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 | α0s + Δ s | (1 - φ1s ) | |
(α0s + Δ s ) (1 - φ1s ) + (α1s + Δ s ) φ1s | ||||
1 | α1s + Δ s | φ1s | ||
0 | 0 | α0s | (1 - φ0s ) | |
α0s (1 - φ0s ) + α1s φ0s | ||||
1 | α1s | φ0s | ||
difference between randomization groups: | Δ s + ψ s ε s , where ε s = φ1s - φ0s , ψ s = α1s - α0s |