The third variable can matter in different ways
Suppose a study compares an exposure with an outcome and notices that age matters. Age could affect who receives the exposure and also relate to the outcome, creating a confounding problem. Alternatively, the exposure’s effect could differ across age groups. Both situations involve age, but they are not the same explanation.
CDC’s field epidemiology guidance distinguishes confounding from effect modification and discusses examining results within strata. The distinction is about the role of the variable in the question, not a permanent label attached to the variable itself.
A hypothetical confounding example
Imagine a nonrandomized comparison of two services. People with more severe needs are more likely to receive Service A and are also more likely to experience an adverse outcome. If Service A’s recipients have worse outcomes, the crude comparison could partly reflect the severity difference rather than the service’s effect.
An appropriate adjustment may address measured severity, depending on the design and assumptions. It cannot automatically address severity that was poorly measured or not recorded. Nor does adding every available variable necessarily improve the causal estimate; some variables may lie on the pathway of interest or create other bias when conditioned on.
The key is defining the effect being estimated and understanding why the groups differ. Confounding is not simply any correlation with a third variable or any change in a coefficient after adjustment.
A hypothetical effect-modification example
Now imagine an intervention reduces an event from 20% to 10% in one group and from 4% to 2% in another. The relative risk is 0.5 in both groups: a halving of risk. The absolute reductions differ, however: 10 percentage points versus 2 percentage points.
| Group | Without intervention | With intervention | Absolute reduction |
|---|---|---|---|
| A | 20% | 10% | 10 percentage points |
| B | 4% | 2% | 2 percentage points |
These invented figures illustrate why the scale needs to be named. There is no modification of the risk ratio in this example, but the risk difference varies. Saying simply that the effect is “the same” or “different” loses that distinction.
For some decisions, an absolute difference is especially relevant because it describes how many events differ over a stated period. For other questions, a relative comparison may be useful. The scales need not produce identical descriptions.
Why adjustment and subgroup analysis have different aims
An adjusted overall estimate may aim to reduce confounding. A subgroup analysis may aim to describe how an effect varies. Combining groups into one average can be useful for one purpose while hiding a relevant difference for another.
The tasks can also occur together. A study may need to address confounding within each subgroup before interpreting subgroup effects. Observing different associations does not automatically establish causal effect modification. Measurement differences, selection, or random variation could also contribute.
This is why the causal question and study design remain important even when the table looks straightforward. Stratifying data creates smaller comparisons; it does not automatically make those comparisons unbiased.
The significance trap
Suppose an estimate is statistically significant in a large subgroup and nonsignificant in a smaller subgroup. That does not establish that the effects differ. The smaller group may simply have a less precise estimate. A comparison of the effects, with appropriate uncertainty, addresses the subgroup-difference question more directly.
Sun and colleagues’ methodological discussion emphasizes evaluating interaction rather than relying on separate significance labels. It also considers whether subgroup claims were anticipated and supported by the broader evidence. Testing many possible subgroups increases opportunities to encounter striking patterns by chance.
Prespecified does not mean proven
A subgroup hypothesis identified before analysis is easier to distinguish from one selected because it looked interesting afterward. That transparency improves interpretation, but it does not guarantee the hypothesis is correct. Estimates can still be imprecise, and replication or other evidence may be needed.
Exploratory subgroup findings can also be useful when described as exploratory. The problem is promoting a tentative pattern into a settled claim without acknowledging how it was found and how uncertain it remains.
What a precise explanation would say
A clear report names the exposure, outcome, population, and effect scale. It explains which factors were treated as confounders and why, then distinguishes any evidence of differing effects across groups. That structure makes the analysis more understandable than referring vaguely to “controlling for variables” or announcing that something worked for one group but not another.
