Skip to main content
SpringerLink
Log in

Analysis of Repeated Measures and Longitudinal Data in Health Services Research

  • Living reference work entry
  • First Online:
Methods in Health Services Research

Part of the book series: Health Services Research ((HEALTHSR))

Abstract

This chapter reviews statistical methods for the analysis of longitudinal data that are commonly found in health services research. The chapter begins by discussing issues inherent in longitudinal data and provides historical background on early methods that were used to analyze data of this type. Next, mixed-effects regression models (MRMs) and covariance-pattern models (CPMs) for longitudinal data are introduced with a focus on linear models for normally distributed outcomes. As an illustration of the use of these methods in practice, MRMs and CPMs are applied to data from the Women Entering Care (WECare) study, a longitudinal depression treatment study. Finally, extensions and alternatives to these models are briefly described. Key phrases: mixed-effects models; random-effects models; covariance-pattern models; effect sizes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  • Berkhof J, Snijders TAB. Variance component testing in multilevel models. J Educ Behav Stat. 2001;26:133–52.

    Article  Google Scholar 

  • Bock RD. Multivariate statistical methods in behavioral research. New York: McGraw-Hill; 1975.

    Google Scholar 

  • Bock RD. Within-subject experimentation in psychiatric research. In: Gibbons RD, Dysken MW, editors. Statistical and methodological advances in psychiatric research. New York: Spectrum; 1983a. p. 59–90.

    Google Scholar 

  • Bock RD. The discrete Bayesian. In: Wainer H, Messick S, editors. Modern advances in psychometric research. Hillsdale: Erlbaum; 1983b. p. 103–15.

    Google Scholar 

  • Bock RD. Measurement of human variation: a two stage model. In: Bock RD, editor. Multilevel analysis of educational data. New York: Academic; 1989.

    Google Scholar 

  • Bryk AS, Raudenbush SW. Hierarchical linear models: applications and data analysis methods. Newbury Park: Sage; 1992.

    Google Scholar 

  • Chi EM, Reinsel GC. Models for longitudinal data with random effects and AR(1) errors. J Am Stat Soc. 1989;84:452–9.

    Article  Google Scholar 

  • Conaway MR. Analysis of repeated categorical measurements with conditional likelihood methods. J Am Stat Assoc. 1989;84:53–61.

    Article  Google Scholar 

  • Daniels MJ, Hogan JW. Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout. Biometrics. 2000;56:1241–8.

    Article  CAS  PubMed  Google Scholar 

  • Daniels MJ, Hogan JW. Missing data in longitudinal studies: strategies for Bayesian modeling and sensitivity analysis. New York: Chapman & Hall/CRC; 2008.

    Google Scholar 

  • de Leeuw J, Kreft I. Random coefficient models for multilevel analysis. J Educ Stat. 1986;11:57–85.

    Google Scholar 

  • Demirtas H, Schafer JL. On the performance of random-coefficient pattern-mixture models for nonignorable dropout. Stat Med. 2003;22:2553–75.

    Article  PubMed  Google Scholar 

  • Dempster AP, Rubin DB, Tsutakawa RK. Estimation in covariance component models. J Am Stat Soc. 1981;76:341–53.

    Article  Google Scholar 

  • Diggle PJ, Heagerty P, Liang K-Y, Zeger SL. Analysis of longitudinal data. 2nd ed. New York: Oxford University Press; 2002.

    Google Scholar 

  • Fitzmaurice GM, Laird NM, Ware JH. Applied longitudinal analysis. 2nd ed. Hoboken: Wiley; 2012.

    Google Scholar 

  • Gibbons RD. Trend in correlated proportions. PhD thesis, University of Chicago, Department of Psychology, 1981.

    Google Scholar 

  • Gibbons RD, Bock RD. Trend in correlated proportions. Psychometrika. 1987;52:113–24.

    Article  Google Scholar 

  • Gibbons RD, Hedeker D, Waternaux CM, Davis JM. Random regression models: a comprehensive approach to the analysis of longitudinal psychiatric data. Psychopharmacol Bull. 1988;24:438–43.

    CAS  PubMed  Google Scholar 

  • Goldstein H. Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika. 1986;73:43–56.

    Article  Google Scholar 

  • Goldstein H. Nonlinear multilevel models, with an application to discrete response data. Biometrika. 1991;78:45–51.

    Article  Google Scholar 

  • Goldstein H. Multilevel statistical models. 4th ed. Hoboken: Wiley; 2011.

