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Intermediate and advanced topics in multilevel logistic regression analysis
Open accessAbstract
Multilevel data occur frequently in health services, population and public health, and epidemiologic research. In such research, binary outcomes are common. Multilevel logistic regression models allow one to account for the clustering of subjects within clusters of higher-level units when estimating the effect of subject and cluster characteristics on subject outcomes. A search of the PubMed database demonstrated that the use of multilevel or hierarchical regression models is increasing rapidly. However, our impression is that many analysts simply use multilevel regression models to account for the nuisance of within-cluster homogeneity that is induced by clustering. In this article, we describe a suite of analyses that can complement the fitting of multilevel logistic regression models. These ancillary analyses permit analysts to estimate the marginal or population-average effect of covariates measured at the subject and cluster level, in contrast to the within-cluster or cluster-specific effects arising from the original multilevel logistic regression model. We describe the interval odds ratio and the proportion of opposed odds ratios, which are summary measures of effect for cluster-level covariates. We describe the variance partition coefficient and the median odds ratio which are measures of components of variance and heterogeneity in outcomes. These measures allow one to quantify the magnitude of the general contextual effect. We describe an R2 measure that allows analysts to quantify the proportion of variation explained by different multilevel logistic regression models. We illustrate the application and interpretation of these measures by analyzing mortality in patients hospitalized with a diagnosis of acute myocardial infarction. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.
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Cites
Hierarchical Linear Models: Applications and Data Analysis Methods.
Longford, N. T., Bryk, A. S., & Raudenbush, S. W. (1993) · Contemporary Sociology · doi:10.2307/2075823 · Cited by 18,724
Hierarchical Linear Models: Applications and Data Analysis Methods
Davidian, M. (2003) · Journal of the American Statistical Association · doi:10.1198/jasa.2003.s288 · Cited by 13,723
Data Analysis Using Regression and Multilevel/Hierarchical Models
Gelman, A., & Hill, J. (2006) · doi:10.1017/cbo9780511790942 · Cited by 13,597
Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence
Singer, J. D., & Willett, J. B. (2003) · doi:10.1093/acprof:oso/9780195152968.001.0001 · Cited by 10,647
Multilevel analysis : an introduction to basic and advanced multilevel modeling
Snijders, T. A. B., & Bosker, R. (1999) · Cited by 6,832
Hospital Volume and Surgical Mortality in the United States
Birkmeyer, J. D., Siewers, A. E., Finlayson, E. V. A., Stukel, T. A., Lucas, F. L., Batista, I., Welch, H. G., & Wennberg, D. E. (2002) · New England Journal of Medicine · doi:10.1056/nejmsa012337 · Cited by 4,999
(2006) · Technometrics · doi:10.1198/tech.2006.s417 · Cited by 4,950
Models for Longitudinal Data: A Generalized Estimating Equation Approach
Zeger, S. L., Liang, K.-Y., & Albert, P. S. (1988) · Biometrics · doi:10.2307/2531734 · Cited by 4,505
Hox, J., Moerbeek, M., & van de Schoot, R. (2010) · doi:10.4324/9780203852279 · Cited by 3,469
Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating
Steyerberg, E. W. (2019) · Statistics for Biology and Health · doi:10.1007/978-3-030-16399-0 · Cited by 3,281
Introducing Multilevel Modeling
Kreft, I., & de Leeuw, J. (1998) · doi:10.4135/9781849209366 · Cited by 2,997
Merlo, J., Chaix, B., Ohlsson, H., Beckman, A., Johnell, K., Hjerpe, P., Råstam, L., & Larsen, K. (2006) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2004.029454 · Cited by 1,673
Self-citationGoldstein, H. (2010) · Wiley Series in Probability and Statistics · doi:10.1002/9780470973394 · Cited by 1,568
Steyerberg, E. W. (2009) · Statistics for Biology and Health · doi:10.1007/978-0-387-77244-8 · Cited by 1,491
Design and Analysis of Cluster Randomization Trials in Health Research
DONNER, A. P., & Klar, N. S. (2000) · Cited by 1,236
Hox, J. J. (1995) · Utrecht University Repository (Utrecht University) · Cited by 1,179
Larsen, K. (2005) · American Journal of Epidemiology · doi:10.1093/aje/kwi017 · Cited by 956
Partitioning Variation in Multilevel Models
Goldstein, H., Browne, W., & Rasbash, J. (2002) · Understanding Statistics · doi:10.1207/s15328031us0104_02 · Cited by 874
Handbook of Advanced Multilevel Analysis
(2011) · Routledge eBooks · doi:10.4324/9780203848852 · Cited by 743
Applied Multilevel Analysis: A Practical Guide for Medical Researchers
Twisk, J. W. R. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610806 · Cited by 685
Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2004.023473 · Cited by 681
Self-citationNeuhaus, J. M., Kalbfleisch, J. D., & Hauck, W. W. (1991) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1403572 · Cited by 543
Between- and Within-Cluster Covariate Effects in the Analysis of Clustered Data
Neuhaus, J. M., & Kalbfleisch, J. D. (1998) · Biometrics · doi:10.2307/3109770 · Cited by 525
A Tutorial on Multilevel Survival Analysis: Methods, Models and Applications
Austin, P. C. (2017) · International Statistical Review · doi:10.1111/insr.12214 · Cited by 483
