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Identification of multivariate responders and non-responders by using Bayesian growth curve latent class models

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  • Benjamin E. Leiby
  • Mary D. Sammel
  • Thomas R. Ten Have
  • Kevin G. Lynch

Abstract

We propose a multivariate growth curve mixture model that groups subjects on the basis of multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden to group subjects on the basis of distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of 'responders' would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott and co-workers are extended to estimate simultaneously the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of "bacillus" Calmette-Guerin in treating symptoms of interstitial cystitis. In contrast with conventional approaches using a single subjective global response assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and to evaluate the performance of our algorithm. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Benjamin E. Leiby & Mary D. Sammel & Thomas R. Ten Have & Kevin G. Lynch, 2009. "Identification of multivariate responders and non-responders by using Bayesian growth curve latent class models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 505-524.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:4:p:505-524
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    References listed on IDEAS

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    1. Steffen Fieuws & Geert Verbeke, 2006. "Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles," Biometrics, The International Biometric Society, vol. 62(2), pages 424-431, June.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    3. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    4. Elizabeth S. Garrett & Scott L. Zeger, 2000. "Latent Class Model Diagnosis," Biometrics, The International Biometric Society, vol. 56(4), pages 1055-1067, December.
    5. Jason Roy & Xihong Lin, 2000. "Latent Variable Models for Longitudinal Data with Multiple Continuous Outcomes," Biometrics, The International Biometric Society, vol. 56(4), pages 1047-1054, December.
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