Quality of Life Research

, Volume 17, Issue 1, pp 47–59

Analyzing growth and change: latent variable growth curve modeling with an application to clinical trials

Article

Abstract

Objective

Typical methods of analyzing data from clinical trials have shortcomings, notably comparisons of group means, use of change scores from pre- and post-treatment assessments, ignoring intervening assessments, and focusing on direct effects of treatment. A comparison of group means disregards the likelihood that individuals have different trajectories of change. Moreover, change scores ignore intervening assessments that may provide useful information about change. This paper compares results from traditional regression-based methods for analyzing data from a clinical trial (e.g., regression with change scores) with those of latent growth curve modeling (LGM).

Methods

LGM is a method that uses structural equation modeling techniques to model individual change, assess treatment effects and the relationship among multiple outcomes simultaneously, and model measurement error. The consequence is more precise parameter estimates while using data from all available time points.

Results

Results demonstrate that LGM can yield stronger parameter estimates than the traditional regression-based approach and explain more variance in the outcome. In trials where there is a true effect, but it is non-significant or marginally significant using the traditional methods, LGM may provide evidence of this effect.

Conclusions

Analysts are encouraged to consider LGM as an additional and informative tool for analyzing clinical trial or other longitudinal data.

Keywords

Longitudinal data analysis Growth curves Growth curve analysis Structural equation modeling 

