Skip to main content
SpringerLink
Log in

Optimal Designs for Multilevel Studies

  • Chapter
Handbook of Multilevel Analysis

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Afshartous. Determination of sample size for multilevel model design. Unpublished manuscript, 1995.

    Google Scholar 

  2. A. C. Atkinson and A. N. Donev. Optimum Experimental Designs. Clarendon Press, Oxford, UK, 1996.

    Google Scholar 

  3. M. P. F. Berger and F. E. S. Tan. Robust designs for linear mixed effects models. Applied Statistics, 53:569–581, 2004.

    MATH  MathSciNet  Google Scholar 

  4. R. J. Bosker, T. A. B. Snijders, and H. Guldemond. PINT Estimating Standard Errors of Regression Coefficients in Hierarchical Linear Models for Power Calculations. User’s Manual Version 1.6. University of Twente, Enschede, The Netherlands, 1999.

    Google Scholar 

  5. W. G. Cochran. Planning and Analysis of Observational Studies. Wiley, New York, 1983.

    Google Scholar 

  6. J. Cohen. A power primer. Psychological Bulletin, 112:155–159, 1992.

    Article  Google Scholar 

  7. M. P. Cohen. Determining sample sizes for surveys with data analyzed by hierarchical linear models. Journal of Official Statistics, 14:267–275, 1998.

    Google Scholar 

  8. A. Donner. A review of inference procedures for the intraclass correlation coefficientin the one-way random effects model. International Statistical Review, 54:67–82, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Donner. Some aspects of the design and analysis of cluster randomization trials. Applied Statistics, 47:95–113, 1998.

    Google Scholar 

  10. A. Donner and N. Klar. Design and Analysis of Cluster Randomization Trials in Health Research. Edward Arnold, London, 2000.

    Google Scholar 

  11. H. A. Feldman and S. M. McKinlay. Cohort versus cross-sectional design in larage field trials: Precision, sample size, and a unifying model. Statistics in Medicine, 13:61–78, 1994.

    Article  Google Scholar 

  12. Z. Feng and J. E. Grizzle. Correlated binomial variates: Properties of estimator of intraclass correlation and its effect on sample size calculation. Statistics in Medicine, 11:1607–1614, 1992.

    Article  Google Scholar 

  13. S. Galbraith and I. C. Marschner. Guidelines for the design of clinical trials with longitudinal outcomes. Controlled Clinical Trials, 23:257–273, 2002.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. H. Goldstein and J. Rasbash. Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 159:505–513, 1996.

    MATH  MathSciNet  Google Scholar 

  16. D. Hedeker and R. D. Gibbons. A random-effects ordinal regression model for multilevel analysis. Biometrics, 50:933–944, 1994.

    Article  MATH  Google Scholar 

  17. D. Hedeker, R. D. Gibbons, and C. Waternaux. Sample size estimation for longitudinal designs with attrition: Comparing time-related contrasts between two groups. Journal of Educational and Behavioral Statistics, 24:70–93, 1999.

    Google Scholar 

  18. F. Y. Hsieh. Sample size formulae for intervention studies with the cluster as unit of randomization. Statistics in Medicine, 8:1195–1201, 1988.

    Article  Google Scholar 

  19. M. Kendall and A. Stuart. The Advanced Theory of Statistics, 4th edition, volume 2. Griffin, London, 1979.

    MATH  Google Scholar 

  20. S. M. Kerry and J. M. Bland. Unequal cluster sizes for trials in English and Welsh general practice: Implications for sample size calculations. Statistics in Medicine, 20:377–390, 2001.

    Article  Google Scholar 

  21. N. M. Laird and F. Wang. Estimating rates of change in randomized clinical trials. Controlled Clinical Trials, 11:405–419, 1990.

    Article  Google Scholar 

  22. S. Lake, E. Kammann, K. Klar, and R. A. Betensky. Sample size re-estimation in cluster randomization trials. Statistics in Medicine, 21:1337–1350, 2002.

    Article  Google Scholar 

  23. E. W. Lee and N. Dubin. Estimation and sample size consideration for clustered binary responses. Statistics in Medicine, 13:1241–1252, 1994.

