# Combining Viral Genetics and Statistical Modeling to Improve HIV-1 Time-of-Infection Estimation towards Enhanced Vaccine Efficacy Assessment

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## Abstract

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## 1. Introduction

- (1)
- Time-dependent marker correlates of risk (CoR) of HIV-1 infection: For studying the correlates of HIV-1 risk, a case-cohort or case-control study design can be used to measure a time-varying potential correlate (marker) of interest as near as possible prior to the time of HIV-1 acquisition for all HIV-1 infected cases. Moreover, for a random sample of participants who complete follow-up testing as HIV-1-negative, the marker(s) is measured at all longitudinal sample time points (e.g., this design was employed in the VaxGen HIV-1 VE trial [20,28] and the Partners in PrEP prevention efficacy trial [29] and is planned for the AMP prevention efficacy trials [27] as well as for the HVTN 702 and HVTN 705 VE trials). In AMP one key marker of interest is VRC01 serum concentration measured by ELISA or serum neutralization titer against a standard panel of viruses by a neutralization assay; population pharmacokinetics/pharmacodynamics (PK/PD) models can be used to provide low-error unbiased estimates for the VRC01 concentration in infected individuals [30], given an accurate estimate of the date of infection. An important goal of the AMP trials is to characterize the relationship between a person’s VRC01 concentration and their instantaneous risk of HIV-1 infection. Identification of a serum neutralization threshold associated with (very) low risk of HIV-1 infection would provide valuable guidance for future vaccine development. What makes it challenging to pinpoint a marker’s value at infection is uncertainty in the date of infection. Even with monthly HIV-1 testing with high adherence to the testing schedule, the estimation methodologies that we previously employed for evaluation of HIV-1 VE trials are inadequate for the requirements of the AMP studies. In Supplementary Section A we illustrate the amount of increase in statistical power to detect such a CoR in the AMP studies that we expect to result from reducing the error in the infection time estimator (Supplementary Figure S1) using our previously applied approach [31].
- (2)
- “Sieve analysis”: How the level of vaccine/prevention efficacy depends on genotypic characteristics of HIV-1 at the time of acquisition: Sieve analysis provides another tool to detect and evaluate correlates of vaccine protection, based on the comparison of viruses that infect placebo recipients with the viruses that infect vaccine recipients, despite the protective barrier induced by vaccination [32]. An ongoing challenge for sieve analysis is that the determination of HIV-1 genetics at the time of HIV-1 acquisition is of fundamental importance for discriminating true sieve effects from post-acquisition effects. That is, whether observed viral genetic differences (across treatment groups, vaccine vs. placebo) can be interpreted as differential blockage of acquisition of incoming variants (a true “sieve effect”) vs. as resulting from differential evolution post-infection of similar starting viruses, resulting for example from effects in which vaccine-induced anamnestic responses impact the early evolution of HIV-1 prior to diagnosis (and sampling for sequencing) [33]. This issue has been critically important in the interpretation of sieve effects for all HIV-1 sieve reports to date [34,35,36,37,38]. Statistical methods have been developed that require the ability to determine which HIV-1 infection events are diagnosed very early prior to significant post-infection evolution [39,40,41]; additional research is needed to ensure that the methods optimally incorporate state-of-the-art infection time estimators.

## 2. Materials and Methods

#### 2.1. Studies, Participants, Diagnostic Testing and HIV-1 Sequencing

#### 2.2. Sequence Data Pre-Processing, Hypermutation Detection, and Recombination Detection

#### 2.3. Infection Time

#### 2.4. True and Artificial Diagnostic Bounds on the Date of Infection

#### 2.5. PFitter Estimate of Days Since Infection

^{−5}unless otherwise specified (and we use this default value). This is computed from the mutation rate per generation (ε = 2.16 × 10

