Abstract
In this article, we present a sensitivity analysis for drawing inferences about parameters that are not estimable from observed data without additional assumptions. We present the methodology using two different examples: a causal parameter that is not identifiable due to violations of the randomization assumption, and a parameter that is not estimable in the nonparametric model due to measurement error. Existing methods for tackling these problems assume a parametric model for the type of violation to the identifiability assumption and require the development of new estimators and inference for every new model. The method we present can be used in conjunction with any existing asymptotically linear estimator of an observed data parameter that approximates the unidentifiable full data parameter and does not require the study of additional models.
References
1. RubinD. Inference and missing data. Biometrika1976;63:581–92.10.1093/biomet/63.3.581Suche in Google Scholar
2. van der LaanM, RobinsJ. Unified methods for censored longitudinal data and causality. New York: Springer, 2003.10.1007/978-0-387-21700-0Suche in Google Scholar
3. GillR, van der LaanM, RobinsJ. Coarsening at random: characterizations, conjectures and counter-examples. In: LinD,FlemingT, editors. Proceedings of the first Seattle symposium in biostatistics. New York: Springer Verlag, 1997:255–94.Suche in Google Scholar
4. HeitjanD, RubinD. Ignorability and coarse data. Ann Stat1991;19:2244–53.10.1214/aos/1176348396Suche in Google Scholar
5. RotnitzkyA, RobinsJM, ScharfsteinDO. Semiparametric regression for repeated outcomes with nonignorable nonresponse. J Am Stat Assoc1998;93:1321–39.10.1080/01621459.1998.10473795Suche in Google Scholar
6. RobinsJM. Association, causation, and marginal structural models. Synthese1999;121:151–79.Suche in Google Scholar
7. RobinsJM, RotnitzkyA, ScharfsteinDO. Sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models. In: Statistical models in epidemiology, the environment and clinical trials. IMA volumes in mathematics and its applications. New York: Springer, 2000:1–94.Suche in Google Scholar
8. RotnitzkyA, ScharfsteinD, SuST, RobinsJ. Methods for conducting sensitivity analysis of trials with potentially nonignorable competing causes of censoring. Biometrics2001;57:103–13.10.1111/j.0006-341X.2001.00103.xSuche in Google Scholar PubMed
9. ScharfsteinDO, RobinsJM. Estimation of the failure time distribution in the presence of informative censoring. Biometrika2002;89:617–34.10.1093/biomet/89.3.617Suche in Google Scholar
10. ScharfsteinDO, RotnitzkyA, RobinsJM. Adjusting for nonignorable drop-out using semiparametric non-response models (with discussion). J Am Stat Assoc1999;94:1096–146.10.1080/01621459.1999.10473862Suche in Google Scholar
11. PearlJ. Causality: models, reasoning, and inference. Cambridge: Cambridge University Press, 2000.Suche in Google Scholar
12. TagerI, HollenbergM, SatarianoW. Association between self-reported leisure-time physical activity and measures of cardiorespiratory fitness in an elderly population. American Journal of Epidemiology1988;147(10):921–31.10.1093/oxfordjournals.aje.a009382Suche in Google Scholar PubMed
13. BembomO, van der LaanM. A practical illustration of the importance of realistic individualized treatment rules in causal inference. Electronic J Stat2007:574–596.10.1214/07-EJS105Suche in Google Scholar PubMed PubMed Central
14. DíazI, van der LaanM. Population intervention causal effects based on stochastic interventions. Biometrics2012;68:541–9. Available at: http://dx.doi.org/10.1111/j.1541-0420.2011.01685.x.10.1111/j.1541-0420.2011.01685.xSuche in Google Scholar PubMed PubMed Central
15. HernánMA, ColeSR. Invited commentary: causal diagrams and measurement bias. Am J Epidemiol2009;170:963–54.10.1093/aje/kwp289Suche in Google Scholar
