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Cited by 130Statistical Methods in Clinical TrialsMeta-analysis and systematic reviewsAdvanced Causal Inference Techniques

Understanding of interaction (subgroup) analysis in clinical trials

Open access
Brankovic, Milos, Kardys, Isabella, Steyerberg, Ewout W., Lemeshow, Stanley, Markovic, Maja, Rizopoulos, Dimitris, Boersma, Eric·2019·European Journal of Clinical Investigation
DOI 10.1111/eci.13145
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Abstract

Background: When the treatment effect on the outcome of interest is influenced by a baseline/demographic factor, investigators say that an interaction is present. In randomized clinical trials (RCTs), this type of analysis is typically referred to as subgroup analysis. Although interaction (or subgroup) analyses are usually stated as a secondary study objective, it is not uncommon that these results lead to changes in treatment protocols or even modify public health policies. Nonetheless, recent reviews have indicated that their proper assessment, interpretation and reporting remain challenging. Results: Therefore, this article provides an overview of these challenges, to help investigators find the best strategy for application of interaction analyses on binary outcomes in RCTs. Specifically, we discuss the key points of formal interaction testing, including the estimation of both additive and multiplicative interaction effects. We also provide recommendations that, if adhered to, could increase the clarity and the completeness of reports of RCTs. Conclusion: Altogether, this article provides a brief non‐statistical guide for clinical investigators on how to perform, interpret and report interaction (subgroup) analyses in RCTs.

AI snapshot

Written from the paper’s full text.

TL;DR

This article is a methodological guide for clinical investigators on interaction/subgroup analysis in randomized trials with binary outcomes and categorical covariates. It explains that interaction depends on additive versus multiplicative scale, shows how to calculate and interpret AERI, RERI, and modified AP, and recommends prespecification and reporting both scales with confidence intervals.

Key findings

  • Interaction presence and direction can differ by scale: in a hypothetical example, women and men both had a 2% risk difference (no additive interaction), but risk ratios were 3 in women and 2 in men (multiplicative interaction); logistic and Cox models test multiplicative interaction, while linear models test additive interaction.
  • In the Head et al. example, 5-year mortality risks were 15.7% (diabetes/PCI), 8.4% (no diabetes/CABG), 10.7% (diabetes/CABG), and 8.7% (no diabetes/PCI); AERI was 4.7% and modified AP was 0.64, suggesting a super-additive interaction and that 64% of the joint effect was due to interaction.
  • In the Andrews et al. example, RERI was 3.55 − 1.91 − 3.09 + 1 = −0.45, suggesting a sub-additive interaction between sepsis-protocol treatment and lower Glasgow coma score.
  • Prior reviews cited found reporting gaps: Assmann et al. (50 RCTs) reported 70% tested interactions, 43% reported the test used, and 37% reported P-values only; Wang et al. (97 RCTs) reported 61% tested interactions, 68% unclear whether prespecified or post hoc, and 27% formal testing; Wallach et al. found 61% of RCTs claiming subgroup heterogeneity in abstracts were not supported by results. Recommendations include reporting both multiplicative and additive interaction effects with 95% CIs, specifying prespecified versus post hoc analyses, reporting subgroup counts and effects using the lowest-risk subgroup as reference, and replicating interactions in subsequent trials.

Methods

  • Design: narrative methodological overview/guide for clinical investigators, focused on binary outcomes and categorical covariates; describes stratification and interaction modelling (treatment + baseline factor + treatment × baseline factor).
  • Data or sample: no new dataset; uses a hypothetical example and re-analyses of published RCT examples (Head et al. and Andrews et al.) to illustrate calculations.
  • Main analysis: explains additive versus multiplicative scales, formulas for AERI, RERI, and modified AP, and provides recommendations for interpretation and reporting; notes available SAS, STATA, R, and Excel code.

