Relaxation penalties and priors for plausible modeling of nonidentied bias sources

Statistical Science

Volumn 24, Issue 2, 2009, Pages 195-210

  Greenland, Sander ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bias; Biostatistics; Causality; Epidemiology; Measurement error; Misclassication; Observational studies; Odds ratio; Relative risk; Risk analysis; Risk assessment; Selection bias; Validation

Indexed keywords

EID: 76349126008     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-STS291     Document Type: Article

References (79)

1. BAKER, S. G. (1996). The analysis of categorical case-control data subject to nonignorable nonresponse. Biometrics 52 362-369.
2. BEDRICK, E.J.,CHRISTENSEN,R.and JOHNSON, W. (1996). A new perspective on generalized linear models. J. Amer. Statist. Assoc. 91 1450-1460.
3. BISHOP,Y.M.M.,FIENBERG,S.E.and HOLLAND,P.W. (1975). Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge, MA.
4. BOX, G. E. P. (1980). Sampling and Bayes inference in scientific modeling and robustness. J. Roy. Statist. Soc. Ser. A 143 383-430.
5. BROSS, I. D. J. (1967). Pertinency of an extraneous variable. Journal of Chronic Diseases 20 487-495.
6. BRUMBACK,B.A.,HERNAN,M.A.,HANEUSE,S.and ROBINS, J. M. (2004). Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures. Statist. Med. 23 749-767.
7. BULL,S.B.,LEWINGER,J.B.and LEE, S. S. F. (2007). Confidence intervals for multinomial logistic regression in sparse data. Statist. Med. 26 903-918.
8. CARROLL,R.J.,RUPPERT,D.,STEFANSKI,L.A.and CRAINICEANU, C. (2006). Measurement Error in Nonlinear Models, 2nd ed. Chapman and Hall, Boca Raton, FL.
9. COPAS, J. B. (1999). What works? Selectivity models and meta-analysis. J. R. Stat. Soc. Ser. B 162 95-109.
10. COX, D. R. (1975). A note on partially Bayes inference and the linear model. Biometrika 62 651-654.
11. DEELY,J.J.and LINDLEY, D. V. (1981). Bayes empirical Bayes. J. Amer. Statist. Assoc. 76 833-841.
12. DREWS,C.,KRAUS,J.F.and GREENLAND, S. (1990). Recall bias in a case-control study of sudden infant death syndrome. International Journal of Epidemiology 19 405-411.
13. EDDY,D.M.,HASSELBLAD,V.and SHACHTER, R. (1992). Meta-Analysis by the Confidence Profile Method. Academic Press, New York.
14. ESPELAND,M.andHUI, S. L. (1987). A general approach to analyzing epidemiologic data that contain misclassification errors. Biometrics 43 1001-1012.
15. FORTES,C.,MASTROENI,S.,MELCHI,F.,PILLA,M.A.,ANTONELLI,G.,CAMAIONI,D.,ALOTTO,M.andPASQUINI, P. (2008). A protective effect of the Mediterranean diet for cutaneous melanoma. International Journal of Epidemiology 37 1018-1029.
16. GELFAND,A.E.andSAHU, S. K. (1999). Identifiability, improper priors, and Gibbs sampling for generalized linear models. J. Amer. Statist. Assoc. 94 247-253.
17. GENELETTI,S.,RICEQUALITYSON,S.andBEST, N. (2009). Adjusting for selection bias in retrospective case-control studies. Biostatistics 10 17-31.
18. GOOD, I. J. (1983). Good Thinking. Univ. Minnesota Press, Minneapolis.
19. GOUBAR,A.,AEDES,A.E.,DEANGELIS,D.,MCGARRIGLE, C. A., MERCER,C.H.,TOOKEY,P.A.,FENTON,K.and GILL, O. N. (2008). Estimates of human immunodeficiency virus prevalence and proportion diagnosed based on Bayesian multiparameter synthesis of surveillance data (with discussion). J. Roy. Statist. Soc. Ser. A 171 541-580.
20. GREENLAND, S. (1992). A semi-Bayes approach to the analysis of correlated associations, with an application to an occupational cancer-mortality study. Statist. Med. 11 219-230.
21. GREENLAND, S. (2000). When should epidemiologic regressions use random coefficients? Biometrics 56 915-921.
22. GREENLAND, S. (2003a). The impact of prior distributions for uncontrolled confounding and response bias: A case study of the relation of wire codes and magnetic fields to childhood leukemia. J. Amer. Statist. Assoc. 98 47-54.
23. GREENLAND, S. (2003b). Generalized conjugate priors for Bayesian analysis of risk and survival regressions. Biometrics 59 92-99.
24. GREENLAND, S. (2003c). Quantifying biases in causal models: Classical confounding versus collider-stratification bias. Epidemiology 14 300-306.
