A suite of empirical Bayes methods to use in pharmacovigilance.

pvEBayes provides a collection of parametric and non-parametric empirical Bayes methods implementation for pharmacovigilance (including signal detection and signal estimation) on spontaneous reporting systems (SRS) data.

An SRS dataset catalogs AE reports on I AE rows across J drug columns. Let \(N_{ij}\) denote the number of reported cases for the i-th AE and the j-th drug, where \(i = 1,..., I\) and \(j = 1,..., J\). We assume that for each AE-drug pair, \(N_{ij} \sim \text{Poisson}(\lambda_{ij} E_{ij})\), where \(E_{ij}\) is expected baseline value measuring the expected count of the AE-drug pair when there is no association between i-th AE and j-th drug. The parameter \(\lambda_{ij} \geq 0\) represents the relative reporting ratio, the signal strength, for the \((i, j)\)-th pair measuring the ratio of the actual expected count arising due to dependence to the null baseline expected count. Current disproportionality analysis mainly focuses on signal detection which seeks to determine whether the observation \(N_{ij}\) is substantially greater than the corresponding null baseline \(E_{ij}\). Under the Poisson model, that is to say, its signal strength \(\lambda_{ij}\) is significantly greater than 1.

In addition to signal detection, Tan et al. (Stat. in Med., 2025) broaden the role of disproportionality to signal estimation. The use of the flexible non-parametric empirical Bayes models enables more nuanced empirical Bayes posterior inference (parameter estimation and uncertainty quantification) on signal strength parameter \(\{ \lambda_{ij} \}\). This allows researchers to distinguish AE-drug pairs that would appear similar under a binary signal detection framework. For example, the AE-drug pairs with signal strengths of 1.5 and 4.0 could both be significantly greater than 1 and detected as a signal. Such differences in signal strength may have distinct implications in medical and clinical contexts.

The methods included in pvEBayes differ by their assumptions on the prior distribution. Implemented methods include the Gamma-Poisson Shrinker (GPS), Koenker-Mizera (KM) method, Efron’s nonparametric empirical Bayes approach, the K-gamma model, and the general-gamma model.

The GPS model uses two gamma mixture prior by assuming the signal/non-signal structure in SRS data. However, in real-world setting, signal strengths \((\lambda_{ij})\) are often heterogeneous and thus follows a multi-modal distribution, making it difficult to assume a parametric prior. Non-parametric empirical Bayes models (KM, Efron, K-gamma and general-gamma) address this challenge by utilizing a flexible prior with general mixture form and estimating the prior distribution in a data-driven way.

pvEBayes offers the first implemention of the bi-level Expectation Conditional Maximization (ECM) algorithm proposed by Tan et al. (2025) for efficient parameter estimation in gamma mixture prior based models: GPS K-gamma and general-gamma.

The KM method has an existing implementation in the REBayes package, but it relies on Mosek, a commercial convex optimization solver, which may limit accessibility due to licensing issue. pvEBayes provides a alternative fully open-source implementation of the KM method using CVXR.

Efron’s method also has a general nonparametric empirical Bayes implementation in the deconvolveR package; however, that implementation does not support an exposure or offset parameter in the Poisson model, which corresponds to the expected null value \(E_{ij}\). In pvEBayes, the implementation of the Efron's method is adapted and modified from deconvolveR to support \(E_{ij}\) in Poisson model.

For an introduction to pvEBayes, see the vignette.

References

Tan Y, Markatou M and Chakraborty S. Flexible Empirical Bayesian Approaches to Pharmacovigilance for Simultaneous Signal Detection and Signal Strength Estimation in Spontaneous Reporting Systems Data. Statistics in Medicine. 2025; 44: 18-19, https://doi.org/10.1002/sim.70195.

Tan Y, Markatou M and Chakraborty S. pvEBayes: An R Package for Empirical Bayes Methods in Pharmacovigilance. arXiv:2512.01057 (stat.AP). https://doi.org/10.48550/arXiv.2512.01057

Koenker R, Mizera I. Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules. Journal of the American Statistical Association 2014; 109(506): 674–685, https://doi.org/10.1080/01621459.2013.869224

Efron B. Empirical Bayes Deconvolution Estimates. Biometrika 2016; 103(1); 1-20, https://doi.org/10.1093/biomet/asv068

DuMouchel W. Bayesian data mining in large frequency tables, with an application to the FDA spontaneous reporting system. The American Statistician. 1999; 1;53(3):177-90.

See also

Useful links:

• https://github.com/YihaoTancn/pvEBayes

• https://yihaotancn.github.io/pvEBayes/

• Report bugs at https://github.com/YihaoTancn/pvEBayes/issues

Author

Yihao Tan, Marianthi Markatou, Saptarshi Chakraborty and Raktim Mukhopadhyay.

Maintainer: Yihao Tan yihaotan@buffalo.edu