03 · What You Need to Know
Planning and Interpreting Subgroup Analyses Responsibly
What Is a Subgroup Analysis?
A subgroup analysis examines a research finding within defined subsets of a study population or investigates whether an effect or association varies according to participant characteristics.
Subgroups may be defined by age, baseline performance, disease severity, institutional setting, digital access, or other relevant characteristics.
For example, researchers may examine whether an educational intervention's effect on writing performance differs according to students' baseline digital access.
However, describing results separately for two groups is not necessarily equivalent to formally testing whether the effect differs between them.
Researchers should distinguish subgroup-specific estimates from an analysis of effect modification.
What Is Effect Modification?
Effect modification occurs when the effect of an exposure or intervention differs across levels of another variable on a specified effect scale.
For example, an intervention may produce a larger mean improvement in writing performance among students with high baseline digital access than among those with limited access.
However, whether an interaction exists can depend on the effect measure and scale being examined.
A difference in risk differences does not necessarily imply a difference in risk ratios, and vice versa.
Researchers should therefore specify the relevant effect scale and scientific interpretation rather than treat effect modification as a property independent of the analytical framework.
How Does a Subgroup Analysis Differ From a Stratified Description?
Stratified description
Reports characteristics, outcomes, or estimates separately within defined groups without necessarily testing whether an effect differs between groups.
Effect-modification analysis
Evaluates whether the association or effect of interest differs across subgroup levels using an appropriate comparison or interaction framework.
Both approaches can be useful, but they answer different questions.
For example, reporting average writing scores separately by digital access may describe educational inequality. Testing whether the intervention effect varies by digital access addresses a different inferential question.
Why Should Important Subgroups Be Specified Before Data Collection?
Prospective specification reduces opportunities to select subgroups because they produce striking or statistically significant findings.
It also ensures that the necessary subgroup variables are collected using appropriate definitions and timing.
For example, baseline digital access must be measured if researchers intend to investigate whether it modifies the intervention effect.
Planning may also reveal whether the study contains enough participants and independent allocation units to support the intended comparisons.
However, prespecification does not guarantee that subgroup estimates will be precise or that an observed interaction represents a genuine difference.
Which Subgroup Variables Should Be Selected?
Subgroups should be selected according to a defensible scientific rationale.
Relevant considerations may include theory, prior empirical findings, plausible mechanisms, clinical or educational relevance, and the consequences of potential heterogeneity.
For example, baseline digital access may be relevant when evaluating an intervention that depends on reliable connectivity.
Researchers should avoid selecting subgroup variables solely because they are readily available or likely to produce significant results.
Where possible, subgroup variables should be measured before intervention or exposure to reduce complications arising from post-treatment selection.
Why Are Baseline Subgroups Often Preferable?
Baseline characteristics are measured before the intervention or exposure of interest and are therefore less likely to have been caused by that intervention.
For example, comparing intervention effects according to students' baseline writing proficiency may support a meaningful effect-modification question.
By contrast, defining subgroups according to whether students completed the intervention can introduce selection problems because completion may be influenced by treatment assignment and other characteristics.
Analyses conditioned on post-randomization variables may no longer preserve the comparability created by randomization.
Such analyses can be useful for certain questions, but they require appropriate causal assumptions and should not automatically be interpreted as ordinary randomized subgroup comparisons.
How Many Subgroup Analyses Should Be Planned?
There is no universal maximum number.
However, a large collection of subgroup tests increases opportunities for chance findings and complicates interpretation.
Researchers should prioritize comparisons with strong scientific justification and practical relevance.
The number of analyses should also reflect the study's sample size, expected precision, and inferential objectives.
For confirmatory subgroup claims, a prespecified multiplicity strategy may be necessary.
Exploratory subgroup analyses may be broader, provided their exploratory status and uncertainty are made explicit.
Why Is Comparing Statistical Significance Across Subgroups Misleading?
A common mistake is to conclude that an effect differs between groups because it is statistically significant in one subgroup but not in another.
Statistical significance depends partly on sample size and precision.
Two groups may have similar estimated effects but different p-values because one subgroup contains fewer observations.
Conversely, estimated effects may differ substantially while each individual subgroup estimate remains imprecise.
Researchers should directly evaluate the difference between effects rather than infer it from separate significance labels.
Gelman and Stern's discussion of differences between significant and nonsignificant results provides an important warning about this reasoning error.
How Are Interaction Effects Tested?
In regression-based analyses, effect modification is often evaluated by including an interaction term between the exposure or treatment variable and the subgroup variable.
For a continuous outcome and a binary subgroup, a simple linear model may take the following form:
In this model, the treatment effect when S equals zero is represented by β₁, while the treatment effect when S equals one is represented by β₁ + β₃.
The interaction coefficient β₃ represents the difference between these treatment effects under the specified linear model.
Other outcomes and models require appropriate interpretation. For example, interaction terms in logistic regression operate on the model's log-odds scale and should not automatically be interpreted as differences in absolute risks.
Should Subgroup Analyses Be Powered Separately?
Important confirmatory subgroup questions may require explicit sample-size or precision planning.
However, a study powered for the overall treatment effect is not necessarily powered to detect an interaction.
Interaction effects can be difficult to estimate precisely, particularly when subgroups are small or unevenly distributed.
Researchers should not assume that a large total sample guarantees adequate power for every subgroup comparison.