^{−5}) [54], the basic reproductive ratio (R

_{0}= 6) [55], and generation time (τ = 2 days) [56]. With these parameters, PFitter estimates the time since infection t using the formula $\widehat{t}$ = (0.9065 * $\widehat{\lambda}$/εn) − 0.205 [57], where λ is naturally estimated by $\widehat{\lambda}$, the maximum likelihood rate of a Poisson fit to the number of mutations k observed out of n total residues in the input alignment: k~Poisson(λ). However, the actual fit is based on k’ ~ Poisson (2$\widehat{\lambda}$), where k’ is the total Hamming distance across all pairs of input sequences, since under the star-like model these models share the same value of λ. Note that since the resulting value of $\widehat{t}$ is rounded to the nearest integer, the constant term −0.205 is effectively negligible. Thus, PFitter’s estimate of t is approximately equal to c × ($\widehat{\lambda}$/n), where c = 0.9065/ε represents the effective mutation rate per base per day. Thus multiplying $\widehat{t}$ by any constant x is nearly equivalent to calling PFitter with an alternative epsilon value ε’ = ε/x, a fact that we utilize during the calibration process to refit mutation rate values without recomputing $\widehat{t}$, as discussed below. Instead we need only compute $\widehat{t}$′ = $\widehat{t}$ × x. During the calibration of the simplest scale-only models (Supplementary Table S3), we find optimal values of x to fit the data, and thus optimal mutation rate parameters.

#### 2.6. Variations on the PFitter Estimator $\widehat{t}$ of t: (syn) and (w/in clusts)

#### 2.7. Clustering Sequences for the Within-Clusters PFitter Method

#### 2.8. PrankenBeast

#### 2.9. Founder Multiplicity Characterization

_{1}−P

_{0}), where P

_{1}and P

_{0}are the fractions of cases predicted to be multiple-founder infections among those truly multiple-founder and among those truly single-founder, respectively. Its (effective) minimum is 0.5, and it is maximized (at 1) when the sensitivity and the specificity are both 1.

#### 2.10. Rolland HVTN Method for Determining Founder Multiplicity

#### 2.11. Tests for Star-Like Phylogeny or Founder Multiplicity

_{c}, where $\lambda $

_{c}is the estimate of the rate of the Poisson process of mutation events that is calculated from the distances between each sequence and the consensus sequence. In the informal “convolution test” (is star-like), the data are declared to “not follow a star-like phylogeny” when there is more than 10% cumulative difference between the mass distribution of the inter-sequence HD histogram and the expected inter-sequence HD distribution. PFitter calculates the expected number of inter-sequence pairs having each possible HD value by convolving the observed HD distribution of distances to the consensus sequence [53,57]. This procedure, while not itself a formal statistical test, defines a sensible strategy for evaluating the hypothesis of a star-like phylogeny by asking whether the inter-sequence HDs are consistent with a convolution of the consensus HDs. Note that these are not designed as tests of multiple-founder infections, as there are other reasons why the star-like phylogeny model might be a poor fit (such as if the data follow a branching phylogeny model instead, as would be the case in later infection). The DS StarPhy Test employs Dempster-Shafer Analysis [63], a fiducial methodology that generalizes Bayesian inference to cases lacking prior distributions, to implement a simple variant of Pfitter’s fits test, which evaluates the assertion that under a star-like phylogeny, the inter-sequence Hamming distance rate is twice the distance-to-consensus rate $\lambda $

_{c}. Details and an implementation of this method are available in the hiv-founder-id github repository (DSStarPhy.Rnw).

#### 2.12. Statistical Methods for Calibrating Predictors of the Indicator of a Multiple-Founder Infection

_{10}plasma viral load (lPVL) and the days elapsed between sample collection and infection diagnosis, and interactions between these variables and each binary uncalibrated predictor (Rolland HVTN, PFitter fits, etc.). We also allowed the inclusion of several additional predictors (Supplementary Table S1), from which the LASSO procedure was allowed to sub select.

#### 2.13. Statistical Methods for Calibrating Predictors of Infection Timing

#### 2.14. Software Pipeline

## 3. Results

#### 3.1. RMSE and Bias of Center-of-Bounds (COB) Estimates of Infection Time

#### 3.2. Prediction Error of Sequence-Based Estimators of Time Since HIV-1 Infection is Improved with Calibration

_{10}plasma viral load, the time since diagnosis, and interactions between these parameters and the days since infection output from PFitter or PrankenBeast. For the sequences from the earlier time-point category (1–2 months post-infection). Figure 1 shows results for the CAPRISA 002 sequences that were estimated separately from those of the RV217 sequences; for the ~6-month time category we present results from a combined model that we trained with both datasets, lending additional robustness to the interpretation of the results. We conclude that, with calibration, simple estimators of time of HIV-1 infection, such as the unmodified Poisson Fitter estimator or the COB estimator, perform as well (or nearly so) as more sophisticated methods.

