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Second-Order Inference for the Mean of a Variable Missing at Random

Author

Listed:
  • Díaz Iván

    (Google Inc. New York, NY)

  • Carone Marco

    (Department of Biostatistics, University of Washington, Seattle, WA, USA)

  • van der Laan Mark J.

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

Abstract

We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator.

Suggested Citation

  • Díaz Iván & Carone Marco & van der Laan Mark J., 2016. "Second-Order Inference for the Mean of a Variable Missing at Random," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 333-349, May.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:333-349:n:14
    DOI: 10.1515/ijb-2015-0031
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    References listed on IDEAS

    as
    1. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    2. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
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