Table 1.
Notation for an Adaptive Treatment Strategy
S1,S2…,SK | States used as inputs to the adaptive treatment decisions. |
A1,A2…,AK | Treatment options at each stage. |
S1,A1,,S2,A2,…,SK,AK,,Y | The order of observation of states and treatments;Y is the overall outcome. |
d1,…,dK | The decision rules at each stage. |
d1(S1) | The initial treatment, given the first state. |
d2(S1,A1,S2) | The second treatment, given the first state, first treatment, and second state. |
dk(S1,A1,Ak–1,Sk) | The treatment at stage k after a series of k states and k-1 treatments. |
E[Y(d)] | The average outcome (for a population of patients), if all of them were treated with the ATS d. |
E[Y(d)]–E[Y(d′)] | The difference in average outcome of two ATS, d and d′. |