Limitations

  • Stated: RCTs are often underpowered to detect subgroup treatment differences; post hoc subgroup analyses may be data-driven; AERI requires absolute risks and unbiased risks; RERI can assess only direction, not magnitude, of additive interaction; unknown confounding cannot be completely excluded from trial data.
  • Stated: interaction meaning is not consistent across statistical models/effect measures, and ratios are asymmetrically distributed, requiring recoding before RERI calculation.
  • Evident: this is a brief non-statistical guide/narrative overview using selected examples, not a systematic review or original empirical study; no formal search strategy, sample, or quantitative synthesis is reported.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1111/eci.13145

Cites

34 of 34 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 37 cited sources checked · 0 supported · 0 flagged

  • Interpretationreasoning

    Because RERI and the synergy index operate with ratios instead of absolute risks, they can only be used to assess the direction, and not the magnitude, of additive interaction for absolute risks, as AERI can.

    “Because these indices operate with ratios (derived from logistic or Cox regression models) instead of absolute risks, they can only be used to assess the direction, and not the magnitude, of additive interaction for absolute risks, as AERI can.”
    Quote in the paperSubstantial claim
  • Premisecitation

    37% of studies testing interaction reported P-values only.

    “In 2000, Assmann et al 3 reviewed 50 RCTs in high-impact journals and found that 70% of trials tested interactions, but only 43% of the studies testing interaction reported the test they used, and 37% of them reported P-values only.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [3] source

      Not checked in the free run.

  • Premisenone given

    Previous reviews of interaction analysis did not consider certain statistical aspects that are important for analysis and interpretation of the results.

    “These reviews were informative but did not consider certain statistical aspects which are important for analysis and interpretation of the results.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning

    Assuming the AERI of 4.7% is unbiased, the direction alone (AERI >0), rather than its magnitude, is what matters for answering whether diabetic patients should be treated with CABG over PCI.

    “Assuming this AERI of 4.7% is unbiased, then the direction alone (AERI >0), rather than its magnitude (4.7%), is important to answer the question whether diabetic patients should be treated with CABG over PCI.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The AERI of 4.7% calculated for the Head et al data is unbiased.
  • Premisecitation

    In a review of 50 RCTs in high-impact journals, 70% of trials tested interactions.

    “In 2000, Assmann et al 3 reviewed 50 RCTs in high-impact journals and found that 70% of trials tested interactions, but only 43% of the studies testing interaction reported the test they used, and 37% of them reported P-values only.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [3] source

      Not checked in the free run.

  • May combine two claims. 19
  • Classified as probably not a substantial claim. 7

  • May combine two claims.

    Findingreasoning

    AERI calculated from the Head et al data is 4.7%, suggesting a super-additive interaction between diabetes and PCI.

    “We calculate AERI using equation 4 from Table 2 as 15.7 + 8.4-10.7-8.7 = 4.7%, suggesting a super-additive interaction between diabetes and PCI.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [16] source

      Not checked in the free run.

    • The authors state this as an assumption: The AERI of 4.7% calculated for the Head et al data is unbiased.

  • May combine two claims.

    Findingreasoning

    In the Head et al study, modified AP is 0.64, suggesting a super-additive interaction and indicating that 64% of the joint effect is due to the interaction between diabetes and PCI.

    “In the study by Head et al, modified AP can be calculated using equation 8 from Table 2 as 4.7 15.7-8.4= 0.64 suggesting a super-additive interaction.It also indicates that 64% of the joint effect is due to the interaction itself between diabetes and PCI”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [16] source

      Not checked in the free run.

  • May combine two claims.

    Findingown data

    RERI calculated from the Andrews et al data is -0.45, suggesting a sub-additive interaction between the sepsis-protocol treatment and the lower GCS score.

    “we calculated RERI using equation 5 from Table 2 as 3.55-1.91-3.09+ 1 = -0.45.The RERI suggested a sub-additive interaction (RERI <0) between the sepsis-protocol treatment and the lower GCS score.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisecitation

    From the public health perspective, additive effects are favourable over multiplicative effects to increase the net benefit by allocating the treatment to the proper subgroup.

    “At the same time, from the public health perspective, additive effects are favourable over multiplicative effects to increase the net benefit by allocating the treatment to the proper subgroup.12,13”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [12] source

      Not checked in the free run.

    • cites [13]

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In 2006, Hernandez et al reported similar results after investigating published cardiovascular RCTs.

