Fig 3. Decision model of diagnosis of current infection under the sequential testing strategy.

In the sequential strategy, the individual’s first test result (circles) can be either: treponemal positive (suggesting past/current infection), or treponemal negative (never any infection); this depends on the Sensitivity (Se) and Specificity (Sp) of the treponemal RDT (Se1 and Sp1, respectively), as well as on the prevalence of past/current infection in the total population (Pr1); the treponemal line provides either a true or false diagnosis of past/current infection; this depends on Positive Predictive Value (PPV) and Negative Predictive Value (NPV) of the treponemal RDT (PPV1 and NPV1, respectively); PPV is calculated as (Se×Pr1)÷(Se×Pr1+(1–Sp)×(1–Pr1)); NPV is calculated as Sp×(1–Pr1)÷((1-Se) ×Pr1+Sp×(1–Pr1)); those with a true negative result for past/current infection are logically also truly negative for current infection; among those with a false negative result for past/current infection, we assume that the prevalence of current infection among false past/current infection negatives is the prevalence of current infection in the population of past/current infections (Pr2); those with either true or false positive results for past/current infection receive a second test; their second test result can be either: dually positive (suggesting current infection), treponemal positive only (past infection), or dually negative (never any infection); for simplicity, we assume that we use only the non-treponemal line; the non-treponemal line provides either a true of false diagnosis of current infection; this depends on PPV and NPV of the non-treponemal line (PPV2b and NPV2b),using the prevalence of current infection in the population of past/current infections (Pr2); red lines indicate pathways to false diagnoses of current infection.