#### 3.3. Multiplicity Assessment is Improved by Calibration with LASSO

#### 3.4. Calibration, Considerations and Results Summary

^{2}values above 0.80) and (b) a mutation rate model which applies a scalar multiple to the estimate that results from the center of bounds approach, or from methods that use sequence data (Poisson Fitter, BEAST, etc.). The presented models in Figure 1 yielded the lowest RMSEs despite having low R

^{2}values (less than 0.20) when evaluating the fit on all of the data, and wide confidence intervals around the estimators (the predictive power of these models relies mostly on the intercept). Models with much higher R

^{2}values (above 0.98) can be obtained by omitting the intercept (Supplementary Figure S4). These models yield interpretable coefficient estimates while retaining the low bias of the best models calibrated with intercepts but have higher RSMEs.

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Fiebig, E.W.; Wright, D.J.; Rawal, B.D.; Garrett, P.E.; Schumacher, R.T.; Peddada, L.; Heldebrant, C.; Smith, R.; Conrad, A.; Kleinman, S.H.; et al. Dynamics of HIV viremia and antibody seroconversion in plasma donors: Implications for diagnosis and staging of primary HIV infection. AIDS
**2003**, 17, 1871–1879. [Google Scholar] [CrossRef] - McMichael, A.J.; Borrow, P.; Tomaras, G.D.; Goonetilleke, N.; Haynes, B.F. The immune response during acute HIV-1 infection: Clues for vaccine development. Nat. Rev. Immunol.
**2010**, 10, 11–23. [Google Scholar] [CrossRef] - Cohen, M.S.; Gay, C.L.; Busch, M.P.; Hecht, F.M. The detection of acute HIV infection. J. Infect. Dis
**2010**, 202 Suppl. 2, S270–S277. [Google Scholar] [CrossRef] - Ananworanich, J.; Fletcher, J.L.; Pinyakorn, S.; van Griensven, F.; Vandergeeten, C.; Schuetz, A.; Pankam, T.; Trichavaroj, R.; Akapirat, S.; Chomchey, N.; et al. A novel acute HIV infection staging system based on 4th generation immunoassay. Retrovirology.
**2013**, 10, 56. [Google Scholar] [CrossRef] - Le, T.; Wright, E.J.; Smith, D.M.; He, W.; Catano, G.; Okulicz, J.F.; Young, J.A.; Clark, R.A.; Richman, D.D.; Little, S.J.; et al. Enhanced CD4+ T-cell recovery with earlier HIV-1 antiretroviral therapy. N Engl. J. Med.
**2013**, 368, 218–230. [Google Scholar] [CrossRef] - Sanders, E.J.; Okuku, H.S.; Smith, A.D.; Mwangome, M.; Wahome, E.; Fegan, G.; Peshu, N.; van der Elst, E.M.; Price, M.A.; McClelland, R.S.; et al. High HIV-1 incidence, correlates of HIV-1 acquisition, and high viral loads following seroconversion among men who have sex with men in coastal Kenya. AIDS (London, England)
**2013**, 27, 437–446. [Google Scholar] [CrossRef] - Mlisana, K.; Werner, L.; Garrett, N.J.; McKinnon, L.R.; van Loggerenberg, F.; Passmore, J.A.; Gray, C.M.; Morris, L.; Williamson, C.; Abdool Karim, S.S.; et al. Rapid disease progression in HIV-1 subtype C-infected South African women. Clin. Infect. Dis.
**2014**, 59, 1322–1331. [Google Scholar] [CrossRef] - Hoenigl, M.; Green, N.; Camacho, M.; Gianella, S.; Mehta, S.R.; Smith, D.M.; Little, S.J. Signs or symptoms of acute HIV infection in a cohort undergoing community-based screening. Emerg. Infect. Dis
**2016**, 22, 532–534. [Google Scholar] [CrossRef] - Moyo, S.; Wilkinson, E.; Novitsky, V.; Vandormael, A.; Gaseitsiwe, S.; Essex, M.; Engelbrecht, S.; de Oliveira, T. Identifying recent HIV infections: From serological assays to genomics. Viruses
**2015**, 7, 