 832-844, January.
    8. Guozhi Gao & Anastasios A. Tsiatis, 2005. "Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure," Biometrika, Biometrika Trust, vol. 92(4), pages 875-891, December.
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    Cited by:

    1. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2020. "Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 85-108, January.
    2. Lihong Qi & Xu Zhang & Yanqing Sun & Lu Wang & Yichuan Zhao, 2019. "Weighted estimating equations for additive hazards models with missing covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 365-387, April.
    3. Lee, Unkyung & Sun, Yanqing & Scheike, Thomas H. & Gilbert, Peter B., 2018. "Analysis of generalized semiparametric regression models for cumulative incidence functions with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 59-79.
    4. Fei Heng & Yanqing Sun & Seunggeun Hyun & Peter B. Gilbert, 2020. "Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 731-760, October.
    5. Yei Eun Shin & Ruth M. Pfeiffer & Barry I. Graubard & Mitchell H. Gail, 2022. "Weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case‐control design," Biometrics, The International Biometric Society, vol. 78(1), pages 179-191, March.
    6. Yanqing Sun & Qiong Shou & Peter B. Gilbert & Fei Heng & Xiyuan Qian, 2023. "Semiparametric additive time‐varying coefficients model for longitudinal data with censored time origin," Biometrics, The International Biometric Society, vol. 79(2), pages 695-710, June.

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