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Local sensitivity approximations for selectivity bias

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  • John Copas
  • Shinto Eguchi

Abstract

Observational data analysis is often based on tacit assumptions of ignorability or randomness. The paper develops a general approach to local sensitivity analysis for selectivity bias, which aims to study the sensitivity of inference to small departures from such assumptions. If M is a model assuming ignorability, we surround M by a small neighbourhood N defined in the sense of Kullback–Leibler divergence and then compare the inference for models in N with that for M. Interpretable bounds for such differences are developed. Applications to missing data and to observational comparisons are discussed. Local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems.

Suggested Citation

  • John Copas & Shinto Eguchi, 2001. "Local sensitivity approximations for selectivity bias," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 871-895.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:871-895
    DOI: 10.1111/1467-9868.00318
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    Cited by:

    1. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    2. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    3. Paul R. Rosenbaum, 2007. "Sensitivity Analysis for m-Estimates, Tests, and Confidence Intervals in Matched Observational Studies," Biometrics, The International Biometric Society, vol. 63(2), pages 456-464, June.
    4. Vikström, Johan, 2009. "Cluster sample inference using sensitivity analysis: the case with few groups," Working Paper Series 2009:15, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    5. R. Bellio & E. Gori, 2003. "Impact evaluation of job training programmes: Selection bias in multilevel models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 893-907.
    6. Xiaoyan Shi & Hongtu Zhu & Joseph G. Ibrahim, 2009. "Local Influence for Generalized Linear Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 65(4), pages 1164-1174, December.
    7. David Todem & KyungMann Kim & Jason Fine & Limin Peng, 2010. "Semiparametric regression models and sensitivity analysis of longitudinal data with non‐random dropouts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 133-156, May.
    8. Masaaki Matsuura & Shinto Eguchi, 2005. "Modeling Late Entry Bias in Survival Analysis," Biometrics, The International Biometric Society, vol. 61(2), pages 559-566, June.
    9. Xavier de Luna & Mathias Lundin, 2014. "Sensitivity analysis of the unconfoundedness assumption with an application to an evaluation of college choice effects on earnings," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1767-1784, August.
    10. Baojiang Chen & Xiao-Hua Zhou, 2011. "Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 830-842, September.
    11. Sander Greenland & Leeka Kheifets, 2006. "Leukemia Attributable to Residential Magnetic Fields: Results from Analyses Allowing for Study Biases," Risk Analysis, John Wiley & Sons, vol. 26(2), pages 471-482, April.
    12. de Luna, Xavier & Lundin, Mathias, 2009. "Sensitivity analysis of the unconfoundedness assumption in observational studies," Working Paper Series 2009:12, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    13. Paul R. Rosenbaum, 2007. "Confidence Intervals for Uncommon but Dramatic Responses to Treatment," Biometrics, The International Biometric Society, vol. 63(4), pages 1164-1171, December.
    14. Paul R. Rosenbaum, 2011. "A New u-Statistic with Superior Design Sensitivity in Matched Observational Studies," Biometrics, The International Biometric Society, vol. 67(3), pages 1017-1027, September.
    15. Xie, Hui, 2012. "Analyzing longitudinal clinical trial data with nonignorable missingness and unknown missingness reasons," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1287-1300.
    16. D. Todem & J. Fine & L. Peng, 2010. "A Global Sensitivity Test for Evaluating Statistical Hypotheses with Nonidentifiable Models," Biometrics, The International Biometric Society, vol. 66(2), pages 558-566, June.
    17. Samaneh Mahabadi & Mojtaba Ganjali, 2015. "A Bayesian approach for sensitivity analysis of incomplete multivariate longitudinal data with potential nonrandom dropout," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 397-417, December.
    18. Ben B. Hansen & Paul R. Rosenbaum & Dylan S. Small, 2014. "Clustered Treatment Assignments and Sensitivity to Unmeasured Biases in Observational Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 133-144, March.

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