ALT Illustration of positivity and overlap in PS-based analyses. Panel (A) shows adequate overlap in propensity score distributions between the treatment and control groups, supporting valid comparisons. Panel (B) shows limited overlap, in which extreme propensity scores may lead to unstable estimates, particularly in inverse probability of treatment weighting. Limited overlap reduces both the validity and generalizability of causal effect estimates.

ALT Venn diagram depicting the joint and marginal probabilities of exposure (E) and disease (D). This diagram is used to illustrate the algebraic equivalence between exposure-based and disease-based odds ratios via Bayes’ theorem.