Supplementary material

References

  1. 1.
    Cronbach, L. J., & Furby, L. (1970). How should we measure ‘change’ - or should we? Psychological Bulletin, 74, 68–80.CrossRefGoogle Scholar
  2. 2.
    Rogossa, D. R. (1988). Myths about longitudinal research. In K. W. Schaie, R. T. Campbell, W. Meredith, & S. C. Rawlings (Eds.), Methodological issues in aging research (pp. 171–209). New York: Springer.Google Scholar
  3. 3.
    Rogossa, D. R. (1995). Myths and methods ‘Myths about longitudinal research’ plus supplemental questions. In J. M. Gottman (Ed.), The analysis of change (pp. 3–66). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  4. 4.
    Duncan T. E., & Duncan, S. C., et al. (2006). An introduction to latent variable growth curve modeling, (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  5. 5.
    Kreft, I., & De Leeuw, J. (1998). Introducing multilevel modeling. Thousand Oaks, CA: Sage.Google Scholar
  6. 6.
    Heck R., & Thomas, L. (2000). An introduction to multilevel modeling techniques. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  7. 7.
    Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models. Applications and data analysis methods. Thousand Oaks, CA: Sage.Google Scholar
  8. 8.
    Chou, C. P., & Bentler, P. M., et al. (1998). Comparisons of two statistical approaches to the study of growth curves: The multilevel model and latent curve analysis. Structural Equation Modeling, 5, 247–266.CrossRefGoogle Scholar
  9. 9.
    Li, F., & Duncan, T. E., et al. (2000). A didactic example of latent curve analysis applicable to the study of aging. Journal of Aging and Health, 12, 388–425.CrossRefGoogle Scholar
  10. 10.
    McArdle, J. J., & Bell, R. Q. (2000). Recent trends in modeling longitudinal data by latent growth curve methods. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: Practical issues, applied approaches, and scientific examples (pp. 69–108). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  11. 11.
    Muthen, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81–117.CrossRefGoogle Scholar
  12. 12.
    Curren, P. J., & Willoughby, M. T. (2003). Implications of latent trajectory models for the study of developmental psychopathology. Development and Psychopathology, 15, 581–612.CrossRefGoogle Scholar
  13. 13.
    Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.Google Scholar
  14. 14.
    Bollen, K. A., & Curren, P. J. (2004). Autoregressive Latent Trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336–383.CrossRefGoogle Scholar
  15. 15.
    Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annual Review of Clinical Psychology, 1, 2.1–2.35.CrossRefGoogle Scholar
  16. 16.
    McArdle, J. J., & Epstein, D. (1988). Dynamic but structural equation modeling of repeated measures data. In R. B. Cattell & J. Nesselroade (Eds.), Handbook of multivariate experimental psychology (pp. 561–614). New York: Plenum.Google Scholar
  17. 17.
    Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.CrossRefGoogle Scholar
  18. 18.
    Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 1–17.CrossRefGoogle Scholar
  19. 19.
    Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19–23.CrossRefGoogle Scholar
  20. 20.
    Kline, R. B. (2005). Principles and practice of structural equation modeling, (2nd ed.). New York: Guilford.Google Scholar
  21. 21.
    Jackson, D. L. (2003). Revisiting sample size and number of parameter estimates: Some support for the N:q hypothesis. Structural Equation Modeling, 10, 128–141.CrossRefGoogle Scholar
  22. 22.
    Cudeck, R., & Henly, S. J. (1991). Model selection in covariance structures analysis and the “Problem” of sample size: A clarification. Psychological Bulletin, 109, 512–519.PubMedCrossRefGoogle Scholar
  23. 23.
    MacCallum, R. C., & Browne, M. W., et al. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1, 131–149.CrossRefGoogle Scholar
  24. 24.
    Schumacker, R. E., & Lomax, R. G. (1996). A beginner’s guide to structural equation modeling. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  25. 25.
    Kaplan, D. (2000). Structural equation modeling. Thousand Oaks, CA: Sage.Google Scholar
  26. 26.
    West, S. G., & Finch, J. F., et al. (1995). Structural equation models with nonnormal variables: Problems and remedies. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 56–75). Thousand Oaks, CA: Sage.Google Scholar
  27. 27.
    Hox, J., & Bechger, T. (1998). An introduction to structural equation modeling. Family Science Review, 11, 354–373.Google Scholar
  28. 28.
    Chou, C. P., & Bentler, P. M. (1995). Estimates and tests in structural equation modeling. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 37–55). Thousand Oaks, CA: Sage.Google Scholar
  29. 29.
    SOLVD Investigators. (1990). Studies of left ventricular dysfunction (SOLVD)–rationale, design and methods: Two trials that evaluate the effect of enalapril in patients with reduced ejection fraction. The American Journal of Cardiology, 66, 315–322.CrossRefGoogle Scholar
  30. 30.
    SOLVD Investigators. (1991). Effect of enalapril on survival in patients with reduced left ventricular ejection fractions and congestive heart failure. The New England Journal of Medicine, 325, 293–302.CrossRefGoogle Scholar
  31. 31.
    Rogers, W. J., & Johnstone D. E., et al. (1994). Quality of life among 5,025 patients with left ventricular dysfunction randomized between placebo and Enalapril: The studies of left ventricular dysfunction. Journal of the American College of Cardiology, 23, 393–400.PubMedCrossRefGoogle Scholar
  32. 32.
    Clarke, S. P., & Frasure-Smith, N., et al. (2000). Psychosocial factors as predictors of functional status at 1 year in patients with left ventricular dysfunction. Research in Nursing and Health, 23, 293–300.Google Scholar
  33. 33.
    Stull, D. E., & Clough, L. A., et al. (2001). Self-report quality of life as a predictor of hospitalization for patients with left ventricular dysfunction: A life course approach. Research in Nursing and Health, 24, 460–469.PubMedCrossRefGoogle Scholar
  34. 34.
    Idler, E. L., & Benyamini, Y. (1997). Self-rated health and mortality: A review of twenty-seven community studies. Journal of Health and Social Behavior, 38, 21–37.PubMedCrossRefGoogle Scholar
  35. 35.
    Kosloski, K., & Stull, D. E., et al. (2005). Longitudinal analysis of the reciprocal effects of self-assessed global health and depressive symptoms. The Journal of Gerontology B. Psychological Sciences and Social Sciences, 60(6), P296–P303.Google Scholar
  36. 36.
    Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.Google Scholar
  37. 37.
    Marsh, H. W., & Hau, K. T., et al. (2004). In Search of Golden Rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling, 11, 320–341.CrossRefGoogle Scholar
  38. 38.
    Bollen, K., & Curran, P. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley.Google Scholar
  39. 39.
    Duncan, T. E., & Duncan, S. C., et al. (2006). An introduction to latent variable growth curve modeling. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  40. 40.
    Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453.CrossRefGoogle Scholar
  41. 41.
    Speer, D. C., & Greenbaum, P. D. (1995). Five methods for computing significant individual client change and improvement rates: Support for an individual growth curve approach. Journal of Consulting and Clinical Psychology, 63, 1044–1048.PubMedCrossRefGoogle Scholar
  42. 42.
    Crosby, R. D., & Kolotkin, R. L., et al. (2003). Defining clinically meaningful change in health-related quality of life. Journal of Clinical Epidemiology, 56, 395–407.PubMedCrossRefGoogle Scholar
  43. 43.
    Wothke, W. (2000). Longitudinal and multi-group modeling with missing data. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  44. 44.
    Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177.PubMedCrossRefGoogle Scholar
  45. 45.
    Joreskog, K. G. (1993). Testing structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 294–316). Newbury Park, CA: Sage.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Research Scientist, Center for Health Outcomes ResearchUnited BioSource CorporationBethesdaUSA

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