Approximate Bayesian Evaluation of Multiple Treatment Effects

Authors

  • Peter F. Thall,

    Corresponding author
    1. Department of Biostatistics, Box 237, M. D. Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030, U.S.A.
      *email:rex@odin.mdacc.tmc.edu
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  • Richard M. Simon,

    1. Biometric Research Branch, National Cancer Institute, 6130 Executive Boulevard, Room 739, Rockville, Maryland 20852, U.S.A.
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  • Yu Shen

    1. Department of Biostatistics, Box 237, M. D. Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030, U.S.A.
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*email:rex@odin.mdacc.tmc.edu

Abstract

Summary. We propose an approximate Bayesian method for comparing an experimental treatment to a control based on a randomized clinical trial with multivariate patient outcomes. Overall treatment effect is characterized by a vector of parameters corresponding to effects on the individual patient outcomes. We partition the parameter space into four sets where, respectively, the experimental treatment is superior to the control, the control is superior to the experimental, the two treatments are equivalent, and the treatment effects are discordant. We compute posterior probabilities of the parameter sets by treating an estimator of the parameter vector like a random variable in the Bayesian paradigm. The approximation may be used in any setting where a consistent, asymptotically normal estimator of the parameter vector is available. The method is illustrated by application to a breast cancer data set consisting of multiple time-to-event outcomes with covariates and to count data arising from a cross-classification of response, infection, and treatment in an acute leukemia trial.

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