25. GREENLAND, S. (2005a). Multiple-bias modeling for analysis of observational data (with discussion). J. Roy. Statist. Soc. Ser. A 168 267-308.
26. GREENLAND, S. (2005b). Contribution to discussion of Prentice, Pettinger, and Anderson. Biometrics 61 920-921.
27. GREENLAND, S. (2006). Bayesian perspectives for epidemiologic research. I. Foundations and basic methods (with comment and reply). International Journal of Epidemiology 35 765-778.
28. GREENLAND, S. (2007a). Bayesian perspectives for epidemiologic research. II. Regression analysis. International Journal of Epidemiology 36 195-202.
29. GREENLAND, S. (2007b). Prior data for non-normal priors. Statist. Med. 26 3578-3590.
30. GREENLAND, S. (2007c). Maximum-likelihood and closed-form estimators of epidemiologic measures under misclassification. J. Statist. Plann. Inference 138 528-538.
31. GREENLAND, S. (2009). Bayesian perspectives for epidemiologic research III. Bias analysis via missing data methods. International Journal of Epidemiology 38 1662-1673.
32. GREENLAND,S.,GAGO-DOMIGUEZ,M.and CASTELLAO,J.E. (2004). The value of risk-factor ("black-box") epidemiology (with discussion). Epidemiology 15 519-535.
33. GREENLAND,S.andKHEIFETS, L. (2006). Leukemia attributable to residential magnetic fields: Results from analyses allowing for study biases. Risk Analysis 26 471-482.
34. GREENLAND,S.andLASH, T. L. (2008). Bias analysis. In Modern Epidemiology, 3rd ed. (K. J. Rothman, S. Greenland and T. L. Lash, eds.) Chapter 19, 345-380. Lippincott-Williams-Wilkins, Philadelphia.
35. GREENLAND,S.andMALDONADO, G. (1994). The interpretation of multiplicative model parameters as standardized parameters. Statist. Med. 13 989-999.
36. GUSTAFSON, P. (2003). Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments. Chapman and Hall/CRC Press, Boca Raton.
37. GUSTAFSON, P. (2005). On model expansion, model contraction, identifiability, and prior information: Two illustrative scenarios involving mismeasured variables (with discussion). Statist. Sci. 20 111-140.
38. GUSTAFSON,P.andGREENLAND, S. (2006). The performance of random coefficient regression in accounting for residual confounding. Biometrics 62 760-768.
39. GUSTAFSON,P.andGREENLAND, S. (2010). Interval estimation for messy observational data. To appear.
40. GUSTAFSON.P.,LE,N.D.andSASKIN, R. (2001). Case-control analysis with partial knowledge of exposure misclassification probabilities. Biometrics 57 598-609.
41. HASTIE,T.andTIBSHIRANI, R. (1990). Generalized Additive Models. Chapman and Hall, New York.
42. HASTIE,T.,TIBSHIRANI,R.andFRIEDMAN, J. (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York.
43. HIGGINS,J.P.T.andSPIEGELHALTER, D. J. (2002). Being skeptical about meta-analyses: A Bayesian perspective on magnesium trials in myocardial infarction. International Journal of Epidemiology 31 96-104, appendix.
44. HUI,S.L.andWALTER, S. D. (1980). Estimating the error rates of diagnostic tests. Biometrics 36 167-171.
45. JOHNSON,W.O.,GASTWIRTH,J.L.andPEARSON,L.M. (2001). Screening without a " Gold Standard" : The Hui-Walter Paradigm revisited. American Journal of Epidemiology 153 921-924.
46. JONES, M. C. (2004). Families of distributions arising from distributions of order statistics. Test 13 1-44.
47. JOSEPH,L.,GYORKOS,T.W.andCOUPAL, L. (1995). Bayesian estimation of disease prevalence and parameters for diagnostic tests in the absence of a gold standard. American Journal of Epidemiology 141 263-272.
48. KADANE, J. B. (1993). Subjective Bayesian analysis for surveys with missing data. The Statistician 42 415-426. Erratum (1996): The Statistician 45 539.
49. KRAUS,J.F.,GREENLAND,S.andBULTERYS, M. G. (1989). Risk factors for sudden infant death syndrome in the U.S. Collaborative Perinatal Project. International Journal of Epidemiology 18 113-120.
50. LASH,T.L.andFINK, A. K. (2003). Semi-automated sensitivity analysis to assess systematic errors in observational epidemiologic data. Epidemiology 14 451-458.
51. LAWLOR,D.A.,DAVEY SMITH,G.,BRUCKDORFER,K.R., KUNDU,D.andEBRAHIM, S. (2004). Those confounded vitamins: What can we learn from the differences between observational versus randomized trial evidence? Lancet 363 1724-1727.
