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Local model uncertainty and Incomplete-data bias

Local model uncertainty and Incomplete-data bias. S. Eguchi, ISM & GUAS This talk was a part of co-work with J. Copas, University of Warwick. Hidden Bias. Publication bias － not all studies are reviewed. Confounding － causal effect only partly explained.

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Local model uncertainty and Incomplete-data bias

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  1. Local model uncertainty and Incomplete-data bias S. Eguchi, ISM & GUAS This talk was a part of co-work with J. Copas, University of Warwick

  2. Hidden Bias Publication bias －not all studies are reviewed Confounding －causal effect only partly explained Measurement error －errors in measure of exposure

  3. Lung cancer & passive smoking 30 25 20 study 15 10 5 0.5 0.3 1.5 2.0 3.0 4.0 5.0 10.0 1.0 Odds ratio

  4. Passive smoke and lung cancer Log relative risk estimates (j =1,…,30) from 30 2x2tables The estimated relative risk 1.24 with 95% confidence interval (1.13, 1.36)

  5. Conventional analysis 30 25 20 study 15 10 5 1.24 0.5 0.3 1.5 2.0 3.0 4.0 5.0 10.0 1.0 Odds ratio

  6. Incomplete Data z = (data on all studies, selection indicators) y = (data on selected studies) z = (response, treatment, potential confounders) y = (response, treatment) z = (disease status, true exposure, error) y = (disease status, observed exposure) y = h(z)

  7. Level Sets of h(z) 1. One-to-one 2. Missing 3. Measurement error 5. Competing risk 4. Interval censor 6.Hidden confounder

  8. Ignorable incompleteness Let Y= h(Z) be a many-to-one mapping. Z is complete; Y is incomplete If Zhas then Y has

  9. Tubular Neighborhood Model Near-model M Copas, Eguchi (2001)

  10. Mis-specification

  11. Near model Model Near-model

  12. Asymtotic bias

  13. From pure misspecification biased perturbed Unbiased perturbed h

  14. The worst case

  15. Nonignorable missingness The model assumes MCAR or MAR

  16. Potential confounder

  17. Problem in estimation of bias The nonignorable model gives the worst case if However is inestimable and untestable: The profile likelihood is flat at

  18. Heckman model for MNAR

  19. Sensitivity analysis The most sensitive model Estimating function of q with fixed e, w

  20. Scenarios A, B, C Inference from using fY Scenario A: Scenario C: Scenario B:

  21. Scenarios A and C Scenario A: Scenario C:

  22. Scenario B Conditional confidence interval

  23. Theorem

  24. Risk from passive smoke

  25. Passive smoke and lung cancer The estimated relative risk 1.24 with 95% confidence interval (1.13, 1.36) Square root rule 95% confidence interval (1.08, 1.41)

  26. Root-2-rule 30 25 20 study 15 10 5 1.24 0.5 0.3 1.5 2.0 3.0 4.0 5.0 10.0 1.0 Odds ratio

  27. Present and Future Does all this matter? Statistics ( missing data, response bias, censoring) Biostatistics (drop-outs, compliance) Epidemiology ( confounding, measurement error) Econometrics (identifiability, instruments) Psychometrics (publication bias, SEM) causality, counter-factuals, ...

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