5508–5524. [Google Scholar] [CrossRef] - Gay, C.; Dibben, O.; Anderson, J.A.; Stacey, A.; Mayo, A.J.; Norris, P.J.; Kuruc, J.D.; Salazar-Gonzalez, J.F.; Li, H.; Keele, B.F.; et al. Cross-sectional detection of acute HIV infection: Timing of transmission, inflammation and antiretroviral therapy. PLoS ONE
**2011**, 6, e19617. [Google Scholar] [CrossRef] - Ciccozzi, M.; Lo Presti, A.; Andreotti, M.; Mancinelli, S.; Ceffa, S.; Galluzzo, C.M.; Buonomo, E.; Luhanga, R.; Jere, H.; Cella, E.; et al. Viral sequence analysis of HIV-positive women and their infected children: Insight on the timing of infection and on the transmission network. AIDS Res. Hum. Retroviruses
**2014**, 30, 1010–1015. [Google Scholar] [CrossRef] - Love, T.M.; Park, S.Y.; Giorgi, E.E.; Mack, W.J.; Perelson, A.S.; Lee, H.Y. Spmm: Estimating infection duration of multivariant HIV-1 infections. Bioinformatics
**2016**, 32, 1308–1315. [Google Scholar] [CrossRef] - Poon, A.F.; McGovern, R.A.; Mo, T.; Knapp, D.J.; Brenner, B.; Routy, J.P.; Wainberg, M.A.; Harrigan, P.R. Dates of HIV infection can be estimated for seroprevalent patients by coalescent analysis of serial next-generation sequencing data. AIDS
**2011**, 25, 2019–2026. [Google Scholar] [CrossRef] - Puller, V.; Neher, R.; Albert, J. Estimating time of HIV-1 infection from next-generation sequence diversity. PLoS Comput. Biol.
**2017**, 13, e1005775. [Google Scholar] [CrossRef] - Shankarappa, R.; Margolick, J.B.; Gange, S.J.; Rodrigo, A.G.; Upchurch, D.; Farzadegan, H.; Gupta, P.; Rinaldo, C.R.; Learn, G.H.; He, X.; et al. Consistent viral evolutionary changes associated with the progression of human immunodeficiency virus type 1 infection. J. Virol.
**1999**, 73, 10489–10502. [Google Scholar] - Kouyos, R.D.; von Wyl, V.; Yerly, S.; Boni, J.; Rieder, P.; Joos, B.; Taffe, P.; Shah, C.; Burgisser, P.; Klimkait, T. , et al. Ambiguous nucleotide calls from population-based sequencing of HIV-1 are a marker for viral diversity and the age of infection. Clin. Infect. Dis.
**2011**, 52, 532–539. [Google Scholar] [CrossRef] - Ragonnet-Cronin, M.; Aris-Brosou, S.; Joanisse, I.; Merks, H.; Vallee, D.; Caminiti, K.; Rekart, M.; Krajden, M.; Cook, D.; Kim, J.; et al. Genetic diversity as a marker for timing infection in HIV-infected patients: Evaluation of a 6-month window and comparison with bed. J. Infect. Dis.
**2012**, 206, 756–764. [Google Scholar] [CrossRef] - Andersson, E.; Shao, W.; Bontell, I.; Cham, F.; Cuong do, D.; Wondwossen, A.; Morris, L.; Hunt, G.; Sonnerborg, A.; Bertagnolio, S.; et al. Evaluation of sequence ambiguities of the HIV-1 pol gene as a method to identify recent HIV-1 infection in transmitted drug resistance surveys. Infect. Genet. Evol.
**2013**, 18, 125–131. [Google Scholar] [CrossRef] [Green Version] - Flynn, N.M.; Forthal, D.N.; Harro, C.D.; Judson, F.N.; Mayer, K.H.; Para, M.F.; Rgp, H.I.V.V.S.G. Placebo-controlled phase 3 trial of a recombinant glycoprotein 120 vaccine to prevent HIV-1 infection. J. Infect. Dis
**2005**, 191, 654–665. [Google Scholar] - Pitisuttithum, P.; Gilbert, P.; Gurwith, M.; Heyward, W.; Martin, M.; van Griensven, F.; Hu, D.; Tappero, J.W.; Choopanya, K.; Bangkok Vaccine Evaluation, G. Randomized, double-blind, placebo-controlled efficacy trial of a bivalent recombinant glycoprotein 120 HIV-1 vaccine among injection drug users in Bangkok, Thailand. J. Infect. Dis
**2006**, 194, 1661–1671. [Google