Causal Inference: Bias, Confounding, and Interaction

Selection Bias

• Occurs when subject selection leads to an apparent association between exposure and disease, even if no real association exists.
• Can arise from:
  • Nonresponse of potential study participants (if response rates differ based on exposure and disease status).
  • Participant losses during follow-up in cohort studies (compare characteristics of those lost vs. not lost).
• Selection of study population affects generalizability (external validity) but selection bias affects internal validity, leading to incorrect estimates of odds ratios (ORs) or relative risks (RRs).
• Exclusion Bias: Applying different eligibility criteria to cases and controls.
• Compensating Bias: Occurs when selection biases in cases and controls are of the same magnitude, leading to an unbiased OR.

Information Bias

• Arises from flawed data collection, resulting in misclassification of exposure or disease status.
• Types:
  • Differential Misclassification: Misclassification rate differs between study groups, leading to spurious associations or masking real ones.
  • Nondifferential Misclassification: Inaccuracy is equal across study groups, diluting the RR or OR towards 1.0.
  • Surveillance Bias: Better disease ascertainment in a monitored population.
  • Recall Bias: Cases recall exposures differently than controls.
  • Reporting Bias: Subjects selectively report exposures.
  • Wish Bias: Subjects unintentionally distort past exposures to align with their beliefs about disease causation.
• Surrogate interviews may introduce inaccuracies in exposure data.

Confounding

• Confounding: A third factor (X) distorts the observed relationship between exposure (A) and disease (B).
  • Factor X is a known risk factor for disease B
  • Factor X is associated with exposure A, but is not a result of exposure A
• Can address confounding in study design (matching) or data analysis (stratification, adjustment).
• Stratification: Evaluating the association within subgroups (strata) of the confounding variable.
  • Calculate the measure of association within each stratum of the confounding variable.
• Confounding is a real phenomenon, not an error; failure to address it leads to biased study conclusions.

Interaction

• Interaction (effect modification): When the incidence rate of disease in the presence of two or more risk factors differs from the rate expected from their individual effects.
• Positive interaction (synergism): Combined effect is greater than expected.
• Negative interaction (antagonism): Combined effect is less than expected.
• Models:
  • Additive: Combined effect is the sum of individual effects.
  • Multiplicative: Combined effect is the product of individual effects.
• Assess interaction by comparing observed incidence with that predicted by additive or multiplicative models.
• The choice between additive and multiplicative models should ideally be based on biologic knowledge.
• Synergistic relationships may have practical policy implications.

Key Equations and Concepts

• Odds Ratio (OR): $OR = \frac{Odds\ of\ exposure\ in\ cases}{Odds\ of\ exposure\ in\ controls}$
• Compensating Bias: When bias in selecting cases and controls is of the same magnitude.
• Additive Model Calculation: Expected $RR = RR<em>A + RR</em>B - 1$.
• Multiplicative Model Calculation: Expected $RR = RR<em>A \times RR</em>B$.