Fig 1.
Empirical time since infection distributions of two available datasets.
On the left, D228 represents 228 samples (from 42 subjects) with recent infection of subtype C in Botswana from 2004 to 2008. Subjects were followed longitudinally for no more than 755 days [17]. On the right, D561 represents a meta database (freely available at Los Alamos HIV public database; accessed August 2014) of 561 samples (from 462 subjects) with subtype B and C. The maximum TSI is 8888 days.
Fig 2.
Hypothetical Time Since Infection distributions.
These distributions have a Beta distribution kernel with parameters a and b. They are meant to represent different epidemic scenarios (akin to those in [18]). The blue line represents the case of an “emerging” epidemic; the orange line a “waning” epidemic; the green line a “stable” epidemic; and the black line an epidemic that has been partially controlled for a period of time, but has recently resurged. The latter scenario is arguably the least likely to be found in reality, and we have included it to mimic the properties of the TSI distribution of D561 in Fig 1.
Fig 3.
(left) Expected diversity evolution for different model behaviors, as determined by parameter h in Eq (3). (right) Diversity values of model f(t) with h = 500 for two standard deviation values: u = 0.05 (purple) and u = 0.2 (red). The profiles of real data commonly relate more to the case of u = 0.2.
Fig 4.
Comparing classification performance of the same assay with different TSI distributions.
With u = 0.2, sample size = 500, h = 500, recency at 6 months. The 95% prediction bounds are obtained from 1000 simulations.
Fig 5.
Comparing classification performance of the same assay with different TSI distribution and two different definitions of recency: at t* = 180 days (left bars) and t* = 365 days (right bars). With u = 0.2, sample size = 500, h = 500. The 95% prediction bounds are obtained from 1000 simulations.
Fig 6.
Comparing classification performance of the same assay with different TSI distribution and different ranges of TSI: 1 day up to tmax = 700 days (left bars) and up to tmax = 1400 days (right bars). With u = 0.2, sample size = 500, h = 500, recency at 365 days. The 95% prediction bounds are obtained from 1000 simulations.
Fig 7.
Classification performance of the same assay using the two TSI distributions from the empirical datasets.
With u = 0.2, h = 500, recency at 6 months. The 95% prediction bounds are obtained from 1000 simulations.
Fig 8.
Comparing the mean performance (i.e., mean of over S = 1000 simulations) of the same hypothetical HIV recency assay using the two empirical TSI distributions (note different y axis, with the left y axis representing the frequency of each of the 2-month TSI groups or bins, and the right y axis representing the mean of
). The assay performs better overall in the dataset D561 which has a bimodal TSI distribution (dark gray, AUC = 93%) than in dataset D228, which has a TSI distribution with a large fraction of cases around the recency cutoff of 6 months (blue, AUC = 74%). In addition, the assay’s sensitivity as a function of TSI is also higher in dataset D561, however, its specificity is higher in dataset D228. For the case of D561, in the range of 6 to 15 months the assay does worse, on average, than a “coin toss” (mean probability < 0.5). Parameter values: u = 0.2, h = 500.