Variable selection and Bayesian model averaging in case-control studies
Covariate and confounder selection in case‐control studies is often carried out using a statistical variable selection method, such as a two‐step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertai...
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| Published in | Statistics in medicine Vol. 20; no. 21; pp. 3215 - 3230 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
15.11.2001
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 |
| DOI | 10.1002/sim.976 |
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| Abstract | Covariate and confounder selection in case‐control studies is often carried out using a statistical variable selection method, such as a two‐step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case‐control studies. This shows that p‐values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case‐control studies with 1000 subjects, of variables declared to be ‘significant’ with p‐values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case‐control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case‐control study of cervical cancer. Copyright © 2001 John Wiley & Sons, Ltd. |
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| AbstractList | Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case-control studies. This shows that p-values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case-control studies with 1000 subjects, of variables declared to be 'significant' with p-values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case-control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case-control study of cervical cancer.Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case-control studies. This shows that p-values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case-control studies with 1000 subjects, of variables declared to be 'significant' with p-values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case-control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case-control study of cervical cancer. Covariate and confounder selection in case‐control studies is often carried out using a statistical variable selection method, such as a two‐step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case‐control studies. This shows that p ‐values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case‐control studies with 1000 subjects, of variables declared to be ‘significant’ with p ‐values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case‐control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case‐control study of cervical cancer. Copyright © 2001 John Wiley & Sons, Ltd. Covariate and confounder selection in case‐control studies is often carried out using a statistical variable selection method, such as a two‐step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case‐control studies. This shows that p‐values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case‐control studies with 1000 subjects, of variables declared to be ‘significant’ with p‐values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case‐control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case‐control study of cervical cancer. Copyright © 2001 John Wiley & Sons, Ltd. Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a stepwise method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so may underestimate uncertainty about relative risks. We report on a simulation study designed to be similar to actual case-control studies. This shows that p-values computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated case-control studies with 1000 subjects, of variables declared to be 'significant' with p-values between 0.01 and 0.05, only 49 per cent actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in case-control studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared in the context of a case-control study of cervical cancer. |
| Author | Richardson, Sylvia Viallefont, Valerie Raftery, Adrian E. |
| Author_xml | – sequence: 1 givenname: Valerie surname: Viallefont fullname: Viallefont, Valerie organization: INSERM-U. 170, 16 av P. Vaillant-Couturier, 94 807 Villejuif Cedex, France – sequence: 2 givenname: Adrian E. surname: Raftery fullname: Raftery, Adrian E. organization: Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322, U.S.A – sequence: 3 givenname: Sylvia surname: Richardson fullname: Richardson, Sylvia organization: INSERM-U. 170, 16 av P. Vaillant-Couturier, 94 807 Villejuif Cedex, France |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14097021$$DView record in Pascal Francis https://www.ncbi.nlm.nih.gov/pubmed/11746314$$D View this record in MEDLINE/PubMed |
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| Keywords | Bayes estimation Human Statistical analysis Average Uterine cervix Case control study Malignant tumor Epidemiology Female genital diseases Statistical method Risk factor Female Uterine cervix diseases |