16. RoseS, van der LaanM. Targeted learning: causal inference for observational and experimental data. New York: Springer, 2011.Suche in Google Scholar
17. van der LaanM, RubinD. Targeted maximum likelihood learning. Int J Biostat2006;2(1):1–40.10.2202/1557-4679.1043Suche in Google Scholar
18. RosenbaumPR, RubinDB. Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. J R Stat Soc. Ser B (Methodol)1983;45(2):212–8.10.1111/j.2517-6161.1983.tb01242.xSuche in Google Scholar
19. LittleRJ. Modeling the drop-out mechanism in repeated-measures studies. J Am Stat Assoc1995;90:1112–21.10.1080/01621459.1995.10476615Suche in Google Scholar
20. LittleRJ, WangY. Pattern-mixture models for multivariate incomplete data with covariates. Biometrics1996;52(1):98–111.10.2307/2533148Suche in Google Scholar
21. VerbekeG, MolenberghsG, ThijsH, LesaffreMG, KenwardE. Sensitivity analysis for nonrandom dropout: a local influence approach. Biometrics2001;57:7–14.10.1111/j.0006-341X.2001.00007.xSuche in Google Scholar PubMed
22. GustafsonP, SrinivasanC, WassermanL. Local sensitivity analysis. Bayesian stat1996;5:197–210.Suche in Google Scholar
23. McCandlessLC, GustafsonP, LevyA. Bayesian sensitivity analysis for unmeasured confounding in observational studies. Stat Med2007;26:2331–47.10.1002/sim.2711Suche in Google Scholar PubMed
24. LukacsE. Inversion formulae for characteristic functions of absolutely continuous distributions. Am Math Monthly1964;71:44–7.10.2307/2311301Suche in Google Scholar
25. ScharfsteinD, McDermottA, OlsonW, WeigandF.Global sensitivity analysis for repeated measures studies with informative drop-out, 2013. Available at: http://www.biostat.jhsph.edu/dscharf/panss_paper_statsci.pdf.Suche in Google Scholar
26. van der LaanM, PolleyE, HubbardA. Super learner. Stat Appl Genet Mol Biol2007;6(1):1–21.10.2202/1544-6115.1309Suche in Google Scholar PubMed
©2013 by Walter de Gruyter Berlin / Boston
Artikel in diesem Heft
- Masthead
- Masthead
- Research Articles
- Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems
- Assessing the Causal Effect of Policies: An Example Using Stochastic Interventions
- Novel Point Estimation from a Semiparametric Ratio Estimator (SPRE): Long-Term Health Outcomes from Short-Term Linear Data, with Application to Weight Loss in Obesity
- Exact Nonparametric Confidence Bands for the Survivor Function
- Semiparametric Regression Analysis of Clustered Interval-Censored Failure Time Data with Informative Cluster Size
- A Weighting Analogue to Pair Matching in Propensity Score Analysis
- Alternative Monotonicity Assumptions for Improving Bounds on Natural Direct Effects
- Estimation of Risk Ratios in Cohort Studies with a Common Outcome: A Simple and Efficient Two-stage Approach
- Distance-Based Mapping of Disease Risk
- The Balanced Survivor Average Causal Effect
- Commentary
- Principal Stratification: A Broader Vision
Artikel in diesem Heft
- Masthead
- Masthead
- Research Articles
- Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems
- Assessing the Causal Effect of Policies: An Example Using Stochastic Interventions
- Novel Point Estimation from a Semiparametric Ratio Estimator (SPRE): Long-Term Health Outcomes from Short-Term Linear Data, with Application to Weight Loss in Obesity
- Exact Nonparametric Confidence Bands for the Survivor Function
- Semiparametric Regression Analysis of Clustered Interval-Censored Failure Time Data with Informative Cluster Size
- A Weighting Analogue to Pair Matching in Propensity Score Analysis
- Alternative Monotonicity Assumptions for Improving Bounds on Natural Direct Effects
- Estimation of Risk Ratios in Cohort Studies with a Common Outcome: A Simple and Efficient Two-stage Approach
- Distance-Based Mapping of Disease Risk
- The Balanced Survivor Average Causal Effect
- Commentary
- Principal Stratification: A Broader Vision