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Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models

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Statistical Models in Epidemiology, the Environment, and Clinical Trials

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 116))

Abstract

In both observational and randomized studies, subjects commonly drop out of the study (i.e., become censored) before end of follow-up. If, conditional on the history of the observed data up to t, the hazard of dropping out of the study (i.e., censoring) at time t does not depend on the possibly unobserved data subsequent to t, we say drop-out is ignorable or explainable (Rubin, 1976). On the other hand, if the hazard of drop-out depends on the possibly unobserved future, we say drop-out is non-ignorable or, equivalently, that there is selection bias on unobservables. Neither the existence of selection bias on unobservables nor its magnitude is identifiable from the joint distribution of the observables. In view of this fact, we argue that the data analyst should conduct a “sensitivity analysis” to quantify how one’s inference concerning an outcome of interest varies as a function of the magnitude of non-identifiable selection bias.

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References

  • Baker, S.G., Rosenberger, W.F., and Dersimonian, R. (1992). Closed-form estimates for missing counts in two-way contingency tables. Statistics in Medicine, 11:643–657.

    Article  Google Scholar 

  • Balke, A. & Pearl, J. (1997). Bounds on Treatment from Studies with Imperfect Compliance. Journal of the American Statistical Association, 92:1171–1176.

    Article  MATH  Google Scholar 

  • Bickel, P.J., Klaassen, C.A.J., Ritov, Y., and Wellner, J.A. (1993). Efficient and Adaptive Inference in Semiparametric Models. Baltimore, MD: Johns Hopkins University Press.

    Google Scholar 

  • Chamberlain, G. (1987). Asymptotic Efficiency in Estimation with Conditional Moment Restrictions. Journal of Econometrics, 34:305–324.

    Article  MathSciNet  MATH  Google Scholar 

  • Cornfield, J., Haenszel, W., Hammond, E.C., Lilienfeld, A.M., Shimkin, M.B., and Wynder, E.L. (1959). Smoking and lung cancer: Recent evidence and a discussion of some questions. Journal of the National Cancer Institute, 22:173–203.

    Google Scholar 

  • Dabrowska, D. (1988). Kaplan-Meier estimate on the plane. Annals of Statistics, 16:1475–1489.

    Article  MathSciNet  MATH  Google Scholar 

  • Gill, R.D. and Robins, J.M. (1996). Sequential Models for Coarsening and missing-ness. Proceedings of the First Seattle Symposium on Survival Analysis, Springer-Verlag Lecture Notes in Statistics, pp. 295–305.

    Google Scholar 

  • Gill, R.D., van der Laan, M.J., and Robins, J.M. (1996). Coarsening at random: Characterizations, conjectures and counterexamples. Proceedings of the First Seattle Symposium on Survival Analysis, Springer-Verlag Lecture Notes in Statistics, pp. 255–294.

    Google Scholar 

  • Heckman, J.J. (1976). The common structure of statistical models of truncation, sample selection and limited dependent variables, and a simple estimator for such models. Ann. Econ. Socl. Measurement., 5:475–492.

    Google Scholar 

  • Heitjan, D.F., and Rubin, D.B. (1991). Ignorability and Coarse Data. The Annals of Statistics, 19:2244–2253.

    Article  MathSciNet  MATH  Google Scholar 

  • Klein, J.P. and Moeschberger, M.L. (1988). Bounds on net survival probabilities for dependent competing risks. Biometrics, 44:528–538.

    Article  MathSciNet  Google Scholar 

  • Lin, D.Y., Psaty, B.M., and Kronmal, R.A. (1998). Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics, 54:948–963.

    Article  MATH  Google Scholar 

  • Little, R.J., and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: John Wiley.

    MATH  Google Scholar 

  • Little, R.J.A. (1994), A Class of Pattern-Mixture Models for Normal Missing Data. Biometrika, 81:471–483.

    Article  MathSciNet  MATH  Google Scholar 

  • Manski, C.F. (1990). Nonparametric bounds on treatment effects. American Economic Reviews, Papers, and Proceedings, 80:319–323.

    Google Scholar 

  • Moeschberger, M.L. and Klein, J.P. (1995). Statistical models for dependent competing risks. Lifetime Data Analysis, 1:195–204.

    Article  MATH  Google Scholar 

  • Newey, W.K. (1990). Semiparametric Efficiency Bounds. Journal of Applied Econometrics, 5:99–135.