52. LEAMER, E. E. (1974). False models and post-data model construction. J. Amer. Statist. Assoc. 69 122-131.
53. LEONARD,T.and HSU, J. S. J. (1999). Bayesian Methods. Cambridge University Press, Cambridge.
54. LITTLE,R.J.A.andRUBIN, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley, New York.
55. LYLES, R. H. (2002). A note on estimating crude odds ratios in case-control studies with differentially misclassified exposure. Biometrics 58 1034-1037.
56. MALDONADO, G. (2008). Adjusting a relative-risk estimate for study imperfections. Journal of Epidemiology and Community Health 62 655-663.
57. MCCANDLESS,L.C.,GUSTAFSON,P.andLEVY, A. (2007). Bayesian sensitivity analysis for unmeasured confounding in observational studies. Statist. Med. 26 2331-2347.
58. MCLACHLAN,G.J.andKRISHNAN, T. (1997). The EM Algorithm and Extensions. Wiley, New York.
59. MESSER,K.andNATARAJAN, L. (2008). Maximum likelihood, multiple imputation and regression calibration for measurement error adjustment. Statist. Med. 27 6332-6350.
60. MOLENBERGHS,G.,KENWARD,M.G.andGOETGHEBEUR,E. (2001). Sensitivity analysis for incomplete contingency tables. Appl. Statist. 50 15-29.
61. MOLITOR,J.,JACKSON,C.,BEST,N.B.andRICEQUALITYSON, S. (2008). Using Bayesian graphical models to model biases in observational studies and to combine multiple data sources: Application to low birthweight and water disinfection by-products. J. Roy. Statist. Soc. Ser. A 172 615-638.
62. NEATH,A.A.andSAMANIEGO, F. J. (1997). On the efficacy of Bayesian inference for nonidentifiable models. Amer. Statist. 51 225-232.
63. PHILLIPS, C. V. (2003). Quantifying and reporting uncertainty from systematic errors. Epidemiology 14 459-466.
64. ROBINS,J.M.,ROTNITZKY,A.andSCHARFSTEIN,D.O. (2000). 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 (Minneapolis, MN, 1997). IMA Vol. Math. Appl. 116 1-94. Springer, New York.
65. ROSENBAUM, P. R. (1999). Choice as an alternative to control in observational studies (with discussion). Statist. Sci. 14 259-304.
66. ROSENBAUM, P. R. (2002). Observational Studies, 2nd ed. Springer, New York.
67. SAMANIEGO,F.J.andNEATH, A. A. (1996). How to be a better Bayesian. J. Amer. Statist. Assoc. 91 733-742.
68. SCHARFSTEIN,D.O.,ROTNITSKY,A.andROBINS,J.M. (1999). Adjusting for nonignorable drop-out using semiparametric nonresponse models. J. Amer. Statist. Assoc. 94 1096-1120.
69. SCHARFSTEIN,D.O.,DANIELS,M.J.andROBINS,J.M. (2003). Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes. Biostatistics 4 495-512.
70. SMALL,D.R.andROSENBAUM, P. R. (2009). Error-free milestones in error-prone measurements. Ann. Appl. Statist. To appear.
71. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. B 58 267-288.
72. TITTERINGTON, D. M. (1985). Common structure of smoothing techniques in statistics. Internat. Statist. Rev. 53 141-170.
73. TURNER,R.M.,SPIEGELHALTER,D.J.,SMITH,G.C.S.and THOMPSON, S. G. (2009). Bias modeling in evidence synthesis. J. Roy. Statist. Soc. Ser. A 172 21-47.
74. VANSTEELANDT,S.,GOETGHEBEUR,E.,KENWARD,M.G.and MOLENBERGHS, G. (2006). Ignorance and uncertainty regions as inferential tools in a sensitivity analysis. Statist. Sinica 16 953-980.
75. WALKER, A. M. (1982). Anamorphic analysis: Sampling and estimation for covariate effects when both exposure and disease are known. Biometrics 38 1025-1032.
76. WELTON,N.J.,ADES,A.E.,CARLIN,J.B.,ALTMAN,D.G. and STERNE, J. B. (2009). Models for potentially biased evidence in meta-analysis using empirically based priors. J. Roy. Statist. Soc. Ser. A 172 119-136.
77. WERLER,M.M.,POBER,B.R.,NELSON,K.andHOLMES, L. B. (1989). Reporting accuracy among mothers of malformed and nonmalformed infants. American Journal of Epidemiology 129 415-421.
78. WHITE, J. E. (1982). A two-stage design for the study of the relationship between a rare exposure and a rare disease. American Journal of Epidemiology 115 119-128.
79. YANAGAWA, T. (1984). Case-control studies: Assessing the effect of a confounding factor. Biometrika 71 191-194.