    Article  Google Scholar 

  24. S. R. Lipsitz and M. Parzen. Sample size calculations for non-randomized studies. The Statistician, 44:81–90, 1995.

    Article  Google Scholar 

  25. G. Liu and K.-Y. Liang. Sample size calculation for studies with correlated observations. Biometrics, 53:937–947, 1997.

    Article  MATH  Google Scholar 

  26. X. Liu. Statistical power and optimum sample allocation ratio for treatment and control having unequal costs per unit of randomization. Journal of Educational and Behavioral Statistics, 28:231–248, 2003.

    Article  Google Scholar 

  27. N. T. Longford. Random Coefficient Models. Oxford University Press, Oxford, UK, 1993.

    MATH  Google Scholar 

  28. A. K. Manatunga, M. G. Hudgens, and S. Chen. Sample size estimation in cluster randomized studies with varying cluster size. Biometrical Journal, 43:75–86, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  29. S. M. McKinlay. Cost-efficient designs of cluster unit trials. Preventive Medicine, 23:606–611, 1994.

    Article  Google Scholar 

  30. M. Moerbeek. Design and Analysis of Multilevel Intervention Studies. PhD thesis, Maastricht University, Maastricht, 2000.

    Google Scholar 

  31. M. Moerbeek. The use of internal pilot studies to derive powerful and cost-efficient designs for studies with nested data. In 2004 Proceedings of the American Statistical Association. American Statistical Association, Alexandria, VA, 2004.

    Google Scholar 

  32. M. Moerbeek. Randomization of clusters versus randomization of persons within clusters: Which is preferable? The American Statistician, 59:72–78, 2005.

    Article  MathSciNet  Google Scholar 

  33. M. Moerbeek. Powerful and cost-efficient designs for longitudinal intervention studies with two treatment groups. Journal of Educational and Behavioral Statistics, forthcoming.

    Google Scholar 

  34. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. Design issues for experiments in multilevel populations. Journal of Educational and Behavioral Statistics, 25:271–284, 2000.

    Google Scholar 

  35. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. Optimal experimental designs for multilevel logistic models. The Statistician, 50:1–14, 2001a.

    Google Scholar 

  36. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. Optimal experimental designs for multilevel models with covariates. Communications in Statistics, Theory and Methods, 30:2683–2697, 2001b.

    Article  MATH  Google Scholar 

  37. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. A comparison between traditional methods and multilevel regression for the analysis of multi-center intervention studies. Journal of Clinical Epidemiology, 56:341–350, 2003a.

    Article  Google Scholar 

  38. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. A comparison of estimation methods for multilevel logistic models. Computational Statistics, 18:19–37, 2003b.

    Google Scholar 

  39. M. Moerbeek, G. J. P. Van Breukelen, and M. P. F. Berger. Optimal sample sizes in experimental designs with individuals nested within clusters. Understanding Statistics, 2:151–175, 2003c.

    Article  Google Scholar 

  40. M. Moerbeek and W. K. Wong. Multiple-objective optimal designs for the hierarchical linear model. Journal of Official Statistics, 18:291–303, 2002.

    Google Scholar 

  41. M. Mok. Sample size requirements for 2-level designs in educational research. Multilevel Modelling Newsletter, 7:11–16, 1996.

    Google Scholar 

  42. D. M. Murray. Design and Analysis of Group-Randomized Trials. Oxford University Press, New York, 1998.

    Google Scholar 

  43. D. M. Murray, S. P. Varnell, and J. L. Blitstein. Design and analysis of group-randomized trials: A review of recent methodological developments. Public Health Matters, 94:423–432, 2004.

    Google Scholar 

  44. B. O. Muthén and P. J. Curran. General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2:371–402, 1997.

    Article  Google Scholar 

  45. L. K. Muthén and B. O. Muthén. How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9:599–620, 2002.

    Article  MathSciNet  Google Scholar 

  46. L. K. Muthén and B. O. Muthén. Mplus User's Guide. Muthén and Muthén, Los Angeles, 2004.

    Google Scholar 

  47. J. M. Neuhaus and J. D. Kalbfleisch. Between- and within-cluster covariate effects in the analysis of clustered data. Biometrics, 54:638–645, 1998.