Self-citationAn Assessment of Estimation Procedures for Multilevel Models with Binary Responses
Rodriguez, G., & Goldman, N. (1995) · Journal of the Royal Statistical Society. Series A (Statistics in Society) · doi:10.2307/2983404 · Cited by 476
Interpreting Parameters in the Logistic Regression Model with Random Effects
Larsen, K., Petersen, J. H., Budtz‐Jørgensen, E., & Endahl, L. (2000) · Biometrics · doi:10.1111/j.0006-341x.2000.00909.x · Cited by 473
Design and Analysis of Cluster Randomization Trials in Health Research
Davis, W. W. (2001) · Journal of the American Statistical Association · doi:10.1198/jasa.2001.s433 · Cited by 442
Variance Partitioning in Multilevel Logistic Models that Exhibit Overdispersion
Browne, W. J., Subramanian, S. V., Jones, K., & Goldstein, H. (2005) · Journal of the Royal Statistical Society Series A: Statistics in Society · doi:10.1111/j.1467-985x.2004.00365.x · Cited by 420
Merlo, J., Yang, M., Chaix, B., Lynch, J., & Råstam, L. (2005) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2004.023929 · Cited by 373
Self-citationEXPLAINED VARIATION FOR LOGISTIC REGRESSION
MITTLBÖCK, M., & SCHEMPER, M. (1996) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19961015)15:19<1987::aid-sim318>3.0.co;2-9 · Cited by 334
Development and validation of the ontario acute myocardial infarction mortality prediction rules
Tu, J. V., Austin, P. C., Walld, R., Roos, L., Agras, J., & McDonald, K. M. (2001) · Journal of the American College of Cardiology · doi:10.1016/s0735-1097(01)01109-3 · Cited by 298
Self-citationMisspecified maximum likelihood estimates and generalised linear mixed models
Heagerty, P. J., & Kurland, B. F. (2001) · Biometrika · doi:10.1093/biomet/88.4.973 · Cited by 294
Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2004.028035 · Cited by 269
Self-citationMerlo, J. (2003) · Journal of Epidemiology and Community Health · doi:10.1136/jech.57.8.550 · Cited by 267
Self-citationMerlo, J., Wagner, P., Ghith, N., & Leckie, G. (2016) · PLOS ONE · doi:10.1371/journal.pone.0153778 · Cited by 230
Self-citationNeuhaus, J. M., & McCulloch, C. E. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2006.00570.x · Cited by 200
The effects of mixture distribution misspecification when fitting mixed-effects logistic models
NEUHAUS, J. M., HAUCK, W. W., & KALBFLEISCH, J. D. (1992) · Biometrika · doi:10.1093/biomet/79.4.755 · Cited by 189
Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter
McCulloch, C. E., & Neuhaus, J. M. (2011) · Statistical Science · doi:10.1214/11-sts361 · Cited by 183
Merlo, J., Ohlsson, H., Lynch, K. F., Chaix, B., & Subramanian, S. V. (2009) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2009.088310 · Cited by 158
Self-citationTemporal changes in the outcomes of acute myocardial infarction in Ontario, 1992-1996.
Tu, J. V., Naylor, C. D., & Austin, P. C. (1999) · Europe PMC (PubMed Central) · Cited by 142
Self-citationMerlo, J. (2014) · American Journal of Epidemiology · doi:10.1093/aje/kwu108 · Cited by 125
Self-citationAustin, P. C., Wagner, P., & Merlo, J. (2016) · Statistics in Medicine · doi:10.1002/sim.7188 · Cited by 107
Self-citationMerlo, J., Asplund, K., Lynch, J. W., Råstam, L., & Dobson, A. J. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh160 · Cited by 103
Self-citationChen, J. (2002) · Biostatistics · doi:10.1093/biostatistics/3.3.347 · Cited by 98
Merlo, J., Viciana, F., & Fariñas, D. R. (2012) · Social Science & Medicine · doi:10.1016/j.socscimed.2012.06.004 · Cited by 75
Self-citationA different kind of contextual effect: geographical clustering of cocaine incidence in the USA
Petronis, K. R., & Anthony, J. C. (2003) · Journal of Epidemiology & Community Health · doi:10.1136/jech.57.11.893 · Cited by 66
Estimation of covariate effects in generalized linear mixed models with informative cluster sizes
Neuhaus, J. M., & McCulloch, C. E. (2011) · Biometrika · doi:10.1093/biomet/asq066 · Cited by 53
Multilevel regression modelling to investigate variation in disease prevalence across locations
Weinmayr, G., Dreyhaupt, J., Jaensch, A., Forastiere, F., & Strachan, D. P. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw274 · Cited by 43
Ghith, N. M. M., Wagner, P., Frølich, A., & Merlo, J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0148187 · Cited by 37
Self-citationComputing measures of explained variation for logistic regression models
Mittlböck, M., & SCHEMPER, M. (1998) · Computer Methods and Programs in Biomedicine · doi:10.1016/s0169-2607(98)00061-3 · Cited by 36
Explained Variance in Multilevel Models
Roberts, J. K., Monaco, J. P., Stovall, H., & Foster, V. (2015) · Routledge eBooks · doi:10.4324/9780203848852.ch12 · Cited by 26
Li, J., Gray, B. R., & Bates, D. M. (2008) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610910802361366 · Cited by 13
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Multilevel geospatial analysis of factors associated with unskilled birth attendance in Ghana
Bediako, V. B., Boateng, E. N. K., Owusu, B. A., & Dickson, K. S. (2021) · PLOS ONE · doi:10.1371/journal.pone.0253603 · Cited by 24
Metadata
- Authors
- Austin, P. C., & Merlo, J.
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2017-05-23
- Volume
- 36
- Issue
- 20
- Pages
- 3257-3277
- ISSN
- 0277-6715 (ISSN-L)
- OpenAlex
- W2618058430
- Cited by
- 649
- References
- 52
- FWCI
- 28.84
- Type
- journal article
- Language
- en
- Open access
- hybrid
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