From: A simple method for analyzing data from a randomized trial with a missing binary outcome
randomization group | unobserved covariate | probability of outcome given group, unobserved covariate, s, not missing | probabilitity of unobserved covariate given group, s, not missing | probability of outcome given group, s not missing |
---|---|---|---|---|
Z | X | pr(Y = 1|z, s, x, R = 1) | pr(x|z, s, R = 1) | pr(Y = 1|z, s, R = 1) |
= pr(Y = 1|z, s, x) if MAR | ||||
1 | 0 | α_{0s }+ Δ_{ s } | (1 - φ_{1s }) | |
(α_{0s }+ Δ_{ s }) (1 - φ_{1s }) + (α_{1s }+ Δ_{ s }) φ_{1s } | ||||
1 | α_{1s }+ Δ_{ s } | φ_{1s } | ||
0 | 0 | α_{0s } | (1 - φ_{0s }) | |
α_{0s }(1 - φ_{0s }) + α_{1s }φ_{0s } | ||||
1 | α_{1s } | φ_{0s } | ||
difference between randomization groups: | Δ_{ s }+ ψ_{ s }ε_{ s }, where ε_{ s }= φ_{1s }- φ_{0s }, ψ_{ s }= α_{1s }- α_{0s } |