Confounding and effect modifier explanation -psm topic

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Confounding and Effect Modification (Effect Modifier) - PSM / Epidemiology

CONFOUNDING

Definition

A confounder is a third variable that distorts the observed association between an exposure and an outcome. It is a source of bias in non-randomized (observational) studies.

Confounding diagram showing Exposure → Disease (true causal), with a Confounder associated with both exposure and disease

Fig: Confounding - the blue arrow = true causal association; the purple path = spurious apparent association due to the confounder.

The Three Mandatory Criteria for a Confounder

A variable must satisfy ALL THREE criteria simultaneously:

Criterion	Explanation
1. Associated with the exposure	It is related to the exposure (risk factor) being studied
2. Associated with the outcome	It is an independent risk factor for the disease/outcome
3. NOT on the causal pathway	It is not an intermediate step between exposure and outcome (i.e., not a mediator)

"A confounder is a factor that is (1) associated with the exposure, (2) associated with the outcome independent of exposure, and (3) not on the pathway between exposure and outcome." -- Firestein & Kelley's Textbook of Rheumatology

Classic Example

Study question: Does high-dose UV exposure cause cutaneous squamous cell carcinoma (SCC)?
Confounder: Age - older people spend more time outdoors (associated with UV exposure) AND are at higher risk of SCC (independent risk factor), but age is not in the causal pathway between UV and SCC.
Result: A crude (unadjusted) association may overestimate or underestimate the true UV-SCC relationship because of this age confounding.

PSM Classic Example (Park's Textbook)

In a study of alcohol and lung cancer: smoking is a classic confounder because:

Smokers tend to drink more (associated with exposure = alcohol)
Smoking causes lung cancer (independent risk factor for outcome)
Smoking is not on the causal pathway between alcohol and lung cancer

So apparent alcohol-lung cancer association may partly or fully reflect confounding by smoking.

Types of Confounding

Type	Description
Measured confounding	The confounder is identified and measured - can be adjusted for
Residual confounding	Confounder is imperfectly measured; adjustment is incomplete
Unmeasured confounding	Confounder not measured at all ("known unknown" or "unknown unknown")
Confounding by indication	The indication for a treatment is itself a risk factor for the outcome (channeling bias) - common in drug studies

How to Detect Confounding

Rule of thumb (Change-in-Estimate method):

$$\text{Magnitude of confounding} = \frac{|\text{RR}{crude} - \text{RR}{adjusted}|}{\text{RR}_{crude}} \times 100$$

If this value is ≥ 10%, confounding is likely present
Example: Crude RR = 1.05, Adjusted RR = 2.01 → magnitude = ~91% → strong confounding present

Note: There is no statistical test for confounding - it is assessed by the change-in-estimate approach.

Methods to Control Confounding

At the Design Stage:

Method	How it works
Randomization	Randomly allocates participants to groups, theoretically balancing both measured and unmeasured confounders - the gold standard
Restriction / Specification	Limit the study to only one level of the confounder (e.g., only women, only non-smokers). Reduces sample size.
Matching	Match cases to controls (or exposed to unexposed) on potential confounders (e.g., age-matched, sex-matched). Often used in case-control studies. Frequency matching (multiple controls per case) preserves power.

Park's PSM Note: "Bias due to confounding can be removed by matching in case-control studies."

At the Analysis Stage:

Method	How it works
Stratification	Analyze the exposure-outcome association separately in each stratum of the confounder; then pool using Mantel-Haenszel method
Multivariable regression	Include confounder(s) as covariates in regression model
Propensity score methods	Use logistic regression to estimate probability of exposure given baseline characteristics; can be used for matching, stratification, or weighting (IPTW)
Marginal structural models	Handle time-varying confounders in longitudinal data
Instrumental variables	Use a variable associated with exposure but not directly with outcome to estimate causal effect

EFFECT MODIFICATION (Effect Modifier)

Definition

An effect modifier (also called moderator or interaction variable) is a variable that changes the magnitude or direction of the association between the exposure and the outcome across its different levels (strata).

