The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Power prior distributions for regression models
Open accessAbstract
We propose a general class of prior distributions for arbitrary regression models. We discuss parametric and semiparametric models. The prior specification for the regression coefficients focuses on observable quantities in that the elicitation is based on the availability of historical data $D_0$ and a scalar quantity $a_0$ quantifying the uncertainty in $D_0$. Then $D_0$ and $a_0$ are used to specify a prior for the regression coefficients in a semiautomatic fashion. The most natural specification of $D_0$ arises when the raw data from a similar previous study are available. The availability of historical data is quite common in clinical trials, carcinogenicity studies, and environmental studies, where large data bases are available from similar previous studies. Although the methodology we present here is quite general, we will focus only on using historical data from similar previous studies to construct the prior distributions. The prior distributions are based on the idea of raising the likelihood function of the historical data to the power $a_0$, where $0 \le a_0 \le 1$. We call such prior distributions power prior distributions. We examine the power prior for four commonly used classes of regression models. These include generalized linear models, generalized linear mixed models, semiparametric proportional hazards models, and cure rate models for survival data. For these classes of models, we discuss the construction of the power prior, prior elicitation issues, propriety conditions, model selection, and several other properties. For each class of models, we present real data sets to demonstrate the proposed methodology.
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Cites
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Self-citationOn assessing prior distributions and Bayesian regression analysis with g-prior distributions
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Self-citationUse of Historical Control Data in Carcinogenicity Studies in Rodents
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Prior Elicitation, Variable Selection and Bayesian Computation for Logistic Regression Models
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Self-citationA Predictive Approach to the Analysis of Designed Experiments
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Self-citationBayesian variable selection for proportional hazards models
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Cited by
Robust meta‐analytic‐predictive priors in clinical trials with historical control information
Schmidli, H., Gsteiger, S., Roychoudhury, S., O'Hagan, A., Spiegelhalter, D., & Neuenschwander, B. (2014) · Biometrics · doi:10.1111/biom.12242 · Cited by 482
Model Averaging and Its Use in Economics
Steel, M. F. J. (2020) · Journal of Economic Literature · doi:10.1257/jel.20191385 · Cited by 321
A General Framework for Updating Belief Distributions
Bissiri, P. G., Holmes, C. C., & Walker, S. G. (2016) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12158 · Cited by 285
Combining randomized and non-randomized evidence in network meta-analysis
Efthimiou, O., Mavridis, D., Debray, T. P. A., Samara, M., Belger, M., Siontis, G. C. M., Leucht, S., Salanti, G., & 4, O. B. O. G. W. P. (2017) · Statistics in Medicine · doi:10.1002/sim.7223 · Cited by 183
Verde, P. E., & Ohmann, C. (2015) · Research Synthesis Methods · doi:10.1002/jrsm.1122 · Cited by 123
Metadata
- Authors
- Chen, M.-H., & Ibrahim, J. G.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 2000-02-01
- Volume
- 15
- Issue
- 1
- Pages
- 46-60
- ISSN
- 0883-4237 (ISSN-L)
- OpenAlex
- W2020946357
- Cited by
- 732
- References
- 13
- FWCI
- 3.75
- Type
- journal article
- Language
- en
- Open access
- bronze
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