Optimal timing of drug sensitivity testing for patients on first-line tuberculosis treatment

Abstract

Effective treatment for tuberculosis (TB) patients on first-line treatment involves triaging those with drug-resistant (DR) TB to appropriate treatment alternatives. Patients likely to have DR TB are identified using results from repeated inexpensive sputum-smear (SS) tests and expensive but definitive drug sensitivity tests (DST). Early DST may lead to high costs and unnecessary testing; late DST may lead to poor health outcomes and disease transmission. We use a partially observable Markov decision process (POMDP) framework to determine optimal DST timing. We develop policy-relevant structural properties of the POMDP model. We apply our model to TB in India to identify the patterns of SS test results that should prompt DST if transmission costs remain at status-quo levels. Unlike previous analyses of personalized treatment policies, we take a societal perspective and consider the effects of disease transmission. The inclusion of such effects can significantly alter the optimal policy. We find that an optimal DST policy could save India approximately $1.9 billion annually.

Keywords: Drug resistance; Optimal testing; POMDP; Tuberculosis.

Appendix Figure 1

Optimal testing policy for regions of India without TB transmission, by age and sex

Appendix Figure 2

Earliest DST month (at end of month) across all possible patient SS test histories for transmission costs between 0 and 10% of the base case ($0 – $1393) and initial DR TB prevalence among first-line TB patients between 0 and 50% of the base case (0 – 0.015)

Appendix Figure 3

Optimal testing policy for regions of India without TB transmission, with imperfect Xpert sensitivity and specificity (97% sensitivity, 95% specificity)

Appendix Figure 4

Expected costs saved over time from early detection of a DR TB case, by age group

Appendix Figure 5

Schematic of belief regions described in proofs of Propositions 3 and 4 and Theorem 3. Panel a: The line demarking half-space H_t, Cβ_t = 0, intersects the lines that form the edges of the belief space at points a, b and c. Panel b: The lines that define half-spaces $S_{t-1,H_t,SS+}$ and $S_{t-1,H_t,SS-}$ can be expressed as linear combinations of $a_{+}^{\prime }$ and $b_{+}^{\prime }$, and similarly for $a_{-}^{\prime }$ and $b_{-}^{\prime }$ (panel c). Panel d: We define the union of the two intersections (given in panel b and c) as U_t−1,t.

Figure 1

Belief regions. Panel a visualizes possible values of states 1, 2, and 3 in β_t (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 H_t and remain on treatment in region ~H_t (panel a). Panels b and c show that the regions that map to H_t and ~H_t at time t − 1 regardless of what SS test result is observed are the intersection of subsets. Panel d illustrates U_t−1,t, the union of the two intersections given in panels b and c.

Figure 2

Model schematic: empirical example of TB in India. This figure depicts the belief update process used in the model at every time period.

Figure 3

Results: Optimal diagnosis algorithm in a region with no TB transmission (with expected percentage of patients shown on each path). The POMDP solution provides the optimal action for every possible combination of no observation, SS+, and SS− results. We represent these results in flowchart form.