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A Bayesian hierarchical mixture model for platelet‐derived growth factor receptor phosphorylation to improve estimation of progression‐free survival in prostate cancer

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  • Satoshi Morita
  • Peter F. Thall
  • B. Nebiyou Bekele
  • Paul Mathew

Abstract

Summary. Advances in understanding the biological underpinnings of many cancers have led increasingly to the use of molecularly targeted anticancer therapies. Because the platelet‐derived growth factor receptor (PDGFR) has been implicated in the progression of prostate cancer bone metastases, it is of great interest to examine possible relationships between PDGFR inhibition and therapeutic outcomes. We analyse the association between change in activated PDGFR (phosphorylated PDGFR) and progression‐free survival time based on large within‐patient samples of cell‐specific phosphorylated PDGFR values taken before and after treatment from each of 88 prostate cancer patients. To utilize these paired samples as covariate data in a regression model for progression‐free survival time, and be cause the phosphorylated PDGFR distributions are bimodal, we first employ a Bayesian hierarchical mixture model to obtain a deconvolution of the pretreatment and post‐treatment within‐patient phosphorylated PDGFR distributions. We evaluate fits of the mixture model and a non‐mixture model that ignores the bimodality by using a supnorm metric to compare the empirical distribution of each phosphorylated PDGFR data set with the corresponding fitted distribution under each model. Our results show that first using the mixture model to account for the bimodality of the within‐patient phosphorylated PDGFR distributions, and then using the posterior within‐patient component mean changes in phosphorylated PDGFR so obtained as covariates in the regression model for progression‐free survival time, provides an improved estimation.

Suggested Citation

  • Satoshi Morita & Peter F. Thall & B. Nebiyou Bekele & Paul Mathew, 2010. "A Bayesian hierarchical mixture model for platelet‐derived growth factor receptor phosphorylation to improve estimation of progression‐free survival in prostate cancer," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 19-34, January.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:1:p:19-34
    DOI: 10.1111/j.1467-9876.2009.00680.x
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    References listed on IDEAS

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    1. 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, October.
    2. Samuel M. Mwalili & Emmanuel Lesaffre & Dominique Declerck, 2005. "A Bayesian ordinal logistic regression model to correct for interobserver measurement error in a geographical oral health study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 77-93, January.
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    Cited by:

    1. Rebecca Graziani & Michele Guindani & Peter F. Thall, 2015. "Bayesian nonparametric estimation of targeted agent effects on biomarker change to predict clinical outcome," Biometrics, The International Biometric Society, vol. 71(1), pages 188-197, March.

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