Scholar] [CrossRef] - Buchbinder, S.P.; Mehrotra, D.V.; Duerr, A.; Fitzgerald, D.W.; Mogg, R.; Li, D.; Gilbert, P.B.; Lama, J.R.; Marmor, M.; Del Rio, C.; et al. Efficacy assessment of a cell-mediated immunity HIV-1 vaccine (the Step study): A double-blind, randomised, placebo-controlled, test-of-concept trial. Lancet
**2008**, 372, 1881–1893. [Google Scholar] [CrossRef] - Rerks-Ngarm, S.; Pitisuttithum, P.; Nitayaphan, S.; Kaewkungwal, J.; Chiu, J.; Paris, R.; Premsri, N.; Namwat, C.; de Souza, M.; Adams, E.; et al. Vaccination with ALVAC and AIDSVAX to prevent HIV-1 infection in Thailand. N Engl. J. Med.
**2009**, 361, 2209–2220. [Google Scholar] [CrossRef] - Gray, G.E.; Allen, M.; Moodie, Z.; Churchyard, G.; Bekker, L.G.; Nchabeleng, M.; Mlisana, K.; Metch, B.; de Bruyn, G.; Latka, M.H.; et al. Safety and efficacy of the HVTN 503/Phambili study of a clade-B-based HIV-1 vaccine in South Arica: A double-blind, randomised, placebo-controlled test-of-concept phase 2b study. Lancet Infect. Dis.
**2011**, 11, 507–515. [Google Scholar] [CrossRef] - Hammer, S.M.; Sobieszczyk, M.E.; Janes, H.; Karuna, S.T.; Mulligan, M.J.; Grove, D.; Koblin, B.A.; Buchbinder, S.P.; Keefer, M.C.; Tomaras, G.D.; et al. Efficacy trial of a DNA/rAd5 HIV-1 preventive vaccine. N Engl. J. Med.
**2013**, 369, 2083–2092. [Google Scholar] [CrossRef] - Gray, G.E.; Laher, F.; Lazarus, E.; Ensoli, B.; Corey, L. Approaches to preventative and therapeutic HIV vaccines. Curr. Opin. Virol.
**2016**, 17, 104–109. [Google Scholar] [CrossRef] [Green Version] - ClinicalTrials.gov. A study to assess the efficacy of a heterologous prime/boost vaccine regimen of ad26.Mos4.Hiv and aluminum phosphate-adjuvanted clade C gp140 in preventing human immunodeficiency virus (HIV)-1 infection in women in Sub-Saharan Africa. Available online: https://clinicaltrials.gov/ct2/show/NCT03060629 (accessed on 3 March 2019).
- Gilbert, P.B.; Juraska, M.; deCamp, A.C.; Karuna, S.; Edupuganti, S.; Mgodi, N.; Donnell, D.J.; Bentley, C.; Sista, N.; Andrew, P.; et al. Basis and statistical design of the passive HIV-1 Antibody Mediated Prevention (AMP) test-of-concept efficacy trials. Stat. Commun. Infect. Dis
**2017**, 9. [Google Scholar] [CrossRef] - Gilbert, P.B.; Peterson, M.L.; Follmann, D.; Hudgens, M.G.; Francis, D.P.; Gurwith, M.; Heyward, W.L.; Jobes, D.V.; Popovic, V.; Self, S.G.; et al. Correlation between immunologic responses to a recombinant glycoprotein 120 vaccine and incidence of HIV-1 infection in a phase 3 HIV-1 preventive vaccine trial. J. Infect. Dis.
**2005**, 191, 666–677. [Google Scholar] [CrossRef] - Baeten, J.M.; Donnell, D.; Ndase, P.; Mugo, N.R.; Campbell, J.D.; Wangisi, J.; Tappero, J.W.; Bukusi, E.A.; Cohen, C.R.; Katabira, E.; et al. Antiretroviral prophylaxis for HIV prevention in heterosexual men and women. N. Engl. J. Med.
**2012**, 367, 399–410. [Google Scholar] [CrossRef] - Huang, Y.; Zhang, L.; Ledgerwood, J.; Grunenberg, N.; Bailer, R.; Isaacs, A.; Seaton, K.; Mayer, K.H.; Capparelli, E.; Corey, L.; et al. Population pharmacokinetics analysis of VRC01, an HIV-1 broadly neutralizing monoclonal antibody, in healthy adults. MAbs
**2017**, 9, 792–800. [Google Scholar] [CrossRef] [Green Version] - Gilbert, P.B.; Zhang, Y.; Rudnicki, E.; Huang, Y. Assessing pharmacokinetic marker correlates of outcome, with application to antibody prevention efficacy trials. Stat. Med.
