Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Longitudinal Models for Count Data

  • Chapter
  • First Online:
Dynamic Mixed Models for Familial Longitudinal Data

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

In longitudinal studies for count data, a small number of repeated count responses along with a set of multidimensional covariates are collected from a large number of independent individuals. For example, in a health care utilization study, the number of visits to a physician by a large number of independent individuals may be recorded annually over a period of several years. Also, the information on the covariates such as gender, number of chronic conditions, education level, and age, may be recorded for each individual.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. Amemiya, T. (1985). Advanced Econometrics. Cambridge, MA: Harvard University Press.

    Google Scholar 

  2. Anderson, T. W., McCarthy, P. J., & Tukey, J. W. (1946). Staircase Method of Sensitivity Testing. Naval Ordinance Report, 35−46. Princeton, NJ: Statistical Research Group.

    Google Scholar 

  3. Atkinson, A. C. (1999). Optimum biased-coin designs for sequential treatment allocation with covariate information. Statist. Med., 18, 1741−1752.

    Article  Google Scholar 

  4. Crowder, M. (1995). On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika, 82, 407−410.

    Article  MATH  Google Scholar 

  5. Derman, C. (1957). Nonparametric up and down experimentation. Ann. Math. Stat., 28, 795−798.

    Article  MATH  MathSciNet  Google Scholar 

  6. Durham, S. D. & Flournoy, N. (1994). Random walks for quantile estimation. In Statistical Decision Theory and Related Topics V (S. S. Gupta and J. O. Berger, eds.) 467−476. New York: Springer.

    Google Scholar 

  7. Farewell, V. T., Viveros, R., & Sprott, D. A. (1993). Statistical consequences of an adaptive treatment allocation in a clinical trial. Canad. J. Statist., 21, 21−27.

    Article  Google Scholar 

  8. Jennison, C. & Turnbull, B. W. (2001). Group sequential tests with outcome-dependent treatment assignment. Sequential Anal., 20, 209−234.

    Article  MATH  MathSciNet  Google Scholar 

  9. Liang, K. Y. & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 78, 13−22.

    Article  MathSciNet  Google Scholar 

  10. Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate Analysis. London: Academic Press.

    Google Scholar 

  11. McCullagh, P. (1983). Quasilikelihood functions. Ann. Statist. 11, 59−67.

    Article  MATH  MathSciNet  Google Scholar 

  12. McKenzie, E. (1988). Some ARMA models for dependent sequences of Poisson counts. Advan. Appl. Probab., 20, 822−835.

    Article  MATH  MathSciNet  Google Scholar 

  13. Nelder, J. & Wedderburn, R. W. M. (1972). Generalized linear models. J. Roy. Statist. Soc. A135, 370−384.

    Google Scholar 

  14. Pocock, S. J. & Simon, R. (1975). Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics, 31, 103−115.

    Article  MATH  Google Scholar 

  15. Rosenberger, W. F. (1996). New directions in adaptive designs. Statist. Sci., 11, 137−149.

    Article  Google Scholar 

  16. Royall, R. M. (1991). Ethics and statistics in randomized clinical trials (with discussion). Statist. Sci., 6, 52−62.

    Article  MATH  MathSciNet  Google Scholar 

  17. Smith, R. L. S. (1984). Properties of bias coin designs in sequential clinical trials.Annal. Statist., 12, 1018−1034.

    Article  MATH  Google Scholar 

  18. Sutradhar, B. C. (2003). An overview on regression models for discrete longitudinal responses. Statist. Sci., 18, 377−393.

    Article  MATH  MathSciNet  Google Scholar 

  19. Sutradhar, B.C., Biswas, A., & Bari, W. (2005). Marginal regression for binary longitudinal data in adaptive clinical trials. Scand. J. Statist., 32, 93−113.

    Article  MATH  MathSciNet  Google Scholar 

  20. Sutradhar, B. C. & Das, K. (1999). On the efficiency of regression estimators in generalized linear models for longitudinal data. Biometrika, 86, 459−465.

    Article  MATH  MathSciNet  Google Scholar 

  21. Sutradhar, B. C. & Jowaheer, V. (2006). Analyzing longitudinal count data from adaptive clinical trials: a weighted generalized quasi-likelihood approach. J. Statist. Comput. Simul., 76, 1079−1093.

    Article  MATH  MathSciNet  Google Scholar 

  22. Sutradhar, B. C. & Kovacevic, M. (2000). Analyzing ordinal longitudinal survey data: Generalized estimating equations approach. Biometrika, 87, 837−848.

    Article  MATH  MathSciNet  Google Scholar 

  23. Storer, B, E, (1989). Design and analysis of phase 1 clinical trial. Biometrics,, 45, 925−937.

    Article  MATH  MathSciNet  Google Scholar 

  24. Tamura, R. N., Faries, D. E., Andersen, J. S., & Heiligenstein, J. H. (1994). A case study of an adaptive clinical trial in the treatment of out-patients with depressive disorder. J. Amer. Stat. Assoc., 89, 768−776.

    Article  Google Scholar 

  25. Temple, R. (1981). Government view points of clinical trials. Drug Inf. J., 16, 10−17.

    Google Scholar 

  26. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439−447.

    MathSciNet  Google Scholar 

  27. Wei, L. J. & Durham, S. (1978). The randomized play-the-winner rule in medical trials. J. Am. Statist. Assoc., 73, 840−843.

    Article  MATH  Google Scholar 

  28. Wei, L. J., Smythe, R. T. Lin, D. Y., & Park, T. S. (1990). Statistical inference with datadependent treatment allocation rules. J. Am. Statist. Assoc., 85, 156−62.

    Article  MathSciNet  Google Scholar 

  29. Zelen, M. (1969). Play-the-winner rule and the controlled clinical trial. J. Am. Statist. Assoc., 64, 131−46.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University, A1C 5S7, Saint John’s, Newfoundland and Labrador, Canada

    Brajendra C. Sutradhar

Authors
  1. Brajendra C. Sutradhar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brajendra C. Sutradhar .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Sutradhar, B.C. (2011). Longitudinal Models for Count Data. In: Dynamic Mixed Models for Familial Longitudinal Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8342-8_6

Download citation

Publish with us

Policies and ethics

Search

Navigation