Using the bootstrap to improve estimation and confidence intervals for regression coefficients selected using backwards variable elimination
Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients a...
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| Published in | Statistics in medicine Vol. 27; no. 17; pp. 3286 - 3300 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
30.07.2008
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 |
| DOI | 10.1002/sim.3104 |
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| Abstract | Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non‐parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack. Copyright © 2007 John Wiley & Sons, Ltd. |
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| AbstractList | Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non-parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack. [PUBLICATION ABSTRACT] Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non‐parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack. Copyright © 2007 John Wiley & Sons, Ltd. Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non-parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack.Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non-parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack. Applied researchers frequently use automated model selection methods, such as backwards variable elimination, to develop parsimonious regression models. Statisticians have criticized the use of these methods for several reasons, amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates. We developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples. In a given bootstrap sample, predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero. Regression coefficients are averaged across the bootstrap samples, and non-parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient. We conducted a series of Monte Carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination. We demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination. We illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack. |
| Author | Austin, Peter C. |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/17940997$$D View this record in MEDLINE/PubMed |
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A bootstrap resampling procedure for model building: application to the Cox regression model. Statistics in Medicine 1992; 11:2093-2109. Koch CG, Khandwala F, Nussmeier N, Blackstone EH. Gender and outcomes after coronary artery bypass grafting: a propensity matched comparison. Journal of Thoracic and Cardiovascular Surgery 2003; 126:2032-2043. Miller AJ. Selection of subsets of regression variables. Journal of the Royal Statistical Society, Series A 1984; 147:389-425. Derkson S, Keselman HJ. Backward, forward and stepwise automated subset selection algorithms: frequency of obtaining authentic and noise variables. British Journal of Mathematical and Statistical Psychology 1992; 45:265-282. Murtaugh PA. Methods of variable selection in regression modeling. Communications in Statistics-Simulation and Computation 1998; 27:711-734. Steyerberg EW, Eijkemans MJC, Harrell Jr FE, Habbema JDF. 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Institute for Clinical Evaluative Sciences: Toronto, Ont., 2004. Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR. A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology 1996; 49:1373-1379. Shishehbor MH, Seshadri N, Aktas M, Acharya N, Gillinov AM, Blackstone EH, Houghtaling PL, Migrino RQ, Ghaffari S. Comparison of outcomes in patients undergoing coronary bypass of patent versus restenosed bare metal stented coronary arteries. American Journal of Cardiology 2005; 96:1416-1419. 1998; 27 1987; 14 1984; 147 2006; 151 2005 2004 1993 2002 1992; 11 2005; 24 1976; 32 2006; 82 2004; 77 1990; 44 2000; 19 2001 2004; 58 2002; 124 2006; 25 2004; 78 1991; 40 2004; 57 2005; 96 2003; 126 1996; 49 1992; 45 2007; 26 2006; 169 e_1_2_1_22_2 e_1_2_1_23_2 e_1_2_1_21_2 e_1_2_1_26_2 e_1_2_1_27_2 e_1_2_1_24_2 e_1_2_1_25_2 e_1_2_1_28_2 e_1_2_1_29_2 Tu JV (e_1_2_1_12_2) 2004 e_1_2_1_6_2 e_1_2_1_30_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_3_2 e_1_2_1_10_2 R Core Development Team (e_1_2_1_20_2) 2005 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_17_2 e_1_2_1_9_2 e_1_2_1_18_2 |
| References_xml | – reference: Shishehbor MH, Seshadri N, Aktas M, Acharya N, Gillinov AM, Blackstone EH, Houghtaling PL, Migrino RQ, Ghaffari S. Comparison of outcomes in patients undergoing coronary bypass of patent versus restenosed bare metal stented coronary arteries. American Journal of Cardiology 2005; 96:1416-1419. – reference: Rice TW, Khuntia D, Rybicki LA, Adelstein DJ, Vogelbaum MA, Mason DP, Murthy SC, Blackstone EH. Brain metastases from esophageal cancer: a phenomenon of adjuvant therapy? Annals of Thoracic Surgery 2006; 82(6):2042-2049, 2049, e1-e2. – reference: Koch CG, Khandwala F, Nussmeier N, Blackstone EH. Gender and outcomes after coronary artery bypass grafting: a propensity matched comparison. Journal of Thoracic and Cardiovascular Surgery 2003; 126:2032-2043. – reference: DeCamp MM, Blackstone EH, Naunheim KS, Krasna MJ, Wood DE, Meli YM, McKenna Jr RJ. NETT Research Group. Patient and surgical factors influencing air leak after lung volume reduction surgery: lessons learned from the National Emphysema Treatment Trial. Annals of Thoracic Surgery 2006; 82(1):197-206. – reference: Tu JV, Donovan LR, Lee DS, Austin PC, Ko DT, Wang JT, Newman AM. Quality of Cardiac Care in Ontario. Institute for Clinical Evaluative Sciences: Toronto, Ont., 2004. – reference: Steyerberg EW, Eijkemans MJC, Harrell Jr FE, Habbema JDF. Prognostic modeling with logistic regression analysis: a comparison of selection and estimation methods in small datasets. Statistics in Medicine 2000; 19:1059-1079. – reference: Hurvich CM, Tsai C-L. The impact of model selection on inference in linear regression. The American Statistician 1990; 44:214-217. – reference: Copas JB, Long T. Estimating the residual variance in orthogonal regression with variable selection. The Statistician 1991; 40:51-59. – reference: Austin PC, Tu JV. 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| SubjectTerms | automated variable selection backwards variable elimination bootstrap Bootstrap method Computer Simulation Confidence Intervals Data Interpretation, Statistical Estimating techniques Female Heart attacks Humans Logistic Models Male Medical statistics Monte Carlo Method Monte Carlo simulation Monte Carlo simulations Myocardial Infarction - therapy Quality of Health Care regression models Research Design |
| Title | Using the bootstrap to improve estimation and confidence intervals for regression coefficients selected using backwards variable elimination |
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