Empirical Bayes Geometric Mean (EBGM)

EBGM applies Bayesian shrinkage to pull observed disproportionality scores toward a null value of 1.0. This directly addresses the small-cell problem in pharmacovigilance, where drug-event combinations with very low report counts (e.g., N=1 or 2) would otherwise generate wildly unstable and unreliable frequentist scores like the Proportional Reporting Ratio (PRR).

• Mechanism: The observed count is treated as a Poisson likelihood, and the prior is a mixture of Gamma distributions estimated from the entire database.
• Effect: A combination with 1 observed report where 0.5 are expected might have a PRR of 2.0 but a shrunken EBGM of 1.1, reflecting high uncertainty.

The EBGM is the geometric mean of the posterior distribution for the true relative reporting ratio (λ). It is calculated as 2^E[log2(λ)], which provides a point estimate that is more robust to extreme values than the arithmetic mean.

• Value > 1: Suggests the drug-event pair is reported more often than expected.
• Value < 1: Suggests the pair is reported less often than expected.
• Threshold: Regulatory scientists often use EBGM ≥ 2.0 as an initial screening threshold for potential safety signals, though this is not a strict rule.

Unlike simple frequentist methods, the MGPS algorithm computes EBGM while stratifying by key covariates to control for confounding. The expected counts are calculated within strata defined by variables such as:

• Age group (e.g., pediatric, adult, geriatric)
• Gender
• Reporting year

This stratification ensures that a high EBGM is not an artifact of demographic imbalances in the reporting database, providing a more specific signal.

Every EBGM score is accompanied by a 90% credible interval, bounded by the 5th percentile (EB05) and the 95th percentile (EB95). These bounds quantify the uncertainty around the point estimate.

• EB05 > 2.0: A common, more conservative signal detection criterion. If the lower bound of the credible interval exceeds 2.0, it indicates high confidence that the true relative reporting ratio is elevated.
• Narrow Interval: Indicates high precision, typically due to a large number of observed reports.
• Wide Interval: Indicates low precision, typically due to sparse data.

EBGM directly addresses the volatility inherent in frequentist disproportionality measures like the Proportional Reporting Ratio (PRR) and Reporting Odds Ratio (ROR).

• PRR/ROR Limitation: These ratios can be infinite or undefined when expected counts are zero, and they produce extreme, unreliable values for low-count cells.
• EBGM Advantage: By borrowing strength from the entire database via the empirical Bayes prior, EBGM provides a stable, conservative estimate even for rare events, dramatically reducing false-positive flags in routine signal detection.

The 'empirical' in EBGM refers to the fact that the prior distribution is estimated directly from the data rather than being subjectively chosen. The MGPS algorithm fits a mixture of two Gamma distributions to the observed counts across all drug-event combinations in the database.

• First Component: Models the bulk of 'null' or non-associated pairs.
• Second Component: Models the tail of potentially associated pairs.
• Result: This data-driven prior allows the algorithm to adapt to the specific characteristics of the spontaneous reporting database being analyzed.

The foundational statistical framework for signal detection in spontaneous reporting databases. It quantifies whether a specific drug-event combination is reported more frequently than expected by comparing observed counts to a background expected value.

• Frequentist methods: Proportional Reporting Ratio (PRR), Reporting Odds Ratio (ROR)
• Bayesian methods: EBGM, Information Component (IC)
• Core assumption: independence between drug and event in the absence of a causal signal

A statistical technique that shrinks observed disproportionality scores toward a null value (typically 1.0 for ratio metrics) to prevent false-positive signals from drug-event pairs with very low report counts.

• Directly addresses the small-cell-count problem in sparse contingency tables
• The EBGM is the shrunken posterior mean of the relative reporting ratio
• Shrinkage magnitude is inversely proportional to the precision of the observed estimate
• Protects against flagging noise in the long tail of rare drug-event combinations

The specific Bayesian hierarchical model used to compute EBGM scores. MGPS extends the Gamma Poisson Shrinker to handle multi-item sets (drug-drug interactions, syndrome detection) and applies empirical Bayes estimation of prior hyperparameters.

• Models observed report counts as Poisson-distributed
• Places a mixture of two Gamma priors on the relative reporting ratios
• Prior parameters estimated directly from the data (empirical Bayes)
• Generates both EBGM and EB05 (lower 5th percentile of posterior) for conservative signal ranking

A frequentist disproportionality measure that serves as the unshrunken counterpart to EBGM. PRR is calculated as the ratio of the observed reporting rate for a specific drug-event pair to the expected reporting rate for that event across all other drugs.

• Formula: PRR = [a/(a+b)] / [c/(c+d)] using a standard 2x2 contingency table
• Highly susceptible to volatility with small cell counts
• Often used with minimum count thresholds (e.g., n ≥ 3) and chi-squared criteria
• EBGM can be understood as a Bayesian-regularized PRR

The end-to-end process in which EBGM serves as a quantitative triage tool. Disproportionality scores are computed across all drug-event combinations in a database, ranked, and subjected to clinical review.

• Triage: Rank drug-event pairs by EBGM or EB05 descending
• Signal Validation: Clinical assessment of top-ranked combinations for causality, confounding, and expectedness
• Prioritization: Focus human review on combinations with high posterior probability of a true association
• EBGM is a hypothesis-generating tool, not a confirmatory test

A Bayesian disproportionality metric closely related to EBGM, used primarily in the WHO Uppsala Monitoring Centre's VigiBase system. The IC is the logarithm (base 2) of the shrunken relative reporting ratio.

• IC = log₂(EBGM); an IC of 0 corresponds to an EBGM of 1 (no association)
• Positive IC values indicate higher-than-expected reporting
• Uses the same Gamma-Poisson shrinkage principles as MGPS
• Often reported with IC025, the lower 95% credibility interval bound