Unlike confounding, effect modification is a real biological phenomenon - it is NOT a bias
It is not something to be removed - it should be reported by stratification
It can be statistically measured (unlike confounding, which cannot be directly tested)

Effect Modification diagram showing Exposure (indoor tanning) → Disease (skin cancer) with Effect Modifier (age) modulating the strength at different levels (younger vs older)

Fig: Effect modification - the thickness of the arrow varies at different levels of the effect modifier (e.g., age), reflecting a stronger association in younger vs. older persons.

How Effect Modification Manifests

Effect modification can be:

Quantitative - associations in the same direction but different strength (e.g., RR = 3.0 in females vs. RR = 1.2 in males)
Qualitative - associations in opposite directions across strata (e.g., protective in one group, harmful in another)
Presence/absence - association present in one stratum, absent in another

Classic Example (from Dermatology textbook)

Exposure: Indoor tanning
Disease: Skin cancer
Effect modifier: Age
Finding: Women exposed to tanning beds in teenage/college years had HIGHER risk of BCC than those exposed later in life. Age modifies the exposure-disease relationship.

Another Clinical Example

Studying TNFi (TNF inhibitor) use and risk of infections:
- RR in females = 3.0
- RR in males = 1.2
- Conclusion: Sex is an effect modifier for this exposure-outcome association

Effect Modification vs. Interaction - Distinction

Feature	Effect Modification	Interaction
Symmetry	Asymmetric - the third variable modifies the effect of the exposure	Symmetric - two exposures jointly affect the outcome
Nature	One variable modifies the effect of another	Two variables have a joint effect beyond their individual effects
Example	Sex modifies the effect of a drug	Smoking interacts with anti-TNF therapy (smokers respond poorly - biological interaction)
Both	Can be assessed on multiplicative scale (RR, OR, HR) and additive scale (risk difference)

KEY COMPARISON: Confounding vs. Effect Modification

Feature	Confounding	Effect Modification
Nature	A bias / nuisance	A real biological phenomenon
Goal	To be controlled / eliminated	To be identified and reported
What to do?	Adjust for it (restrict, match, stratify, regression)	Stratify and report separately for each level
Statistical test?	No - assessed by change-in-estimate (≥10%)	Yes - Breslow-Day test for homogeneity
Effect on estimates	Makes crude estimate differ from adjusted estimate	Makes stratum-specific estimates differ from each other
Relationship with exposure	Associated with exposure AND outcome, NOT on causal pathway	Modulates the strength/direction of exposure-outcome association
On causal pathway?	Must NOT be	Irrelevant
Pooling strata?	After adjustment, pool to get summary estimate	Do NOT pool - report each stratum separately

STRATIFICATION - The Common Approach for Both

When you stratify data by a third variable Z:

If stratum-specific estimates ≈ each other AND differ from crude estimate → Confounding (Z is a confounder; pool the adjusted estimate)
If stratum-specific estimates differ significantly from each other → Effect modification (Z is an effect modifier; present stratum-specific results)
If stratum-specific estimates ≈ each other AND ≈ crude estimate → Neither (Z is neither)

MANTEL-HAENSZEL METHOD

Used in stratified analysis to:

Calculate stratum-specific RR or OR
Test for homogeneity across strata (Breslow-Day test)
If homogeneous (no effect modification): calculate pooled Mantel-Haenszel summary estimate (removes confounding)

Memory Aid

Confounder = Complicates the picture - Control it

Effect Modifier = Enhances understanding - Explain it (report it)

Sources:

Firestein & Kelley's Textbook of Rheumatology (confounding definition, types, control methods, effect modification, Breslow-Day test)
Dermatology 2-Volume Set 5e (effect modifier diagram, tanning bed example)
Park's Textbook of Preventive and Social Medicine (confounding as bias in case-control studies, matching as control)
Berek & Novak's Gynecology (confounder definition)

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