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. Author manuscript; available in PMC: 2009 Sep 8.
Published in final edited form as: Annu Rev Med. 2008;59:443–453. doi: 10.1146/annurev.med.59.062606.122232

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′.
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