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. Author manuscript; available in PMC: 2011 Dec 10.
Published in final edited form as: Stat Med. 2010 Dec 10;29(28):2869–2879. doi: 10.1002/sim.4027

Table 1.

Joint distribution of counterfactual surrogate S and outcome Y under monotonicity assumption

T(0, S(0)), T(1, S(1))
(0,0) (0,1) (1,1)
S(0), S(1) (0,0) π 11 π 12 π 13 π 1+
(0,1) π 21 π 22 π 23 π 2+
(1,1) π 31 π 32 π 33 π 3+
π +1 π +2 π +3 1