    “In 2006, Hernandez et al 4 reported similar results after investigating published cardiovascular RCTs.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [4] source

      Not checked in the free run.

  • May combine two claims.

    Premisereasoning

    In a linear regression model, the beta coefficient for an interaction term estimates a deviation from the sum of treatment subgroup effects, implying that a linear regression model uses an additive scale for interaction testing.

    “In a linear regression model, the β coefficient for an interaction term estimates a deviation from the sum of treatment subgroup effects.This implies that a linear regression model utilizes an additive scale for interaction testing.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given

    The AERI can only be calculated if absolute risks are known, and under the assumption that the risks are unbiased (without confounding).

    “The AERI can only be calculated if absolute risks are known, and under the assumption that the risks are unbiased (ie without confounding).”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The absolute risks used to calculate AERI are unbiased (i.e., without confounding).

  • May combine two claims.

    Premisereasoning

    In logistic and Cox regression models, a ratio for an interaction term estimates a deviation from the product of treatment subgroup effects, implying that these exponential models use a multiplicative scale for interaction testing.

    “In logistic and Cox regression models, a ratio for an interaction term estimates a deviation from the product of treatment subgroup effects.This implies that these exponential models utilize a multiplicative scale for interaction testing.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    A few reports have addressed some of these statistical aspects but were mainly intended for an epidemiological audience.

    “To date, a few reports 8,9 have addressed some of these aspects but they were mainly intended for an epidemiological audience.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [8] source

      Not checked in the free run.

    • cites [9] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    The benefits of interaction testing in regression models include multivariable adjustment, testing interactions between more than two factors and continuous factors, and testing treatment effects across subgroups defined by a risk model.

    “The benefits of interaction testing in regression models include the following: multivariable adjustment, testing interactions between >2 factors and continuous factors, and testing treatment effects across subgroups defined by a risk model.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    In 2007, Wang et al evaluated 97 RCTs, of which 61% tested interactions.

    “In 2007, Wang et al 1 evaluated 97 RCTs of which 61% tested interactions, but in 68% of the studies testing interaction, it was unclear whether analyses were prespecified”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    An interaction does not have a consistent meaning across statistical models, because different models estimate different effect measures.

    “Of note is that an interaction does not have a consistent meaning across statistical models.This is because different models estimate different effect measures”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The 95% CI for RERI can be calculated using the delta method or the first percentile Bootstrap method, the latter being more suitable for continuous factors.

    “The 95% CI for RERI can be calculated using the delta method 22 or using the first percentile Bootstrap method.23 The latter is more suitable for continuous factors. 15”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [22] source

      Not checked in the free run.

    • cites [23] source

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    • cites [15] source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    In the Head et al study, the 5-year mortality risk was 15.7% in patients with diabetes treated with PCI, 8.4% in patients without diabetes treated with CABG, 10.7% in patients with diabetes treated with CABG, and 8.7% in patients without diabetes treated with PCI.

    “In their study, the 5-year mortality risk was 15.7% in patients with diabetes treated with PCI, 8.4% in patients without diabetes treated with CABG, 10.7% in patients with diabetes treated with CABG, and 8.7% in patients without diabetes treated with PCI.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [16] source

      Not checked in the free run.

  • May combine two claims.

    Premisereasoning

    Randomization accounts for unbiased comparability of treatment arms but does not account for imbalances between the subgroups themselves that affect the outcome.

    “This is because randomization accounts for unbiased comparability of treatment arms, but does not account for imbalances between the subgroups themselves that affect the outcome.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    RCTs are principally conducted assuming homogeneous effects of the treatment within subgroups, and based on this assumption sample size is usually calculated by estimating only one (relative) effect supposed to hold for all eligible participants.

    “Randomized clinical trials are principally conducted assuming homogeneous effects of the treatment within subgroups.Based on this assumption, sample size is usually calculated by estimating only one (relative) effect that is supposed to hold for all eligible study participants.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    In the Andrews et al RCT, treatment based on a sepsis protocol increased in-hospital mortality compared to usual care in septic patients with hypotension, and this was only the case in the subgroup with normal Glasgow coma score (GCS >=13) at baseline.

