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Intrinsic efficiency and multiple robustness in longitudinal studies with drop-out

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  • Peisong Han

Abstract

Intrinsic efficiency and multiple robustness are desirable properties in missing data analysis. We establish both for estimating the mean of a response at the end of a longitudinal study with drop-out. The idea is to calibrate the estimated missingness probability at each visit using data from past visits. We consider one working model for the missingness probability and multiple working models for the data distribution. Intrinsic efficiency guarantees that, when the missingness probability is correctly modelled, the multiple data distribution models, combined with data prior to the end of the study, are optimally accommodated to maximize efficiency. The efficiency generally increases with the number of data distribution models, except where one such model is correctly specified as well, in which case all the proposed estimators attain the semiparametric efficiency bound. Multiple robustness ensures estimation consistency if the missingness probability model is misspecified but one data distribution model is correct. Our proposed estimators are all convex combinations of the observed responses, and thus always fall within the parameter space.

Suggested Citation

  • Peisong Han, 2016. "Intrinsic efficiency and multiple robustness in longitudinal studies with drop-out," Biometrika, Biometrika Trust, vol. 103(3), pages 683-700.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:683-700.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw024
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    References listed on IDEAS

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    1. Jing Qin & Biao Zhang, 2007. "Empirical‐likelihood‐based inference in missing response problems and its application in observational studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 101-122, February.
    2. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-42, May.
    3. Tan Zhiqiang, 2008. "Comment: Improved Local Efficiency and Double Robustness," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-11, June.
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    Cited by:

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    2. Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    3. Lan Wen & Miguel A. Hernán & James M. Robins, 2022. "Multiply robust estimators of causal effects for survival outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1304-1328, September.
    4. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    5. Lucia Babino & Andrea Rotnitzky & James Robins, 2019. "Multiple robust estimation of marginal structural mean models for unconstrained outcomes," Biometrics, The International Biometric Society, vol. 75(1), pages 90-99, March.
    6. Vahe Avagyan & Stijn Vansteelandt, 2021. "Stable inverse probability weighting estimation for longitudinal studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1046-1067, September.
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    9. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2019. "Calibration estimation of semiparametric copula models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 85-109.

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