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Power Conjugate Multilevel Models with Applications to Genomics

Author

Listed:
  • Brian Caffo

    (The Johns Hopkins Bloomberg School of Public Health)

  • Liu Dongmei

    (Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics)

  • Giovanni Parmigiani

    (The Sydney Kimmel Comprehensive Cancer Center, Johns Hopkins University & Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health)

Abstract

In the simultaneous estimation of a large number of related quantities, multilevel models provide a formal mechanism for effciently making use of the ensemble of information for deriving individual estimates. In this article we present a novel and flexible class of normal multilevel models, referred to as the "power conjugate family". This family overcomes some of the severe restrictions posed by standard conjugate normal models in describing the relationship between sources of variations at different levels of the model, while retaining attractive properties from the point of view of computations. We show that estimates based on this generalized family of conjugate distributions, outperform currently prevalent methods in a range of plausible simulated experiments. Our work was motivated by the analysis of data from high-throughput experiments in genomics. We illustrate the use of the power conjugate family on two such data sets, one of which gives an example where uncritical application of standard conjugate models can produce poor results.

Suggested Citation

  • Brian Caffo & Liu Dongmei & Giovanni Parmigiani, 2004. "Power Conjugate Multilevel Models with Applications to Genomics," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1062, Berkeley Electronic Press.
    • Handle: RePEc:bep:jhubio:1062
    Note: oai:bepress.com:jhubiostat-1062
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    References listed on IDEAS

    as
    1. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
    2. Giovanni Parmigiani & Elizabeth S. Garrett & Ramaswamy Anbazhagan & Edward Gabrielson, 2002. "A statistical framework for expression‐based molecular classification in cancer," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 717-736, October.
    3. Ibrahim J. G. & Chen M-H. & Gray R. J., 2002. "Bayesian Models for Gene Expression With DNA Microarray Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 88-99, March.
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