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.
Keywords
- Influence Function
- Semiparametric Model
- Current Status Data
- Marginal Structural Model
- Consistency Assumption
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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.
Balke, A. & Pearl, J. (1997). Bounds on Treatment from Studies with Imperfect Compliance. Journal of the American Statistical Association, 92:1171–1176.
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.
Chamberlain, G. (1987). Asymptotic Efficiency in Estimation with Conditional Moment Restrictions. Journal of Econometrics, 34:305–324.
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.
Dabrowska, D. (1988). Kaplan-Meier estimate on the plane. Annals of Statistics, 16:1475–1489.
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.
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.
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.
Heitjan, D.F., and Rubin, D.B. (1991). Ignorability and Coarse Data. The Annals of Statistics, 19:2244–2253.
Klein, J.P. and Moeschberger, M.L. (1988). Bounds on net survival probabilities for dependent competing risks. Biometrics, 44:528–538.
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.
Little, R.J., and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: John Wiley.
Little, R.J.A. (1994), A Class of Pattern-Mixture Models for Normal Missing Data. Biometrika, 81:471–483.
Manski, C.F. (1990). Nonparametric bounds on treatment effects. American Economic Reviews, Papers, and Proceedings, 80:319–323.
Moeschberger, M.L. and Klein, J.P. (1995). Statistical models for dependent competing risks. Lifetime Data Analysis, 1:195–204.
Newey, W.K. (1990). Semiparametric Efficiency Bounds. Journal of Applied Econometrics, 5:99–135.
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.
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.
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.
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.
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.
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.
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.
Robins, J.M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika, 79:321–334.
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.
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.
Robins, J.M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics, 23:2379–2412.
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.
Robins, J.M. (1997a). Non-response models for the analysis of non-monotone nonignorable missing data. Statistics in Medicine, 16:21–37.
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.
Robins, J.M. (1998a). Marginal structural models. In: 1997 Proceedings of the American Statistical Association, Section on Bayesian Statistical Science, pp. 1–10.
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.
Robins, J.M. (1998c). Correction for non-compliance in equivalence trials. Statistics in Medicine, 17:269–302.
Robins, J.M. and Gill, R. (1997). Non-response models for the analysis of nonmonotone ignorable missing data. Statistics in Medicine, 16:39–56.
Robins, J.M. and Ritov, Y. (1997). A curse of dimensionality appropriate (CODA) asymptotic theory for semiparametric models. Statistics in Medicine, 16:285–319.
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.
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.
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).
Rosenbaum, P.R. (1995). Observational Studies. New York: Springer-Verlag.
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.
Rotnitzky, A., and Robins, J.M. (1997). Analysis of semiparametric regression models with non-ignorable non-response. Statistics in Medicine, 16:81–102.
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.
Rubin, D.B. (1976). Inference and Missing Data. Biometrika, 63:581–592.
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).
Schlesselman J.J. (1978). Assessing effects of confounding variables. American Journal of Epidemiology, 108:3–8.
Slud, E.V. and Rubenstein, L.V. (1983). Dependent competing risks and summary survival curves. Biometrika, 70:643–649.
Spirtes, P., Glymour, C, and Scheines, R. (1993). Causation, Prediction, and Search. New York: Springer Verlag.
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.
Van Der Vaart, A. (1991). On differentiable functionals. Annals of Statistics, 19:178–204.
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.
Zheng, M. and Klein, J.P. (1995). Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika, 82:127–138.
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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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