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Weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case‐control design

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  • Yei Eun Shin
  • Ruth M. Pfeiffer
  • Barry I. Graubard
  • Mitchell H. Gail

Abstract

We study the efficiency of covariate‐specific estimates of pure risk (one minus the survival function) when some covariates are only available for case‐control samples nested in a cohort. We focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time‐varying or time‐invariant coefficients. A published approach uses the design‐based inclusion probabilities to reweight the nested case‐control data. We obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort, for both time‐varying and time‐invariant covariate coefficients. We develop explicit variance formulas for the weight‐calibrated estimates based on influence functions. Simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality. Examples are provided using data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study (PLCO).

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:1:p:179-191
    DOI: 10.1111/biom.13413
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    References listed on IDEAS

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    1. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    2. 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.
    3. Thomas Lumley & Pamela A. Shaw & James Y. Dai, 2011. "Connections between Survey Calibration Estimators and Semiparametric Models for Incomplete Data," International Statistical Review, International Statistical Institute, vol. 79(2), pages 200-220, August.
    4. 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.
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