    Article  MATH  Google Scholar 

  • Newey, W.K., and Mcfadden, D. (1993). Estimation in Large Samples. Handbook of Econometrics (Vol. 4), D. McFadden and R. Engler, eds., Amsterdam: North Holland.

    Google Scholar 

  • Nordheim, E.V. (1984). Inference from Nonrandomly Missing Categorical Data: An Example from a Genetic Study on Turner’s Syndrome. Journal of the American Statistical Association, 7:772–780.

    Article  Google Scholar 

  • Pearl, J., and Verma, T. (1991). A theory of inferred causation. In Principles of Knowledge Representation and Reasoning: Proceedings of the 2nd International Conference. J.A. Allen, R. Fikes, and E. Sandewall, eds., pp. 441–452. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Ritov, Y., and Wellner, J.A. (1988). Censoring, Martingales, and the Cox Model. Contemporary Mathematical Statistics Inf. Stochastic Procedures, N.U. Prabhu, editor, American Mathematical Society, 80:191–220.

    Google Scholar 

  • Robins, J.M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods — Application to control of the healthy worker survivor effect. Mathematical Modelling, 7:1393–1512.

    Article  MathSciNet  MATH  Google Scholar 

  • Robins, J.M. (1987). Addendum to “A new approach to causal inference in mortality studies with sustained exposure periods — Application to control of the healthy worker survivor effect.” Computers and Mathematics with Applications, 14:923–945.

    Article  MathSciNet  MATH  Google Scholar 

  • Robins, J.M. (1989). The analysis of randomized and non-randomized AIDS treatment trials using a new approach to causal inference in longitudinal studies. Health Service Research Methodology: A Focus on AIDS. Sechrest L., Freeman H., and Mulley A., eds., NCHSR, U.S. Public Health Service, pp. 113–159.

    Google Scholar 

  • Robins, J.M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika, 79:321–334.

    Article  MathSciNet  MATH  Google Scholar 

  • Robins, J.M., Blevins D, Ritter G, and Wulfsohn M. (1992). G-estimation of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology, 3:319–336.

    Article  Google Scholar 

  • Robins, J.M., Blevins D, Ritter G, and Wulfsohn M. (1993). Errata to G-estimation of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology, 4:189.

    Article  Google Scholar 

  • Robins, J.M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics, 23:2379–2412.

    Article  MathSciNet  MATH  Google Scholar 

  • Robins, J.M. (1996). Locally efficient median regression with random censoring and surrogate markers. Proceedings of the 1994 Conference on Lifetime Data Models in Reliability and Survival Analysis, Boston, MA. In: Lifetime Data: Models in Reliability and Survival Analysis, N.P. Jewell et al., eds., Kluwer Academic Publishers, 263–274.

    Google Scholar 

  • Robins, J.M. (1997a). Non-response models for the analysis of non-monotone nonignorable missing data. Statistics in Medicine, 16:21–37.

    Article  Google Scholar 

  • Robins, J.M. (1997b). Causal inference from complex longitudinal data. In: Latent Variable Modeling and Applications to Causality. Lecture Notes in Statistics (120), M. Berkane, editor. NY: Springer Verlag, pp. 69–117.

    Chapter  Google Scholar 

  • Robins, J.M. (1998a). Marginal structural models. In: 1997 Proceedings of the American Statistical Association, Section on Bayesian Statistical Science, pp. 1–10.

    Google Scholar 

  • Robins, J.M. (1999b). Marginal Structural Models versus Structural Nested Models as Tools for Causal Inference. Statistical Models in Epidemiology, the Environment and Clinical Trials, M. Elizabeth Halloran and Donald Berry, editors, NY: Springer-Verlag, pp. 95–134.

    Google Scholar 

  • Robins, J.M. (1998c). Correction for non-compliance in equivalence trials. Statistics in Medicine, 17:269–302.

    Article  MATH  Google Scholar 

  • Robins, J.M. and Gill, R. (1997). Non-response models for the analysis of nonmonotone ignorable missing data. Statistics in Medicine, 16:39–56.

    Article  Google Scholar 

  • Robins, J.M. and Ritov, Y. (1997). A curse of dimensionality appropriate (CODA) asymptotic theory for semiparametric models. Statistics in Medicine, 16:285–319.