When subgroup analyses are exploratory, reporting confidence intervals and acknowledging limited precision may be more appropriate than making definitive claims.
How Do Unequal Subgroup Sizes Affect Interpretation?
Unequal subgroup sizes can produce different levels of statistical precision.
For example, a study may include substantially more students with reliable connectivity than students with limited connectivity.
The smaller subgroup may produce wider confidence intervals even when its estimated effect is similar.
Researchers should report subgroup sample sizes and uncertainty rather than interpret differences in statistical significance as evidence of heterogeneity.
Severe imbalance may also limit the feasibility of complex interaction models.
Should Continuous Subgroup Variables Be Categorized?
Not automatically. Categorizing a continuous variable can discard information and create artificial boundaries.
For example, dividing students into high and low baseline proficiency groups using an arbitrary cutoff may obscure how treatment effects vary across the proficiency distribution.
Where scientifically appropriate, researchers may model interactions with continuous variables or use flexible functional forms.
However, flexible models may require larger samples and careful interpretation.
If categories are necessary for a substantive or practical reason, their definitions should be justified and preferably specified prospectively.
Can Subgroup Analyses Be Conducted in Observational Studies?
Yes. Researchers may examine whether an association or estimated causal effect varies across population groups.
However, observational subgroup analyses must address the study's underlying confounding and selection problems.
Different subgroups may have different distributions of confounders, exposure opportunities, or measurement quality.
Researchers should therefore evaluate whether comparisons across groups support the intended interpretation.
An observed interaction in an observational regression model does not automatically establish causal effect modification.
Can Subgroup Analyses Be Used in Cluster Randomized Trials?
Yes, but the analysis must account for the clustered design.
For example, a trial randomizing classrooms may examine whether intervention effects differ by students' baseline digital access.
The analysis should account for within-classroom correlation and the relevant number of independent clusters.
Subgroups defined at the cluster level may present particular precision limitations when the number of clusters is small.
Researchers should consider these issues during sample-size planning for clustered and repeated-measures designs.
How Does Multiplicity Affect Subgroup Analysis?
Testing many subgroup interactions increases the possibility of chance findings.
The appropriate response depends on whether subgroup analyses are confirmatory or exploratory.
For confirmatory claims, researchers may need to control a relevant error rate or establish a hierarchical testing procedure.
For exploratory analyses, explicit acknowledgment of multiplicity, cautious interpretation, and independent confirmation may be appropriate.
Researchers should not interpret an isolated statistically significant interaction without considering the number of comparisons performed and the plausibility of the finding.
Can Subgroup Analyses Be Added After Data Collection?
Yes. Unexpected findings may generate legitimate questions about heterogeneity.
However, analyses developed after observing results should be identified as exploratory or post hoc.
For example, a researcher may notice that an intervention appears particularly effective among students using a particular device type.
This observation may justify further investigation, but it does not automatically establish a reliable subgroup effect.
The analysis may be affected by multiple testing, sparse data, measurement differences, or chance.
Independent replication or a prospectively designed subsequent study may be needed before making strong claims.
What Makes a Subgroup Finding Credible?
Credibility depends on more than a statistically significant interaction.
Relevant considerations include prior scientific rationale, prospective specification, appropriate statistical testing, adequate precision, consistency with related evidence, and the plausibility of the proposed explanation.
Sun and colleagues developed criteria for assessing the credibility of subgroup effects in randomized trials.
These criteria provide a structured way to examine subgroup claims, although no checklist can guarantee that an observed interaction is genuine.
Researchers should evaluate the totality of evidence rather than treat one criterion as decisive.
Should Subgroup Findings Change Practice or Policy?
Potentially, but the strength of the evidence matters.
A credible and sufficiently precise subgroup effect may inform decisions about targeting or adapting an intervention.
However, exploratory subgroup findings should rarely be treated as definitive evidence that an intervention should be restricted to one population.
For example, an educational intervention should not automatically be withheld from students with limited digital access because a small subgroup analysis produced an imprecise estimate.
Researchers should consider the overall evidence, uncertainty, practical consequences, and whether the finding has been independently supported.
How Should Subgroup Analyses Be Included in the SAP?
The statistical analysis plan should identify the subgroup variable, its measurement timing, coding, scientific rationale, and the intended comparison.
It should also specify the analytical model, interaction test, effect scale, uncertainty measures, and any relevant multiplicity procedure.
For important confirmatory analyses, the plan should consider whether the sample supports the intended interaction claim.
Researchers should distinguish subgroup-specific descriptive estimates from formal tests of heterogeneity.
The broader requirements for statistical analysis plan detail also apply to subgroup analysis planning.
How Should Subgroup Findings Be Reported?
Reports should present the subgroup definitions, sample sizes, effect estimates, confidence intervals, and relevant interaction results.
Researchers should disclose whether analyses were prespecified and how many subgroup comparisons were examined.
Forest plots may help display estimates and uncertainty across groups, but their visual presentation should not replace appropriate interaction testing.
Subgroup findings should be interpreted in relation to the primary analysis and the study's inferential limitations.
Researchers should avoid selectively reporting only subgroups with statistically significant results.
Watch Out
A statistically significant treatment effect in one subgroup and a nonsignificant effect in another do not establish a statistically significant difference between subgroup effects. Evaluate the interaction directly and consider its precision, scientific plausibility, and multiplicity.
