Towards Estimation of HIV-1 Date of Infection: A Time-Continuous IgG-Model Shows That Seroconversion Does Not Occur at the Midpoint between Negative and Positive Tests

<div><p>Estimating date of infection for HIV-1-infected patients is vital for disease tracking and informed public health decisions, but is difficult to obtain because most patients have an established infection of unknown duration at diagnosis. Previous studies have used HIV-1-specific immunoglobulin G (IgG) levels as measured by the IgG capture BED enzyme immunoassay (BED assay) to indicate if a patient was infected recently, but a time-continuous model has not been available. Therefore, we developed a logistic model of IgG production over time. We used previously published metadata from 792 patients for whom the HIV-1-specific IgG levels had been longitudinally measured using the BED assay. To account for patient variability, we used mixed effects modeling to estimate general population parameters. The typical patient IgG production rate was estimated at <i>r</i> = 6.72[approximate 95% CI 6.17,7.33]×10⁻³ OD-n units day⁻¹, and the carrying capacity at <i>K</i> = 1.84[1.75,1.95] OD-n units, predicting how recently patients seroconverted in the interval ^∧<i>t</i> = (31,711) days. Final model selection and validation was performed on new BED data from a population of 819 Swedish HIV-1 patients diagnosed in 2002–2010. On an appropriate subset of 350 patients, the best model parameterization had an accuracy of 94% finding a realistic seroconversion date. We found that seroconversion on average is at the midpoint between last negative and first positive HIV-1 test for patients diagnosed in prospective/cohort studies such as those included in the training dataset. In contrast, seroconversion is strongly skewed towards the first positive sample for patients identified by regular public health diagnostic testing as illustrated in the validation dataset. Our model opens the door to more accurate estimates of date of infection for HIV-1 patients, which may facilitate a better understanding of HIV-1 epidemiology on a population level and individualized prevention, such as guidance during contact tracing.</p> </div

Mean absolute error as a function of the low-frequency cutoff (<i>x</i>_<i>c</i>).

<p>Different diversity measures perform very similarly when the cutoff <i>x</i>_<i>c</i> is greater than approximately 10%. Average pairwise distance and entropy outperform fraction of polymorphic sites for low <i>x</i>_<i>c</i>. This graph is based on diversity in <i>pol</i>. Solid lines correspond to using all sites, dashed lines to diversity at 3rd codon positions.</p

(Left) Distribution of the estimation error. (Right) Estimated time of infection (ETI) versus actual time of infection (TI). Displayed for the training and the validation data sets.

<p>(Genetic region: 3rd codon positions in <i>pol</i>, diversity measure: average pairwise distance, <i>x</i>_<i>c</i> = 0.003. Connected data points belong to the same patient.)</p

Comparison of inferred time since seroconversion to serological interval.

<p>(<b>A</b>) The model-inferred time since seroconversion [grey circles with 95% confidence interval as grey lines] from 350 Swedish patients was compared to their known serological intervals [(<i>T₍₊₎,T₍₋₎</i>), blue lines]. When the inferred time since seroconversion did not hit the serological interval, the point estimate and 95% confidence interval is marked in red; 94% of the intervals overlapped. (<b>B</b>) The relative positioning parameter τ measures the normalized position of the inferred time since seroconversion to the serological interval. Values outside this interval are shown in grey at τ = 0 and τ = 1. The relative positioning was biased towards the most recent positive HIV test result at large τ. (<b>C</b>) Distribution of the inferred time since seroconversion, i.e., the times between BED tests and <i>τ</i>-corrected dates of seroconversion.</p

Logistic modeling of IgG-capture BED-enzyme immunoassay absorbance as a function of time since seroconversion.

<p>The resulting logistic model is predictive when BED OD-n = (0.07, 1.84), corresponding to 31–711 days. This model describes the typical patient estimated by the SAR mixed effects model (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0060906#pone-0060906-t001" target="_blank">Table 1</a>), where parameter values correspond to the whole population.</p

(Left) Distribution of the estimation error. (Right) Estimated time of infection (ETI) versus actual time of infection (TI).

<p>(Genetic region: 3rd codon positions in <i>pol</i>, diversity measure: average pairwise distance. The encircled outliers are discussed in the text.)</p

Definitions of dates and time intervals relative to BED testing.

<p>The time since seroconversion (<i>t</i>) is the time from the date a patient seroconverted (<i>T</i>_sc) to when a sample for BED testing was collected (<i>T</i>_BED). We estimate <i>t</i> by a logistic IgG model (Eq. 1) as ^∧<i>t</i>. Date of infection (<i>T</i>_inf) occurred on average 21 days prior to <i>T</i>_sc<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0060906#pone.0060906-Fiebig1" target="_blank">[9]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0060906#pone.0060906-Cohen1" target="_blank">[10]</a>. When available, the patient history also includes the dates of last negative HIV-1 antibody testing (<i>T</i>₍₋₎) and first positive HIV-1 antibody testing (<i>T</i>₍₊₎), defining the serological interval. Note that <i>T₍₊₎</i> and <i>T_BED</i> may often occur at the same date. To reevaluate national Swedish HIV surveillance data we compared ^∧<i>T</i>_inf with <i>T</i>₍₊₎, resulting in a time difference Δ.</p

Mean absolute prediction error of TI as a function of position in genome and different sizes of the genome window (<i>ws</i>).

<p>Straight solid lines correspond to the error when estimation is based on diversity in the genes <i>gag</i>, <i>pol</i> or <i>env</i>. The dashed lines are analogous estimates using diversity only at 3rd codon position. Diversity measure: average pairwise distance, <i>x</i>_<i>c</i> = 0.003.</p

Antiretroviral drug use in Sweden 1987–2011.

<p>The graphs depict the proportion of patients on ART exposed to each individual drug per calendar year, revealing trends in usage prevalence overtime.</p