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On Inverse Probability Weighting for Nonmonotone Missing at Random Data

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  • BaoLuo Sun
  • Eric J. Tchetgen Tchetgen

Abstract

The development of coherent missing data models to account for nonmonotone missing at random (MAR) data by inverse probability weighting (IPW) remains to date largely unresolved. As a consequence, IPW has essentially been restricted for use only in monotone MAR settings. We propose a class of models for nonmonotone missing data mechanisms that spans the MAR model, while allowing the underlying full data law to remain unrestricted. For parametric specifications within the proposed class, we introduce an unconstrained maximum likelihood estimator for estimating the missing data probabilities which is easily implemented using existing software. To circumvent potential convergence issues with this procedure, we also introduce a constrained Bayesian approach to estimate the missing data process which is guaranteed to yield inferences that respect all model restrictions. The efficiency of standard IPW estimation is improved by incorporating information from incomplete cases through an augmented estimating equation which is optimal within a large class of estimating equations. We investigate the finite-sample properties of the proposed estimators in extensive simulations and illustrate the new methodology in an application evaluating key correlates of preterm delivery for infants born to HIV-infected mothers in Botswana, Africa. Supplementary materials for this article are available online.

Suggested Citation

  • BaoLuo Sun & Eric J. Tchetgen Tchetgen, 2018. "On Inverse Probability Weighting for Nonmonotone Missing at Random Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 369-379, January.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:521:p:369-379
    DOI: 10.1080/01621459.2016.1256814
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    Cited by:

    1. Soyoung Kim & Jae-Kwang Kim & Kwang Woo Ahn, 2022. "A calibrated Bayesian method for the stratified proportional hazards model with missing covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 169-193, April.
    2. Yang Zhao, 2022. "Diagnostic checking of multiple imputation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 271-286, June.
    3. Yang Zhao, 2023. "Maximum likelihood estimation of missing data probability for nonmonotone missing at random data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 197-209, March.
    4. Daniel O. Scharfstein & Jon Steingrimsson & Aidan McDermott & Chenguang Wang & Souvik Ray & Aimee Campbell & Edward Nunes & Abigail Matthews, 2022. "Global sensitivity analysis of randomized trials with nonmonotone missing binary outcomes: Application to studies of substance use disorders," Biometrics, The International Biometric Society, vol. 78(2), pages 649-659, June.
    5. Yang Zhao & Meng Liu, 2021. "Unified approach for regression models with nonmonotone missing at random data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 87-101, March.
    6. Yang Zhao, 2021. "Semiparametric model for regression analysis with nonmonotone missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 461-475, June.

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