    “Consider another RCT by Andrews et al, 27 who found that treatment based on a sepsis protocol has paradoxically increased in-hospital mortality compared to usual care in septic patients with hypotension.They reported that this was only the case in the subgroup of patients with normal Glasgow coma score (GCS ≥13) at baseline.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationnone given

    The best way to validate a statistical interaction is to replicate it in subsequent trials.

    “Finally, the best way to validate a statistical interaction is to replicate it in subsequent trials.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisenone given

    Although randomization accounts for comparability between treatment arms even across subgroups, imbalances can still occur due to chance.

    “Although randomization accounts for comparability between treatment arms even across subgroups, imbalances can still occur due to chance.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Statistical interaction between the treatment and a baseline/demographic factor can be interpreted as effect-measure modification or as causal interaction.

    “Statistical interaction between the treatment and a baseline/demographic factor can be interpreted as effect-measure modification or as causal interaction.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [30] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    In the Head et al study, the subgroup analysis would validly indicate that CABG is more effective than PCI in diabetic patients, but concluding that diabetes itself is responsible for the subgroup effects requires controlling for other baseline factors affecting survival that are unequally distributed between subgroups.

    “The subgroup analysis would validly indicate that CABG is more effective than PCI in diabetic patients.However, concluding that diabetes itself is responsible for the subgroup effects is only possible if the investigators had controlled for other baseline factors that affect patient survival and are unequally distributed between the subgroups.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [16] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    For effect-measure modification, controlling for confounding is generally unnecessary but can be helpful in some instances.

    “For effect-measure modification, controlling for confounding is generally unnecessary but can be helpful in some instances.”
    Quote in the paperSubstantial claim
22 of 22

  • The authors state this as an assumption.

    The absolute risks used to calculate AERI are unbiased (i.e., without confounding).

    “The AERI can only be calculated if absolute risks are known, and under the assumption that the risks are unbiased (ie without confounding).”

  • The authors state this as an assumption.

    The AERI of 4.7% calculated for the Head et al data is unbiased.

    “Assuming this AERI of 4.7% is unbiased, then the direction alone (AERI >0), rather than its magnitude (4.7%), is important to answer the question whether diabetic patients should be treated with CABG over PCI.”
2 of 2

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Cites

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Research works printed but not linked: 1

  1. Rothman KJ, 2008, Modern Epidemiology

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Related

Authors
Brankovic, M., Kardys, I., Steyerberg, E. W., Lemeshow, S., Markovic, M., Rizopoulos, D., & Boersma, E.
Affiliations
  • Erasmus MC (NL)
  • Leiden University Medical Center (NL)
  • The Ohio State University (US)
Corresponding author
Boersma, Eric
ORCID
Venue
European Journal of Clinical Investigation
Publisher
Wiley
Published
2019-06-14
Volume
49
Issue
8
Pages
e13145-e13145
ISSN
  • 0014-2972 (ISSN-L)
  • 1365-2362
DOI
10.1111/eci.13145
OpenAlex
W2947669221
Semantic Scholar
27e2342ff1b5b6a9401f6e4515a4d6b147a303e7
Cited by
130
References
34
Citations by year
2026: 22 · 2025: 17 · 2024: 24 · 2023: 24 · 2022: 13 · 2021: 24 · 2020: 6
FWCI
1.57
Type
journal article
Language
en
Open access
Licence
Locations
  • European Journal of Clinical Investigation (publishedVersion, cc-by-nc)
  • PubMed (publishedVersion)
  • EUR Research Repository (Erasmus University Rotterdam) (acceptedVersion, other-oa)
  • EUR Research Repository (Erasmus University Rotterdam) (submittedVersion, other-oa)
  • RePub (Erasmus University Rotterdam) (submittedVersion, other-oa)
  • Data Archiving and Networked Services (DANS) (submittedVersion)
  • Leiden Repository (Leiden University) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords
interaction analysis, subgroup analysis, treatment effect modification, binary outcomes, additive interaction, multiplicative interaction, interaction testing, randomized controlled trials, baseline covariates
MeSH terms
Data Interpretation, Statistical, Humans, Models, Statistical, Randomized Controlled Trials as Topic

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