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Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach

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  • Geert Verbeke
  • Geert Molenberghs
  • Herbert Thijs
  • Emmanuel Lesaffre
  • Michael G. Kenward

Abstract

Summary. Diggle and Kenward (1994, Applied Statistics43, 49–93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B48, 133–169). The influence of perturbing a missing‐at‐random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.

Suggested Citation

  • Geert Verbeke & Geert Molenberghs & Herbert Thijs & Emmanuel Lesaffre & Michael G. Kenward, 2001. "Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach," Biometrics, The International Biometric Society, vol. 57(1), pages 7-14, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:7-14
    DOI: 10.1111/j.0006-341X.2001.00007.x
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    1. P. Diggle & M. G. Kenward, 1994. "Informative Drop‐Out in Longitudinal Data Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 49-73, March.
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    1. D. Nitsch & B. L. DeStavola & S. M. B. Morton & D. A. Leon, 2006. "Linkage bias in estimating the association between childhood exposures and propensity to become a mother: an example of simple sensitivity analyses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 493-505, July.
    2. Ivy Jansen & Geert Molenberghs & Marc Aerts & Herbert Thijs & Kristel Van Steen, 2003. "A Local Influence Approach Applied to Binary Data from a Psychiatric Study," Biometrics, The International Biometric Society, vol. 59(2), pages 410-419, June.
    3. Jan R. Magnus & Andrey L. Vasnev, 2007. "Local sensitivity and diagnostic tests," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 166-192, March.
    4. Chan, Jennifer S.K. & Leung, Doris Y.P. & Boris Choy, S.T. & Wan, Wai Y., 2009. "Nonignorable dropout models for longitudinal binary data with random effects: An application of Monte Carlo approximation through the Gibbs output," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4530-4545, October.
    5. 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.
    6. 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.
    7. Trias Wahyuni Rakhmawati & Geert Molenberghs & Geert Verbeke & Christel Faes, 2016. "Local influence diagnostics for incomplete overdispersed longitudinal counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(9), pages 1722-1737, July.
    8. Jason Roy & Xihong Lin, 2005. "Missing Covariates in Longitudinal Data with Informative Dropouts: Bias Analysis and Inference," Biometrics, The International Biometric Society, vol. 61(3), pages 837-846, September.
    9. Ivy Jansen & Ann Van den Troost & Geert Molenberghs & Ad A. Vermulst & Jan R. M. Gerris, 2006. "Modeling Partially Incomplete Marital Satisfaction Data," Sociological Methods & Research, , vol. 35(1), pages 113-136, 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. S. Eftekhari Mahabadi & M. Ganjali, 2012. "An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2327-2348, July.
    12. Vasnev, A.L., 2006. "Local sensitivity in econometrics," Other publications TiSEM 789cc7a5-57da-4c5c-b5af-2, Tilburg University, School of Economics and Management.
    13. Sinha, Sanjoy K. & Kaushal, Amit & Xiao, Wenzhong, 2014. "Inference for longitudinal data with nonignorable nonmonotone missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 77-91.
    14. Caroline Beunckens & Cristina Sotto & Geert Molenberghs & Geert Verbeke, 2009. "A multifaceted sensitivity analysis of the Slovenian public opinion survey data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(2), pages 171-196, May.
    15. Dantan Etienne & Proust-Lima Cécile & Letenneur Luc & Jacqmin-Gadda Helene, 2008. "Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-26, July.
    16. Niansheng Tang & Sy-Miin Chow & Joseph G. Ibrahim & Hongtu Zhu, 2017. "Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 875-903, December.
    17. Weiping Zhang & Feiyue Xie & Jiaxin Tan, 2020. "A robust joint modeling approach for longitudinal data with informative dropouts," Computational Statistics, Springer, vol. 35(4), pages 1759-1783, December.
    18. Ivy Jansen & Geert Molenberghs, 2008. "A flexible marginal modelling strategy for non‐monotone missing data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 347-373, April.
    19. O'Hara Hines, R.J. & Hines, W.G.S., 2007. "Covariance miss-specification and the local influence approach in sensitivity analyses of longitudinal data with drop-outs," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5537-5546, August.
    20. Colin O. Wu & Kai F. Yu, 2002. "Nonparametric Varying-Coefficient Models for the Analysis of Longitudinal Data," International Statistical Review, International Statistical Institute, vol. 70(3), pages 373-393, December.
    21. 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.
    22. 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.
    23. Betsy J. Feldman & Sophia Rabe-Hesketh, 2012. "Modeling Achievement Trajectories When Attrition Is Informative," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 703-736, December.
    24. Díaz Iván & van der Laan Mark J., 2013. "Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 149-160, November.
    25. Andrew Gelman & Iven Van Mechelen & Geert Verbeke & Daniel F. Heitjan & Michel Meulders, 2005. "Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data," Biometrics, The International Biometric Society, vol. 61(1), pages 74-85, March.

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