    Article  Google Scholar 

  • Robins, J.M., and Rotnitzky, A. (1992). Recovery of information and adjustment for dependent censoring using surrogate markers. In: AIDS Epidemiology — Methodological Issues. Jewell N., Dietz K. and Farewell V., eds., Boston, MA: Birkhäuser, pp. 297–331.

    Google Scholar 

  • Robins, J.M., Rotnitzky, A., Zhao LP. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89:846–866.

    Article  MathSciNet  MATH  Google Scholar 

  • Robins, J.M. and Wasserman, L. (1999). On the impossibility of inferring causation from association without background knowledge. Computation, Causation, and Discovery. C. Glymour and G. Cooper., eds., Cambridge, MA: The MIT Press (to appear).

    Google Scholar 

  • Rosenbaum, P.R. (1995). Observational Studies. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Rosenbaum, P.R., and Rubin, D.B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society, Series B, 11:212–218.

    Google Scholar 

  • Rotnitzky, A., and Robins, J.M. (1997). Analysis of semiparametric regression models with non-ignorable non-response. Statistics in Medicine, 16:81–102.

    Article  Google Scholar 

  • Rotnitzky, A., Robins, J.M. and Scharfstein, D. (1998). Semiparametric regression for repeated outcomes with non-ignorable non-response. Journal of the American Statistical Association,. 93:1321–1339.

    Article  MathSciNet  MATH  Google Scholar 

  • Rubin, D.B. (1976). Inference and Missing Data. Biometrika, 63:581–592.

    Article  MathSciNet  MATH  Google Scholar 

  • Scharfstein, D., Rotnitzky, A., and Robins, J.M. (1999). Adjusting for nonignorable drop-out with semiparametric non-response models (to appear, Journal of the American Statistical Association).

    Google Scholar 

  • Schlesselman J.J. (1978). Assessing effects of confounding variables. American Journal of Epidemiology, 108:3–8.

    Google Scholar 

  • Slud, E.V. and Rubenstein, L.V. (1983). Dependent competing risks and summary survival curves. Biometrika, 70:643–649.

    Article  MathSciNet  MATH  Google Scholar 

  • Spirtes, P., Glymour, C, and Scheines, R. (1993). Causation, Prediction, and Search. New York: Springer Verlag.

    Book  MATH  Google Scholar 

  • Van Der Laan, M.J. and Robins, J.M. (1998). Locally efficient estimation with current status data and time-dependent covariates. Journal of the American Statistical Association, 93:693–701.

    Article  MathSciNet  MATH  Google Scholar 

  • Van Der Vaart, A. (1991). On differentiable functionals. Annals of Statistics, 19:178–204.

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng, M. and Klein, J.P. (1994). A self-consistent estimator of marginal survival functions based on dependent competing risks and an assumed copula. Communication in Statistics — Theory and Methods, 23:2299–2311.

    Article  MATH  Google Scholar 

  • Zheng, M. and Klein, J.P. (1995). Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika, 82:127–138.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departments of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Avenue, Boston, MA, 02115, USA

    James M. Robins

  2. Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA

    Andrea Rotnitzky

  3. Department of Biostatistics, Johns Hopkins School of Hygiene and Public Health, Baltimore, MD, 21205, USA

    Daniel O. Scharfstein

Authors
  1. James M. Robins
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  2. Andrea Rotnitzky
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  3. Daniel O. Scharfstein
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Editor information

Editors and Affiliations

  1. Department of Biostatistics, Rollins School of Public Health, Emory University, 1518 Clifton Road, GA 30322, Atlanta, NE, USA

    M. Elizabeth Halloran

  2. Institute of Statistics and Decision Sciences and Cancer Center Biostatistics, Duke University, Box 90251, 223 Old Chemistry Bldg., Main Campus, 27708-0251, Durham, NC, USA

    Donald Berry

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Robins, J.M., Rotnitzky, A., Scharfstein, D.O. (2000). Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models. In: Halloran, M.E., Berry, D. (eds) Statistical Models in Epidemiology, the Environment, and Clinical Trials. The IMA Volumes in Mathematics and its Applications, vol 116. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1284-3_1

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  • DOI: https://doi.org/10.1007/978-1-4612-1284-3_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7078-2

  • Online ISBN: 978-1-4612-1284-3

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