Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

doi:10.1177/0962280215596550

. 2017 Oct;26(5):2257-2269.

doi: 10.1177/0962280215596550. Epub 2015 Aug 11.

Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

Kevin A Rader^{1

2}, Stuart R Lipsitz³, Garrett M Fitzmaurice⁴, David P Harrington^{1

2}, Michael Parzen², Debajyoti Sinha⁵

Affiliations

¹ 1 Harvard T H Chan School of Public Health, Harvard University, Boston, MA, USA.
² 4 Statistics Department, Harvard University, Cambridge, MA, USA.
³ 2 Brigham and Women's Hospital, Boston, MA, USA.
⁴ 3 Harvard Medical School, Boston, MA, USA.
⁵ 5 Florida State University, Tallahassee, FL, USA.

PMID: 26265769
PMCID: PMC5799008
DOI: 10.1177/0962280215596550

Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

Kevin A Rader et al. Stat Methods Med Res. 2017 Oct.

. 2017 Oct;26(5):2257-2269.

doi: 10.1177/0962280215596550. Epub 2015 Aug 11.

Authors

Kevin A Rader^{1

2}, Stuart R Lipsitz³, Garrett M Fitzmaurice⁴, David P Harrington^{1

2}, Michael Parzen², Debajyoti Sinha⁵

Affiliations

¹ 1 Harvard T H Chan School of Public Health, Harvard University, Boston, MA, USA.
² 4 Statistics Department, Harvard University, Cambridge, MA, USA.
³ 2 Brigham and Women's Hospital, Boston, MA, USA.
⁴ 3 Harvard Medical School, Boston, MA, USA.
⁵ 5 Florida State University, Tallahassee, FL, USA.

PMID: 26265769
PMCID: PMC5799008
DOI: 10.1177/0962280215596550

Abstract

For complex surveys with a binary outcome, logistic regression is widely used to model the outcome as a function of covariates. Complex survey sampling designs are typically stratified cluster samples, but consistent and asymptotically unbiased estimates of the logistic regression parameters can be obtained using weighted estimating equations (WEEs) under the naive assumption that subjects within a cluster are independent. Despite the relatively large samples typical of many complex surveys, with rare outcomes, many interaction terms, or analysis of subgroups, the logistic regression parameters estimates from WEE can be markedly biased, just as with independent samples. In this paper, we propose bias-corrected WEEs for complex survey data. The proposed method is motivated by a study of postoperative complications in laparoscopic cystectomy, using data from the 2009 United States' Nationwide Inpatient Sample complex survey of hospitals.

Keywords: Binary responses; bladder cancer; population survey; stratified cluster sampling; weighted estimating equations.

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References

1. Johnson CL, Dohrmann SM, Burt VL, Mohadjer LK. National Health and Nutrition Examination Survey: Sample design, 2011–2014. National Center for Health Statistics. Vital and Health Statistics Series. 2014;2(168) - PubMed
1. Albert A, Anderson JA. On the existence of maximum likelihood estimates in logistic regression models. Biometrika. 1984;71:1–10.
1. Box MJ. Bias in nonlinear estimation. Journal of the Royal Statistical Society Series B (Methodology) 1971;33:171–201.
1. Firth D. Bias reduction of maximum likelihood estimates. Biometrika. 1993;80:27–38.
1. Kosmidis I, Firth D. Bias reduction in exponential family nonlinear models. Biometrika. 2009;96:793–804.

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[1] Johnson CL, Dohrmann SM, Burt VL, Mohadjer LK. National Health and Nutrition Examination Survey: Sample design, 2011–2014. National Center for Health Statistics. Vital and Health Statistics Series. 2014;2(168) - PubMed

[2] Johnson CL, Dohrmann SM, Burt VL, Mohadjer LK. National Health and Nutrition Examination Survey: Sample design, 2011–2014. National Center for Health Statistics. Vital and Health Statistics Series. 2014;2(168) - PubMed

[3] Albert A, Anderson JA. On the existence of maximum likelihood estimates in logistic regression models. Biometrika. 1984;71:1–10.

[4] Albert A, Anderson JA. On the existence of maximum likelihood estimates in logistic regression models. Biometrika. 1984;71:1–10.

[5] Box MJ. Bias in nonlinear estimation. Journal of the Royal Statistical Society Series B (Methodology) 1971;33:171–201.

[6] Box MJ. Bias in nonlinear estimation. Journal of the Royal Statistical Society Series B (Methodology) 1971;33:171–201.

[7] Firth D. Bias reduction of maximum likelihood estimates. Biometrika. 1993;80:27–38.

[8] Firth D. Bias reduction of maximum likelihood estimates. Biometrika. 1993;80:27–38.

[9] Kosmidis I, Firth D. Bias reduction in exponential family nonlinear models. Biometrika. 2009;96:793–804.

[10] Kosmidis I, Firth D. Bias reduction in exponential family nonlinear models. Biometrika. 2009;96:793–804.

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Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

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Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

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