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| References | Racine A, Grieve AP, Fluhler H, Smith AFM. Bayesian methods in practice: experiences in the pharmaceutical industry (with discussion). Applied Statistics 1986; 35:93-150. Madigan D, Raftery AE. Model selection and accounting for model uncertainty in graphical models using Occam's window. Journal of the American Statistical Association 1994; 89:1535-1546. Armitage P. Statistical Methods in Medical Research. Blackwell Scientific Publications: Oxford, UK, 1971. Berger JO, Delampady M. Testing precise hypotheses (with discussion). Statistical Science 1987; 3:317-352. Richardson S, Gerber M, Cénée S. The role of fat, animal protein and some vitamin consumption in breast cancer: a case-control study in southern France. International Journal of Cancer 1991; 48:1-9. Bernardo JM, Smith AFM. Bayesian Theory. Wiley: New York, 1994. Miller AJ. Subset Selection in Regression. Chapman and Hall: London, UK, 1990. Chatfield CC. Model uncertainty, data mining and statistical inference (with discussion). Journal of the Royal Statistical Society, Series A 1995; 158:419-466. Kleinbaum DG, Kupper LL, Morgenstern H. Epidemiologic ResearchPrinciples and Quantitative Methods. Lifetime Learning Publications: Belmont, CA, 1982. Breslow NE. Statistics in epidemiology: the case-control study. Journal of the American Statistical Association 1996; 91:14-28. Raftery AE. Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika 1996; 83:251-266. Draper D. Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society, Series B 1995; 57:45-98. Lee PM. Bayesian Statistics: An Introduction. Oxford University Press: Oxford, U.K., 1989. Volinsky CT, Madigan D, Raftery AE, Kronmal RA. Bayesian model averaging in proportional hazard models: predicting the risk of a stroke. Applied Statistics 1997; 46:443-448. Jeffreys H. Theory of Probability. 3rd edn. Oxford University Press: Oxford, U.K., 1961. Savitz DA, Tolo K-A, Poole C. Statistical significance testing in the American Journal of Epidemiology, 1970 -1990. American Journal of Epidemiology 1994; 139(10):1047-1052. Hosmer DW, Lemeshow S. Applied Logistic Regression. Wiley: New York, 1989. Leamer EE. Specification Searches: Ad Hoc Inference With Nonexperimental Data. Wiley: New York, 1978. Hoeting JA, Raftery AE, Madigan D. A method for simultaneous variable selection and outlier identification in linear regression. Journal of Computational Statistics 1995; 22:251-271. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis. Chapman and Hall: London, 1995. Mickey RM, Greenland S. The impact of confounder selection criteria on effect estimation. American Journal of Epidemiology 1989; 129(1):125-137. Rubin DB, Schenker N. Efficiently simulating the coverage properties of interval estimates. Applied Statistics 1986; 35:159-167. Raftery AE, Madigan D, Hoeting JA. Model selection and accounting for model uncertainty in linear regression models. Journal of the American Statistical Association 1997; 92:179-191. Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association 1995; 90:773-795. Breslow NE, Day NE. Statistical Methods in Cancer Research. Vol. 1: The Analysis of Case-control Studies. IARC scientific publication no. 32: Lyon, 1980. Peters RK, Thomas D, Hagan DG, Mack TM, Henderson BE. Risk factors for invasive cervical cancer among latinas and non-latinas in Los Angeles county. Journal of the National Cancer Institute 1986; 77(5):1063-1077. Rothman KJ, Greenland S. Modern Epidemiology. 2nd edn. Lippincott, Williams & Wilkins: Philadelphia, 1998. Freedman DA. A note on screening regression equations. American Statistician 1983; 37:152-155. 1987; 3 1994; 139 1995; 90 1986; 77 1995; 57 1986; 35 1997; 46 1994; 89 1998 1996 1995 1994 1995; 158 1971 1996; 91 1983; 37 1978 1989; 129 1997; 92 1991; 48 1990 1980; 1 1995; 22 1996; 83 1961 1982 1989 Raftery AE (e_1_2_1_26_2) 1996 Jeffreys H (e_1_2_1_29_2) 1961 e_1_2_1_23_2 e_1_2_1_20_2 Leamer EE (e_1_2_1_10_2) 1978 e_1_2_1_21_2 Savitz DA (e_1_2_1_6_2) 1994; 139 Volinsky CT (e_1_2_1_27_2) 1997; 46 Raftery AE (e_1_2_1_12_2) 1995 e_1_2_1_24_2 Lee PM (e_1_2_1_19_2) 1989 Hoeting JA (e_1_2_1_18_2) 1995; 22 e_1_2_1_28_2 Kleinbaum DG (e_1_2_1_30_2) 1982 Peters RK (e_1_2_1_9_2) 1986; 77 Armitage P (e_1_2_1_31_2) 1971 Raftery AE (e_1_2_1_22_2) 1995 Breslow NE (e_1_2_1_2_2) 1980 e_1_2_1_7_2 e_1_2_1_4_2 Rothman KJ (e_1_2_1_32_2) 1998 e_1_2_1_11_2 e_1_2_1_3_2 Richardson S (e_1_2_1_25_2) 1991; 48 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 Hosmer DW (e_1_2_1_5_2) 1989 e_1_2_1_8_2 e_1_2_1_17_2 |
| References_xml | – reference: Breslow NE, Day NE. Statistical Methods in Cancer Research. Vol. 1: The Analysis of Case-control Studies. IARC scientific publication no. 32: Lyon, 1980. – reference: Lee PM. Bayesian Statistics: An Introduction. Oxford University Press: Oxford, U.K., 1989. – reference: Volinsky CT, Madigan D, Raftery AE, Kronmal RA. Bayesian model averaging in proportional hazard models: predicting the risk of a stroke. Applied Statistics 1997; 46:443-448. – reference: Miller AJ. Subset Selection in Regression. Chapman and Hall: London, UK, 1990. – reference: Mickey RM, Greenland S. The impact of confounder selection criteria on effect estimation. American Journal of Epidemiology 1989; 129(1):125-137. – reference: Raftery AE. Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika 1996; 83:251-266. – reference: Richardson S, Gerber M, Cénée S. The role of fat, animal protein and some vitamin consumption in breast cancer: a case-control study in southern France. International Journal of Cancer 1991; 48:1-9. – reference: Leamer EE. Specification Searches: Ad Hoc Inference With Nonexperimental Data. Wiley: New York, 1978. – reference: Hoeting JA, Raftery AE, Madigan D. A method for simultaneous variable selection and outlier identification in linear regression. Journal of Computational Statistics 1995; 22:251-271. – reference: Berger JO, Delampady M. Testing precise hypotheses (with discussion). Statistical Science 1987; 3:317-352. – reference: Freedman DA. A note on screening regression equations. American Statistician 1983; 37:152-155. – reference: Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis. Chapman and Hall: London, 1995. – reference: Raftery AE, Madigan D, Hoeting JA. Model selection and accounting for model uncertainty in linear regression models. Journal of the American Statistical Association 1997; 92:179-191. – reference: Chatfield CC. Model uncertainty, data mining and statistical inference (with discussion). Journal of the Royal Statistical Society, Series A 1995; 158:419-466. – reference: Bernardo JM, Smith AFM. Bayesian Theory. Wiley: New York, 1994. – reference: Rubin DB, Schenker N. Efficiently simulating the coverage properties of interval estimates. Applied Statistics 1986; 35:159-167. – reference: Jeffreys H. Theory of Probability. 3rd edn. Oxford University Press: Oxford, U.K., 1961. – reference: Hosmer DW, Lemeshow S. Applied Logistic Regression. Wiley: New York, 1989. – reference: Draper D. Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society, Series B 1995; 57:45-98. – reference: Savitz DA, Tolo K-A, Poole C. Statistical significance testing in the American Journal of Epidemiology, 1970 -1990. American Journal of Epidemiology 1994; 139(10):1047-1052. – reference: Rothman KJ, Greenland S. Modern Epidemiology. 2nd edn. Lippincott, Williams & Wilkins: Philadelphia, 1998. – reference: Kleinbaum DG, Kupper LL, Morgenstern H. Epidemiologic ResearchPrinciples and Quantitative Methods. Lifetime Learning Publications: Belmont, CA, 1982. – reference: Armitage P. Statistical Methods in Medical Research. Blackwell Scientific Publications: Oxford, UK, 1971. – reference: Racine A, Grieve AP, Fluhler H, Smith AFM. Bayesian methods in practice: experiences in the pharmaceutical industry (with discussion). Applied Statistics 1986; 35:93-150. – reference: Madigan D, Raftery AE. Model selection and accounting for model uncertainty in graphical models using Occam's window. Journal of the American Statistical Association 1994; 89:1535-1546. – reference: Peters RK, Thomas D, Hagan DG, Mack TM, Henderson BE. Risk factors for invasive cervical cancer among latinas and non-latinas in Los Angeles county. Journal of the National Cancer Institute 1986; 77(5):1063-1077. – reference: Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association 1995; 90:773-795. – reference: Breslow NE. Statistics in epidemiology: the case-control study. Journal of the American Statistical Association 1996; 91:14-28. – volume: 46 start-page: 443 year: 1997 end-page: 448 article-title: Bayesian model averaging in proportional hazard models: predicting the risk of a stroke publication-title: Applied Statistics – start-page: 12 year: 1996 end-page: 353 – volume: 91 start-page: 14 year: 1996 end-page: 28 article-title: Statistics in epidemiology: the case‐control study publication-title: Journal of the American Statistical Association – volume: 1 year: 1980 – volume: 3 start-page: 317 year: 1987 end-page: 352 article-title: Testing precise hypotheses (with discussion) publication-title: Statistical Science – year: 1989 – volume: 90 start-page: 773 year: 1995 end-page: 795 article-title: Bayes factors publication-title: Journal of the American Statistical Association – year: 1971 – volume: 48 start-page: 1 year: 1991 end-page: 9 article-title: The role of fat, animal protein and some vitamin consumption in breast cancer: a case‐control 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– volume-title: Epidemiologic ResearchPrinciples and Quantitative Methods year: 1982 ident: e_1_2_1_30_2 – ident: e_1_2_1_3_2 doi: 10.1080/01621459.1996.10476660 – ident: e_1_2_1_21_2 doi: 10.1111/j.1574-6941.2001.tb00841.x – volume-title: Bayesian Statistics: An Introduction year: 1989 ident: e_1_2_1_19_2 – ident: e_1_2_1_4_2 doi: 10.1093/oxfordjournals.aje.a115101 – volume-title: Specification Searches: Ad Hoc Inference With Nonexperimental Data year: 1978 ident: e_1_2_1_10_2 – ident: e_1_2_1_16_2 doi: 10.2307/2983440 – ident: e_1_2_1_11_2 doi: 10.1080/01621459.1994.10476894 – ident: e_1_2_1_28_2 doi: 10.1214/ss/1177013238 – volume-title: Statistical Methods in Medical Research year: 1971 ident: e_1_2_1_31_2 – start-page: 323 volume-title: Bayesian Statistics 5 year: 1995 ident: e_1_2_1_22_2 – start-page: 12 volume-title: Bayesian Biostatistics year: 1996 ident: e_1_2_1_26_2 – ident: e_1_2_1_20_2 doi: 10.1002/9780470316870 – volume: 77 start-page: 1063 issue: 5 year: 1986 ident: 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| Snippet | Covariate and confounder selection in case‐control studies is often carried out using a statistical variable selection method, such as a two‐step method or a... Covariate and confounder selection in case-control studies is often carried out using a statistical variable selection method, such as a two-step method or a... |
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| SubjectTerms | Analysis of Variance Bayes Theorem Biological and medical sciences Biometry Case-Control Studies Female Female genital diseases Gynecology. Andrology. Obstetrics Humans Medical sciences Odds Ratio Risk Factors Tumors Uterine Cervical Neoplasms - epidemiology |
| Title | Variable selection and Bayesian model averaging in case-control studies |
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