Questions: Stratified Analysis and Adjustment for Confounding

Question 1

A study of aspirin use and stroke finds a crude OR = 0.5, suggesting strong protection. After stratifying by age, the OR is 0.85 in younger adults and 0.80 in older adults. What does this pattern indicate?

• A. Age is an effect modifier; stratum-specific ORs must be reported separately
• B. The crude OR is still the most valid estimate because it reflects the real-world distribution of age
• C. Negative confounding was present — age made aspirin appear more protective than it is; the adjusted estimate near 0.82 is more valid
• D. The study should be discarded because the crude and adjusted estimates disagree

Answer: (C)

The stratum-specific ORs (0.85, 0.80) are homogeneous — no effect modification — but both differ from the crude OR (0.5). This is classic negative confounding: age was associated with both aspirin use and stroke risk in a way that exaggerated aspirin's protective effect. Within strata, age cannot confound because it does not vary. The Mantel-Haenszel adjusted OR near 0.82 is the valid, confounder-controlled estimate.

Question 2

A study of a new drug finds OR = 0.5 among women and OR = 3.0 among men. A researcher computes a Mantel-Haenszel summary OR of 1.1 and plans to report it as the confounder-adjusted estimate. What is wrong with this approach?

• A. The Mantel-Haenszel method requires at least three strata to be valid
• B. The large difference between stratum-specific ORs indicates effect modification; combining them into a single summary obscures a real and clinically important difference
• C. A summary OR of 1.1 is too close to the null and therefore meaningless
• D. Nothing is wrong; combining stratum-specific estimates via Mantel-Haenszel is always appropriate after stratification

Answer: (B)

Substantial heterogeneity across strata — OR = 0.5 versus OR = 3.0 — signals effect modification, not simple confounding. Sex is not just distorting the overall estimate; the drug's effect is genuinely different in men and women. A summary OR of 1.1 would falsely suggest near-null association and hide both the benefit in women and the harm in men. When effect modification is present, stratum-specific estimates must be reported.

Question 3

Within a stratum defined by a single level of a confounder (e.g., all current smokers), that confounder cannot distort the exposure-outcome association because it does not vary within the stratum.

• T. True
• F. False

Answer: True

Confounding requires the confounder to be associated with both the exposure and the outcome. Inside a stratum where everyone has the same confounder value, there is no variation — so there is no association between the confounder and exposure or outcome within that stratum. The distortion disappears, and the stratum-specific exposure-outcome estimate reflects the true association.

Question 4

When stratum-specific effect estimates differ substantially across strata, the Mantel-Haenszel method should be used to pool them into a single confounder-adjusted summary estimate.

• T. True
• F. False

Answer: False

Substantial heterogeneity across strata means the stratifying variable is an effect modifier, not merely a confounder. The Mantel-Haenszel estimator assumes homogeneity — that a single underlying effect exists across strata. Pooling heterogeneous estimates produces a misleading average that correctly describes no subgroup. The right response is to report stratum-specific estimates and describe the interaction.

Question 5

Stratified analysis simultaneously controls for confounding and tests for effect modification. Explain why these two goals lead to different decisions about how to report results.

Model answer: If stratum-specific estimates are homogeneous (similar across strata), the stratifying variable is a confounder and a single Mantel-Haenszel adjusted estimate is appropriate — it removes the distortion while efficiently summarizing the exposure effect. If stratum-specific estimates differ substantially, the variable modifies the effect — the association is genuinely different across groups. In that case, a combined summary misrepresents reality and stratum-specific estimates must be reported separately to capture who benefits and who is harmed.

The decision hinge is heterogeneity: homogeneous strata → confounding → combine; heterogeneous strata → effect modification → report separately. Failing to distinguish these leads either to spurious summary estimates or to missed interactions that are central to clinical and public health decisions.