Stratified Analysis¶
Stratification method — instantiates Confounder Control
Splits the data into strata within which a confounder is held roughly constant, estimates the exposure-outcome relationship inside each, then interprets or pools the stratum-specific results.
Stratified Analysis controls a confounder by refusing to let it vary within a comparison: it divides the data into strata inside which the confounder is (nearly) constant, estimates the exposure-outcome relationship in each stratum, and then either pools the pieces or reports them separately. What sets it apart from its siblings is that it is non-parametric — it imposes no model form on how the confounder relates to the outcome — and that it therefore makes effect modification visible: if the exposure's effect genuinely differs across strata, stratification shows it rather than averaging it away. It is the mechanism that catches a Simpson reversal, where an aggregate relationship flips once the confounder is conditioned on.
Example¶
A university's overall figures show women admitted at a lower rate than men, which looks like admissions bias (exposure = applicant gender, outcome = admission). Stratified Analysis conditions on the obvious common cause — the department applied to — by computing admission rates within each department. Department by department, the rates are roughly equal or slightly favor women; the aggregate gap arose because women applied disproportionately to the most competitive, low-admit departments.
Conditioning on the confounder reverses the headline — the hallmark of Simpson's paradox.[n1] The stratified picture is not just "less biased"; it is qualitatively different, and it also answers a question a single number cannot: whether the exposure's effect is uniform across departments or varies among them.
How it works¶
The distinguishing procedure is to condition by partitioning rather than modeling: split on the confounder, estimate the exposure effect within each stratum where the groups are now comparable on that confounder, then decide whether to pool. Pooling (via standardization or a Mantel-Haenszel summary) is appropriate only when the stratum-specific effects are homogeneous; when they differ, the honest output is the set of stratum-specific effects, not an average that hides the heterogeneity. No functional form is assumed, which is exactly why the method scales poorly past a few confounders.
Tuning parameters¶
- Stratifying variable(s) — which confounder(s) define the strata; each must be a genuine common cause, not a mediator.
- Number and width of strata — finer strata control the confounder more tightly but empty the cells, yielding sparse, unstable within-stratum estimates.
- Pooling rule — pool under an assumption of homogeneity, or report per stratum to preserve effect modification.
- Standardization weights — when pooling, which population's distribution the combined estimate is standardized to, and thus which target it speaks to.
When it helps, and when it misleads¶
Its strength is transparency with few assumptions: anyone can see the within-stratum comparisons, and it exposes both confounding and effect modification — including Simpson reversals — that a single fitted model would silently blend.
Its binding limit is dimensionality. You can stratify on one or two confounders before the cells thin out; controlling many at once empties the strata and destabilizes the estimates — the exact situation where regression-based adjustment takes over. The classic misuse is pooling across strata whose effects genuinely differ, presenting one averaged number that conceals a real interaction. The discipline is to test for homogeneity before pooling and to report per-stratum effects when they diverge.
How it implements the components¶
adjustment_strategy— stratification is itself a confounder-adjustment strategy: conditioning on the confounder by partition rather than by model, then aggregating.comparability_check— within each stratum the exposed and unexposed groups are comparable on the stratifying confounder, and the within-stratum contrast is where that comparability is verified.
It does not scale to many confounders simultaneously (regression-based Statistical Adjustment does), and it does not decide which variable to stratify on (that comes from Causal Diagramming's adjustment set).
Related¶
- Instantiates: Confounder Control — Stratified Analysis adjusts for a confounder by conditioning within strata.
- Consumes: Causal Diagramming supplies the confounder to stratify on.
- Compare: Stratified Analysis Protocol shares the split-into-strata move but is a pre-registered subgroup-audit discipline whose output is an audited breakdown table with a cell-size floor, diagnosis-agnostic. This page is a confounder-adjustment estimation method: its output is the de-confounded effect, and it is what catches a Simpson reversal.
- Sibling mechanisms: Statistical Adjustment · Matched Comparison · Causal Diagramming · Random Assignment · Control Group Design · Restriction or Eligibility Control · Instrumental Variable Strategy · Sensitivity Analysis for Unmeasured Confounding · Negative Control Check
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Stratified Analysis operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it splits the data into strata within which a confounder is held roughly constant, estimates the exposure-outcome relationship inside each, then interprets or pools the stratum-specific results.
Independent corroboration: The frozen evidence defines Stratified Analysis as 'Splits the data into strata within which a confounder is held roughly constant, estimates the exposure-outcome relationship inside each, then interprets or pools the stratum-specific results', so its operative form is Analysis, Modeling & Optimization.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Statistics & Experimental Design
Origin pattern: Single lineage
Present-day reach: Multi-domain
Rationale: Conditioning within confounder strata is canonical epidemiological statistics.
Related originating lineages:
- Data Science & Analytics — Data science, analytics, and operational monitoring supplies a parallel or contributing lineage for the mechanism's defining operation: splits the data into strata within which a confounder is held roughly constant, estimates the exposure-outcome relationship inside each, then interprets or pools the….
- Mathematics — Mathematical modeling, proof, and abstract-structure practice supplies a parallel or contributing lineage for the mechanism's defining operation: splits the data into strata within which a confounder is held roughly constant, estimates the exposure-outcome relationship inside each, then interprets or pools the….
- Medicine & Healthcare — Epidemiology institutionalized stratification.
Review resolution: The blind reviewers agree that statistics_experimental_design is the primary origin and differ only on alternate origin disagreement, domain reach disagreement. I preserve every independently explained alternate from both records rather than imposing a numeric cap. I retain single_lineage because the combined evidence shows one traceable formative lineage. The broader reach of multi_domain records portability separately from historical provenance; encyclopedia_synthesis=false preserves the affirmative synthesis judgment where either reviewer identified one.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] Simpson's paradox is the reversal or disappearance of an aggregate association once the data are split by a confounder. Stratification is the standard way to reveal it — and the reason a pooled estimate should not be trusted until the stratum-specific effects have been inspected for heterogeneity. ↩