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Double Bias: Estimation of Causal Effects from Length-Biased Samples in the Presence of Confounding

Author

Listed:
  • Ertefaie Ashkan

    (Department of Statistics, University of Pennsylvania, Philadelphia, PA, USA)

  • Asgharian Masoud

    (Department of Mathematics and Statistics, McGill University, Montréal, QC, Canada)

  • Stephens David A.

    (Department of Mathematics and Statistics, McGill University, Montréal, QC, Canada)

Abstract

Length bias in survival data occurs in observational studies when, for example, subjects with shorter lifetimes are less likely to be present in the recorded data. In this paper, we consider estimating the causal exposure (treatment) effect on survival time from observational data when, in addition to the lack of randomization and consequent potential for confounding, the data constitute a length-biased sample; we hence term this a double-bias problem. We develop estimating equations that can be used to estimate the causal effect indexing the structural Cox proportional hazard and accelerated failure time models for point exposures in double-bias settings. The approaches rely on propensity score-based adjustments, and we demonstrate that estimation of the propensity score must be adjusted to acknowledge the length-biased sampling. Large sample properties of the estimators are established and their small sample behavior is studied using simulations. We apply the proposed methods to a set of, partly synthesized, length-biased survival data collected as part of the Canadian Study of Health and Aging (CSHA) to compare survival of subjects with dementia among institutionalized patients versus those recruited from the community and depict their adjusted survival curves.

Suggested Citation

  • Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2015. "Double Bias: Estimation of Causal Effects from Length-Biased Samples in the Presence of Confounding," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 69-89, May.
  • Handle: RePEc:bpj:ijbist:v:11:y:2015:i:1:p:69-89:n:7
    DOI: 10.1515/ijb-2014-0037
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    References listed on IDEAS

    as
    1. Yu-Jen Cheng & Mei-Cheng Wang, 2012. "Estimating Propensity Scores and Causal Survival Functions Using Prevalent Survival Data," Biometrics, The International Biometric Society, vol. 68(3), pages 707-716, September.
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    3. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    4. Xiaodong Luo & Wei Yann Tsai & Qiang Xu, 2009. "Pseudo-partial likelihood estimators for the Cox regression model with missing covariates," Biometrika, Biometrika Trust, vol. 96(3), pages 617-633.
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    6. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, December.
    7. Xiaodong Luo & Wei Yann Tsai, 2009. "Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach," Biometrika, Biometrika Trust, vol. 96(4), pages 873-886.
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