Constrained Statistical Decisions in Evolving Environments,
by Elijah Gaioni, Dipak Dey, and
Intelligent Systems, to appear.
Evaluation of Port Access Devices,
by Brenda Nurse, M.D., and Daniel Larose.
A Bayesian Meta-Analysis of the
Relationship Between Duration of Estrogen Exposure and Endometrial Cancer
in Meta-Analysis in Medicine and Health Policy,
D. Berry and D. Stangl, Eds., Marcel-Dekker, New York, 2000.
A Bayesian random-effect model
is presented for combining exposure-response information from
several studies examining possible association between estrogen
exposure and endometrial cancer. A Wishart distribution is used
to model the within-study dependence of the vector of log
relative risks. Data from 17 published studies which provided
exposure-response information were combined. Samples from the
joint posterior were generated by the Gibbs sampler. Results
indicate evidence of a significant exposure-response
relationship between estrogen and endometrial cancer.
Bayesian Duration-Response Meta-Analysis of Estrogen and Endometrial Cancer
Proceedings of the Section on Bayesian Statistical Science, American Statistical Association, Alexandria, Virginia, 1998.
Modeling Publication Bias Using
Weighted Distributions in a Bayesian Framework Computational Statistics and Data Analysis, Vol 26, 279-302, 1998.
Meta-analysis refers to the quantitative synthesis of evidence from a
set of related studies. Inference based on naive use of meta-analysis may be erroneous,
however, due to publication bias, the tendency of investigators or editors to base decisions
regarding submission or acceptance of manuscripts for publication depending on the strength
of the investigator's study findings. Weighted distributions are ideally suited to model
this phenomenon, since the weight function is proportional to the probability that the
observation (in this case, the results of a study) enters the record. Models induced by several
competing weight functions are compared, using the education data of Hedges and Olkin (1985).
Here, such models are fit hierarchically from a Bayesian perspective using noninformative
priors in order to let the data drive the inference. Several model selection criteria are used
in the spirit of exploratory data analysis for the appropriate choice of the weight function.
Grouped Random Effects Models
for Bayesian Meta-Analysis
Statistics in Medicine, Vol. 16, 1817-1829, 1997.
Weighted Distributions Viewed in the Context of
Model Selection: a Bayesian Perspective
Test, The Journal of the Spanish Statistical
Society, Vol. 5, 1, 227-246, 1996.
In Section 2, a Bayesian formulation of the
weighted model is motivated and derived. Section 3 presents the general
form of the Bayes factor for weighted vs. unweighted model selection, as well as a convenient
computational form. Section 4 discusses the behavior of the Bayes factor under known
weight functions for the one parameter exponential family, and a table of closed form
expressions for the Bayes factor under conjugate prior. In Section 5, a Bayes factor form is
derived for unknown weight functions followed by an example. Section 6 outlines
alternatives when closed form
expressions for the Bayes factor turn out to be analytically intractable. Section 7 discusses
mixture distributions as weighted distributions and Section 8 illustrates the use of the Monte
Carlo estimate of the Bayes factor presented in Section 6.
Modeling Heterogeneity and
Extraneous Variation using Weighted Distributions
Model-Oriented Data Analysis 4, Kitsos and Muller, eds, Physica
Verlag, Heidelberg, Germany, 1995.