Cited by 338Statistical Methods in EpidemiologyStatistical Methods in Clinical TrialsAdvanced Causal Inference Techniques

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Shrinkage observed-to-expected ratios for robust and transparent large-scale pattern discovery

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Norén, G Niklas, Hopstadius, Johan, Bate, Andrew·2013·Statistical Methods in Medical Research

DOI 10.1177/0962280211403604PMC PMC6331976

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Abstract

Large observational data sets are a great asset to better understand the effects of medicines in clinical practice and, ultimately, improve patient care. For an empirical pattern in observational data to be of practical relevance, it should represent a substantial deviation from the null model. For the purpose of identifying such deviations, statistical significance tests are inadequate, as they do not on their own distinguish the magnitude of an effect from its data support. The observed-to-expected (OE) ratio on the other hand directly measures strength of association and is an intuitive basis to identify a range of patterns related to event rates, including pairwise associations, higher order interactions and temporal associations between events over time. It is sensitive to random fluctuations for rare events with low expected counts but statistical shrinkage can protect against spurious associations. Shrinkage OE ratios provide a simple but powerful framework for large-scale pattern discovery. In this article, we outline a range of patterns that are naturally viewed in terms of OE ratios and propose a straightforward and effective statistical shrinkage transformation that can be applied to any such ratio. The proposed approach retains emphasis on the practical relevance and transparency of highlighted patterns, while protecting against spurious associations.

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Figure 1. Schematic overview of an interaction between two conditions A and B relative to an additive baseine model. The bars correspond to the frequency of the event of interest (1) in the absence of both A and B, (2) with A but not B, (3) with B but not A, and (4) with A and B together. The shades correspond to: the marginal relative frequency of the event (lightest), the increased frequency attributable to A, the increased frequency attributable to B, and the increased frequency attributable to an interaction between A and B (darkest).CC BY-NC · PubMed Central

Figure 2. Visualisation of OE ratios over time, for the association in a collection of electronic patient records between first prescriptions of an antihypertensive medicine and diagnoses of swelling. The top panel displays the logarithm of the OE ratio (with shrinkage) over time. The bottom panel displays the underlying observed and expected numbers of events. Reproduced from Norén et al. [9] with permission from Springer.CC BY-NC · PubMed Central

Figure 3. Visualisation of the retrospective evolution over time of the OE ratio for the association between fluoxetine and neonatal withdrawal syndrome in the WHO Global Individual Case Safety Reports database, VigiBase. The top panel displays the logarithm of the OE ratio (with shrinkage) over time. The bottom panel displays the underlying observed and expected numbers of events.CC BY-NC · PubMed Central

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Authors: Norén, G. N., Hopstadius, J., & Bate, A.
Affiliations: Uppsala Monitoring Centre (SE)
Corresponding author: Norén, G Niklas
ORCID: Norén, G Niklas
Bate, Andrew
Venue: Statistical Methods in Medical Research
Publisher: SAGE Publications
Published: 2011-06-24
Volume: 22
Issue: 1
Pages: 57-69
ISSN: 0962-2802 (ISSN-L)
1477-0334
DOI: 10.1177/0962280211403604
PMC: PMC6331976
OpenAlex: W2005366883
Cited by: 336
References: 26
Citations by year: 2026: 45 · 2025: 45 · 2024: 48 · 2023: 46 · 2022: 53 · 2021: 21 · 2020: 17 · 2019: 9 · 2018: 11 · 2017: 5 · 2016: 5 · 2015: 8 · 2014: 10 · 2013: 7 · 2012: 6
FWCI: 6.43
Type: journal article
Language: en
Open access: hybrid
doi.org
Licence: cc-by-nc
journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations: Statistical Methods in Medical Research (publishedVersion, cc-by-nc)
Europe PMC (PubMed Central) (publishedVersion, cc-by-nc)
PubMed Central (publishedVersion, cc-by-nc)
PubMed (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords: observed-to-expected ratio, pattern discovery, observational data, spurious association, rare events, higher-order interactions, temporal association, associative strength, clinical practice
MeSH terms: Models, Statistical

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