The fraction F of deaths averted by intervention is calculated by dividing CrAg+ AHD patients into three groups: those with symptomatic (we assume that multiple symptoms of CM would be detected in this group) CM at presentation (Group 1, p1), those with sub‐clinical CSF‐positive cryptococcal disease (Group 2, p2) and those with CSF‐negative cryptococcal antigenemia (CrAg+ but CSF–, Group 3, p3), such that
We assume Group 1, those with symptomatic CM, are easily diagnosed and receive whichever of the two CM treatment regimens is available. Groups 2 and 3 must first be screened for AHD and correctly identified as such (α). If identified as AHD, Group 2 receive a test for cryptococcal antigenemia (coverage c2), followed a test for CSF‐positivity (coverage c1); a positive CSF test is followed by the available treatment regimen, while a negative CSF test is followed by pre‐emptive therapy. If identified as AHD, Group 3 receive a test for cryptococcal antigenemia followed by pre‐emptive therapy.
As with the TB model, the effect of CD4 testing on cryptococcal disease/CM mortality comes entirely through the identification of AHD, in this case for Groups 2 and 3. We assume that testing for both CrAg‐positivity and CSF‐positivity was indicated equally for all AHD cases, whether identified by clinical staging or CD4 testing. We assumed that CD4 testing would successfully identify all PLHIV with CD4 <200 cells/mm3 as having AHD. There are limitations of clinical staging for the identification of CD4 <200 cells/mm3; estimates of the sensitivity of clinical staging can vary but results from Munthali et al. showed that 60% of AHD cases (CD4 <200 cells/mm3) were identified by clinical staging [26 (link)], which we have adopted in our analysis.