Resolution:
## Figure 1.
BK-plot of bias from an unobserved binary covariate among subjects not missing outcome.
The upper diagonal line is the probability of outcome among subjects not missing outcome
in randomization group
Z = 1. The lower diagonal line is the probability of outcome among subjects not missing
outcome in randomization group group Z = 0. For subjects in group 0, the fraction with X = 1 is φ_{0s }and the probability of outcome is indicated by point A. For subjects in group 1, the
fraction with X = 1 is φ_{1s }and the probability of outcome is indicated by point B. The true treatment effect
Δ_{s }is the difference between the diagonal lines. The apparent treatment effect Δ_{s }is the vertical distance between points A and B, which equals Δ + ψ_{s}ε_{s}, where ε_{s }= φ_{1s }- φ_{0s }and ψ_{s }= α_{1s }- α_{0s }= the slope of each diagonal line. To bound the overall bias Σ_{s}ψ_{s}ε_{s}pr(S = s), we specify an upper bound for ε_{s }based only on the fraction missing and a plausible value for the maximum of ψ_{s }based on the estimates of ψ_{s }if an observed covariate were missing.
Baker and Freedman |