    Google Scholar 

  • Grady JJ, Helms RW. Model selection techniques for the covariance matrix for incomplete longitudinal data. Stat Med. 1995;14:1397–416.

    Article  CAS  PubMed  Google Scholar 

  • Guo W, Ratcliffe SJ, Ten Have TR. A random pattern-mixture model for longitudinal data with dropouts. J Am Stat Assoc. 2004;99:929–37.

    Article  Google Scholar 

  • Hardin JW, Hilbe JM. Generalized estimating equations. 2nd ed. New York: Chapman and Hall; 2012.

    Google Scholar 

  • Hedeker D. Random regression models with autocorrelated errors. PhD thesis, University of Chicago, Department of Psychology, 1989.

    Google Scholar 

  • Hedeker D, Gibbons RD. Longitudinal data analysis. New York: Wiley; 2006.

    Google Scholar 

  • Hui SL, Berger JO. Empirical Bayes estimation of rates in longitudinal studies. J Am Stat Assoc. 1983;78:753–9.

    Article  Google Scholar 

  • Ibrahim J, Molenberghs G. Missing data methods in longitudinal studies: a review (with discussion). TEST. 2009;18:1–43.

    Article  PubMed  PubMed Central  Google Scholar 

  • Kaplan D, George R. Evaluating latent growth models through ex post simulation. J Educ Behav Stat. 1998;23:216–35.

    Article  Google Scholar 

  • Kenward MG, Molenberghs G. Parametric models for incomplete continuous and categorical longitudinal data. Stat Methods Med Res. 1999;8(1):51–83.

    Article  CAS  PubMed  Google Scholar 

  • Laird NM. Missing data in longitudinal studies. Stat Med. 1988;7:305–15.

    Article  CAS  PubMed  Google Scholar 

  • Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982;38:963–74.

    Article  CAS  PubMed  Google Scholar 

  • Liang K-Y, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika. 1986;73:13–22.

    Article  Google Scholar 

  • Little RJA. Modeling the drop-out mechanism in repeated-measures studies. J Am Stat Assoc. 1995;90:1112–21.

    Article  Google Scholar 

  • Little RJA, Rubin DB. Statistical analysis with missing data. 2nd ed. New York: Wiley; 2002.

    Google Scholar 

  • Longford NT. A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika. 1987;74:817–27.

    Article  Google Scholar 

  • Longford NT. Random coefficient models. New York: Oxford University Press; 1993.

    Google Scholar 

  • Miranda J, Chung JY, Green BL, Krupnick J, Siddique J, Revicki DA, Belin T. Treating depression in predominantly low-income young minority women. J Am Med Assoc. 2003;290:57–65.

    Article  Google Scholar 

  • Miranda J, Chung JY, Green BL, Krupnick J, Siddique J, Revicki DA. One year outcomes of treating depression in predominantly low-income young minority women. J Clin Consult Psychol. 2006;74:99–111.

    Article  Google Scholar 

  • Muth’en BO. Latent variable analysis: growth mixture modeling and related techniques for longitudinal data. In: Kaplan D, editor. Handbook of quantitative methodology for the social sciences. Newbury Park: Sage; 2004.

    Google Scholar 

  • Muth’en B, Shedden K. Finite mixture modeling with mixture outcomes using the em algorithm. Biometrics. 1999;55:463–9.

    Article  Google Scholar 

  • Muth’en B, Brown CH, Masyn K, Jo B, Khoo ST, Yang CC, Wang CP, Kellam SG, Carlin JB, Liao J. General growth mixture modeling for randomized preventive interventions. Biostatistics. 2002;3(4):459–75.

    Article  Google Scholar 

  • Muth’en BO, Brown CH, Leuchter A, Hunter A. General approaches to analysis of course: applying growth mixture modeling to randomized trials of depression medication. In: Shrout PE, editor. Causality and psychopathology: finding the determinants of disorders and their cures. Washington, DC: American Psychiatric Publishing; 2009. Forthcoming.

    Google Scholar 

  • Neuhaus JM, Kalbfleisch JD, Hauck WW. A comparison of cluster-specific and population-averaged approaches for analyzing correlated binary data. Int Stat Rev. 1991;59:25–35.

    Article  Google Scholar 

  • Potthoff RF, Roy SN. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika. 1964;51:313–6.

    Article  Google Scholar 

  • Raudenbush SW, Bryk AS. A hierarchical model for studying school effects. Sociol Educ. 1986;59:1–17.

