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.
Similar content being viewed by others
References
Cronbach, L. J., & Furby, L. (1970). How should we measure ‘change’ - or should we? Psychological Bulletin, 74, 68–80.
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.
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.
Duncan T. E., & Duncan, S. C., et al. (2006). An introduction to latent variable growth curve modeling, (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.
Kreft, I., & De Leeuw, J. (1998). Introducing multilevel modeling. Thousand Oaks, CA: Sage.
Heck R., & Thomas, L. (2000). An introduction to multilevel modeling techniques. Mahwah, NJ: Lawrence Erlbaum.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models. Applications and data analysis methods. Thousand Oaks, CA: Sage.
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.
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.
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.
Muthen, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81–117.
Curren, P. J., & Willoughby, M. T. (2003). Implications of latent trajectory models for the study of developmental psychopathology. Development and Psychopathology, 15, 581–612.
Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.
Bollen, K. A., & Curren, P. J. (2004). Autoregressive Latent Trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336–383.
Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annual Review of Clinical Psychology, 1, 2.1–2.35.
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.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 1–17.
Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19–23.
Kline, R. B. (2005). Principles and practice of structural equation modeling, (2nd ed.). New York: Guilford.
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.
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.
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.
Schumacker, R. E., & Lomax, R. G. (1996). A beginner’s guide to structural equation modeling. Mahwah, NJ: Lawrence Erlbaum.
Kaplan, D. (2000). Structural equation modeling. Thousand Oaks, CA: Sage.
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.
Hox, J., & Bechger, T. (1998). An introduction to structural equation modeling. Family Science Review, 11, 354–373.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Bollen, K., & Curran, P. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley.
Duncan, T. E., & Duncan, S. C., et al. (2006). An introduction to latent variable growth curve modeling. Mahwah, NJ: Lawrence Erlbaum.
Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453.
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.
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.
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.
Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177.
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.
Acknowledgements
The author thanks Drs. Karl Kosloski and Kyle Kercher for their extremely helpful comments on earlier drafts of this manuscript, and the comments and suggestions of two anonymous reviewers that led to a more didactic and comparative paper. Two versions of summary data (means, variances, and covariances for listwise missing and full information maximum likelihood methods of estimation of missing data) can be downloaded from the Quality of Life Research Web site or upon request to the author. The summary matrices can be used to run the example analysis using Mplus. The names of the two files are “11136_2007_9290_MOESM1.dat” and “11136_2007_9290_MOESM2.dat”.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Appendix: Mplus 4.2 syntax for evaluation of the model in Fig. 3
Appendix: Mplus 4.2 syntax for evaluation of the model in Fig. 3
Rights and permissions
About this article
Cite this article
Stull, D.E. Analyzing growth and change: latent variable growth curve modeling with an application to clinical trials. Qual Life Res 17, 47–59 (2008). https://doi.org/10.1007/s11136-007-9290-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11136-007-9290-5