A counterfactual approach to bias and effect modification in terms of response types

Table 2 Enumeration of 16 response types for outcome D and corresponding potential outcomes

^a Under the assumption of positive monotonicity (i.e., D _ce(ω) ≥ D _{c ' e '}(ω) for ∀ω whenever c ≥ c ' and e ≥ e '), these response types are excluded.
^b Given no interaction at the individual level on the additive scale between C and E in the counterfactual framework (i.e., D ₁₁(ω) − D ₀₁(ω) − D ₁₀(ω) + D ₀₀(ω) = 0 for ∀ω), these response types are excluded.
^c Given no interaction at the individual level on the multiplicative scale between C and E in the counterfactual framework (i.e., D ₁₁(ω)D ₀₀(ω) = D ₀₁(ω)D ₁₀(ω) for ∀ω), these response types are excluded.

ISSN: 1471-2288