    Article  MATH  Google Scholar 

  48. J. Rasbash, F. Steele, W. J. Browne, and B. Prosser. A User's Guide to MLwiN. Version 2.0. Centre for Multilevel Modelling, University of Bristol, Bristol, UK, 2005.

    Google Scholar 

  49. S. W. Raudenbush. Statistical analysis and optimal design for cluster randomized trials. Psychological Methods, 2:173–185, 1997.

    Article  Google Scholar 

  50. S. W. Raudenbush and X. Liu. Statistical power and optimal design for multisite randomized trials. Psychological Methods, 5:199–213, 2000.

    Article  Google Scholar 

  51. S. W. Raudenbush and X. Liu. Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6:387–401, 2001.

    Article  Google Scholar 

  52. S. W. Raudenbush, J. Spybrook, X. Liu, and R. Congdon. Optimal Design for Longitudinal and Multilevel Research: Documentation for the Optimal Design Software. University of Michigan, Ann Arbor, 2004.

    Google Scholar 

  53. G. Rodríguez and N. Goldman. An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158:73–89, 1995.

    Google Scholar 

  54. G. Rodríguez and N. Goldman. Improved estimation procedures for multilevel models with binary response: A case-study. Journal of the Royal Statistical Society, Series A, 164:339–355, 2001.

    MATH  Google Scholar 

  55. W. J. Shih. Sample size and power calculations for periodontal and other studies with clustered samples using the method of generalized estimation equations. Biometrical Journal, 39:899–908, 1997.

    Article  MATH  Google Scholar 

  56. S. D. Silvey. Optimal Design. Chapman & Hall, London, 1980.

    MATH  Google Scholar 

  57. T. A. B. Snijders and R. J. Bosker. Standard errors and sample sizes for two-level research. Journal of Educational Statistics, 18:237–259, 1993.

    Article  Google Scholar 

  58. T. A. B. Snijders and R. J. Bosker. Modeled variance in two-level models. Sociological Methods & Research, 22:342–363, 1994.

    Article  Google Scholar 

  59. D. J. Spiegelhalter. Bayesian methods for cluster randomized trials with continuous responses. Statistics in Medicine, 20:435–452, 2001.

    Article  Google Scholar 

  60. D. J. Spiegelhalter, A. Thomas, N. G. Best, and D. Lunn. WinBUGS User Manual, Version 1.4. MRC Biostatistics Unit, University of Cambridge, Cambridge, UK, 2003.

    Google Scholar 

  61. R. M. Turner, A. T. Prevost, and S. G. Thompson. Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials. Statistics in Medicine, 23:1195–1214, 2004.

    Article  Google Scholar 

  62. G. J. P. Van Breukelen. ANCOVA versus change from baseline: more power in randomized studies, more bias in nonrandomized studies. Journal of Clinical Epidemiology, 59:920–925, 2006.

    Article  Google Scholar 

  63. G. J. P. Van Breukelen, M. J. J. M. Candel, and M. P. F. Berger. Relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials. Statistics in Medicine, 26:2589–2603, 2007.

    Article  MathSciNet  Google Scholar 

  64. B. Winkens, H. J. A. Schouten, G. J. P. Van Breukelen, and M. P. F. Berger. Optimal time-points in clinical trials with linearly divergent treatment effects. Statistics in Medicine, 24:3743–3756, 2005.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Methodology and Statistics, Utrecht University, PO Box 80140, 3508TC Utrecht, The Netherlands

    Mirjam Moerbeek

  2. Department of Methodology and Statistics, Maastricht University, PO Box 616, 6200MD Maastricht, The Netherlands

    Gerard J. P. Van Breukelen & Martijn P.F. Berger

Authors
  1. Mirjam Moerbeek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerard J. P. Van Breukelen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martijn P.F. Berger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics, University of California at Los Angeles, Los Angeles, CA 90095-1554, USA

    Jan de Leeuw

  2. RAND Corporation, 1776 Main St, PO Box 2138, Santa Monica, CA 90407-2138, USA

    Erik Meijer

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Moerbeek, M., Breukelen, G.J.P.V., Berger, M.P. (2008). Optimal Designs for Multilevel Studies. In: Leeuw, J.d., Meijer, E. (eds) Handbook of Multilevel Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73186-5_4

Download citation

Publish with us

Policies and ethics

Search

Navigation