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. Author manuscript; available in PMC: 2018 Dec 1.
Published in final edited form as: Health Care Manag Sci. 2017 Aug 31:10.1007/s10729-017-9416-4. doi: 10.1007/s10729-017-9416-4

Figure 1.

Figure 1

Belief regions. Panel a visualizes possible values of states 1, 2, and 3 in βt (area enclosed by red lines); these are represented as points in R3. We depict only the first three states for visual clarity and because we are concerned with the belief regions where the optimal action is to DST or not (no actions are possible in states 4–7). The corners of the feasible space represent beliefs that the patient is cured, has DS TB, or has DR TB with certainty. Suppose it is optimal to administer DST for all beliefs in region Ht and remain on treatment in region ~Ht (panel a). Panels b and c show that the regions that map to Ht and ~Ht at time t − 1 regardless of what SS test result is observed are the intersection of subsets. Panel d illustrates Ut−1,t, the union of the two intersections given in panels b and c.