    Article  Google Scholar 

  • Raudenbush SW, Bryk AS. Hierarchical linear models. 2nd ed. Thousand Oaks: Sage; 2002.

    Google Scholar 

  • Rubin DB. Inference and missing data. Biometrika. 1976;63:581–92.

    Article  Google Scholar 

  • Siddique J, Brown CH, Hedeker D, Duan N, Gibbons RD, Miranda J, Lavori PW. Missing data in longitudinal trials–part B, analytic issues. Psychiatr Ann. 2008;38(12):793–801.

    Article  PubMed  PubMed Central  Google Scholar 

  • Siddique J, Chung JY, Brown CH, Miranda J. Comparative effectiveness of medication versus cognitive behavioral therapy in a randomized controlled trial of low-income young minority women with depression. J Consult Clin Psychol. 2012;80:995–1006.

    Article  PubMed  PubMed Central  Google Scholar 

  • Singer JD, Willett JB. Applied longitudinal data analysis. New York: Oxford University Press; 2003.

    Book  Google Scholar 

  • Stiratelli R, Laird NM, Ware JH. Random-effects models for serial observations with binary response. Biometrics. 1984;40:961–71.

    Article  CAS  PubMed  Google Scholar 

  • Strenio JF, Weisberg HI, Bryk AS. Empirical Bayes estimation of individual growth curve parameters and their relationship to covariates. Biometrics. 1983;39:71–86.

    Article  CAS  PubMed  Google Scholar 

  • Verbeke G, Molenberghs G. Linear mixed models for longitudinal data. New York: Springer; 2000.

    Google Scholar 

  • Weiss RE. Modeling longitudinal data. New York: Springer; 2005.

    Google Scholar 

  • Wolfinger RD. Covariance structure selection in general mixed models. Commun Stat Simul Comput. 1993;22:1079–106.

    Article  Google Scholar 

  • Wong GY, Mason WM. The hierarchical logistic regression model for multilevel analysis. J Am Stat Assoc. 1985;80:513–24.

    Article  Google Scholar 

  • Xu W, Hedeker D. A random-effects models for classifying treatment response in longitudinal clinical trials. J Biopharm Stat. 2002;11:253–73.

    Article  Google Scholar 

  • Zeger SL, Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics. 1986;42:121–30.

    Article  CAS  PubMed  Google Scholar 

  • Zeger SL, Liang KY, Albert PS. Models for longitudinal data: a generalized estimating equation approach. Biometrics. 1988;44:1049–60.

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

The authors wish to thank Jeanne Miranda for use of the WECare data. Dr. Siddique’s work was supported by grant K07 CA154862-01 from the National Cancer Institute and R03 HS018815-01 from the Agency for Healthcare Research and Quality. Dr. Hedeker’s work was supported by Award Number P01 CA098262 from the National Cancer Institute. Dr. Gibbons’ work was supported by R01 MH8012201 from the National Institute of Mental Health. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute, Agency for Healthcare Research and Quality, or the National Institutes of Health.

Author information

Authors and Affiliations

  1. Department of Preventive Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL, USA

    Juned Siddique

  2. Department of Public Health Sciences, University of Chicago, 5841 S. Maryland Avenue, MC 2000, Chicago, IL, 60637, USA

    Donald Hedeker

  3. Departments of Medicine and Public Health Sciences, University of Chicago, 5841 S. Maryland Avenue, MC 2007, Chicago, IL, 60637, USA

    Robert D. Gibbons

Authors
  1. Juned Siddique
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donald Hedeker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert D. Gibbons
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juned Siddique .

Editor information

Editors and Affiliations

  1. University of British Columbia Dept. Health Care & Epidemiology, Vancouver, British Columbia, Canada

    Boris Sobolev

  2. Center for Statistical Sciences, Brown University Center for Statistical Sciences, PROVIDENCE, Rhode Island, USA

    Constantine Gatsonis

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this entry

Cite this entry

Siddique, J., Hedeker, D., Gibbons, R.D. (2017). Analysis of Repeated Measures and Longitudinal Data in Health Services Research. In: Sobolev, B., Gatsonis, C. (eds) Methods in Health Services Research. Health Services Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4939-6704-9_1-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-6704-9_1-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4939-6704-9

  • Online ISBN: 978-1-4939-6704-9

  • eBook Packages: Springer Reference MedicineReference Module Medicine

Publish with us

Policies and ethics

Search

Navigation