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Weight calibration to improve the efficiency of pure risk estimates from case‐control samples nested in a cohort

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

Abstract

Cohort studies provide information on relative hazards and pure risks of disease. For rare outcomes, large cohorts are needed to have sufficient numbers of events, making it costly to obtain covariate information on all cohort members. We focus on nested case‐control designs that are used to estimate relative hazard in the Cox regression model. In 1997, Langholz and Borgan showed that pure risk can also be estimated from nested case‐control data. However, these approaches do not take advantage of some covariates that may be available on all cohort members. Researchers have used weight calibration to increase the efficiency of relative hazard estimates from case‐cohort studies and nested cased‐control studies. Our objective is to extend weight calibration approaches to nested case‐control designs to improve precision of estimates of relative hazards and pure risks. We show that calibrating sample weights additionally against follow‐up times multiplied by relative hazards during the risk projection period improves estimates of pure risk. Efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks. We develop explicit variance formulas for the weight‐calibrated estimates. Simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality. Examples are provided using data from the American Association of Retired Persons Diet and Health Cohort Study.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1087-1097
    DOI: 10.1111/biom.13209
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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. 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.
    3. Donglin Zeng & D. Y. Lin, 2014. "Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 371-383, March.
    4. 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.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
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    Cited by:

    1. Lola Etievant & Mitchell H. Gail, 2024. "Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(3), pages 572-599, July.
    2. Yei Eun Shin & Takumi Saegusa, 2024. "Nested case–control sampling without replacement," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 776-799, October.

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