**2019**, in press. [Google Scholar] - Gilbert, P.B. Interpretability and robustness of sieve analysis models for assessing HIV strain variations in vaccine efficacy. Stat. Med.
**2001**, 20, 263–279. [Google Scholar] [CrossRef] - Edlefsen, P.T.; Gilbert, P.B.; Rolland, M. Sieve analysis in HIV-1 vaccine efficacy trials. Curr. Opin. HIV AIDS
**2013**, 8, 432–436. [Google Scholar] [CrossRef] [Green Version] - Rolland, M.; Edlefsen, P.T.; Larsen, B.B.; Tovanabutra, S.; Sanders-Buell, E.; Hertz, T.; deCamp, A.C.; Carrico, C.; Menis, S.; Magaret, C.A.; et al. Increased HIV-1 vaccine efficacy against viruses with genetic signatures in Env V2. Nature
**2012**, 490, 417–420. [Google Scholar] [CrossRef] - Rolland, M.; Tovanabutra, S.; deCamp, A.C.; Frahm, N.; Gilbert, P.B.; Sanders-Buell, E.; Heath, L.; Magaret, C.A.; Bose, M.; Bradfield, A.; et al. Genetic impact of vaccination on breakthrough HIV-1 sequences from the Step trial. Nat. Med.
**2011**, 17, 366–371. [Google Scholar] [CrossRef] - Edlefsen, P.T.; Rolland, M.; Hertz, T.; Tovanabutra, S.; Gartland, A.J.; deCamp, A.C.; Magaret, C.A.; Ahmed, H.; Gottardo, R.; Juraska, M.; et al. Comprehensive sieve analysis of breakthrough HIV-1 sequences in the RV144 vaccine efficacy trial. PLoS Comput. Biol.
**2015**, 11, e1003973. [Google Scholar] [CrossRef] - Hertz, T.; Logan, M.G.; Rolland, M.; Magaret, C.A.; Rademeyer, C.; Fiore-Gartland, A.; Edlefsen, P.T.; DeCamp, A.; Ahmed, H.; Ngandu, N.; et al. A study of vaccine-induced immune pressure on breakthrough infections in the Phambili phase 2b HIV-1 vaccine efficacy trial. Vaccine
**2016**, 34, 5792–5801. [Google Scholar] [CrossRef] [Green Version] - deCamp, A.C.; Rolland, M.; Edlefsen, P.T.; Sanders-Buell, E.; Hall, B.; Magaret, C.A.; Fiore-Gartland, A.J.; Juraska, M.; Carpp, L.N.; Karuna, S.T.; et al. Sieve analysis of breakthrough HIV-1 sequences in HVTN 505 identifies vaccine pressure targeting the CD4 binding site of Env-gp120. PLoS ONE
**2017**, 12, e0185959. [Google Scholar] [CrossRef] - Sun, Y.; Gilbert, P.B. Estimation of stratified mark-specific proportional hazards models with missing marks. Scand. Stat. Theory Appl.
**2012**, 39, 34–52. [Google Scholar] [CrossRef] - Juraska, M.; Gilbert, P.B. Mark-specific hazard ratio model with missing multivariate marks. Lifetime Data Anal.
**2016**, 22, 606–625. [Google Scholar] [CrossRef] - Gilbert, P.B.; Sun, Y. Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to HIV vaccine efficacy trials. J. R Stat. Soc. Ser. C Appl. Stat.
**2015**, 64, 49–73. [Google Scholar] [CrossRef] - Robb, M.L.; Eller, L.A.; Kibuuka, H.; Rono, K.; Maganga, L.; Nitayaphan, S.; Kroon, E.; Sawe, F.K.; Sinei, S.; Sriplienchan, S.; et al. Prospective study of acute HIV-1 infection in adults in east Africa and Thailand. N Engl. J. Med.
**2016**, 374, 2120–2130. [Google Scholar] [CrossRef] - Salazar-Gonzalez, J.F.; Bailes, E.; Pham, K.T.; Salazar, M.G.; Guffey, M.B.; Keele, B.F.; Derdeyn, C.A.; Farmer, P.; Hunter, E.; Allen, S.; et al. Deciphering human immunodeficiency virus type 1 transmission and early envelope diversification by single-genome amplification and sequencing. J. Virol.
**2008**, 82, 3952–3970. [Google Scholar] [CrossRef] - Van Loggerenberg, F.; Mlisana, K.; Williamson, C.; Auld, S.C.; Morris, L.; Gray, C.M.; Abdool Karim, Q.; Grobler, A.; Barnabas, N.; Iriogbe, I. , et al. Establishing a cohort at high risk of HIV infection in South Africa: Challenges and experiences of the CAPRISA 002 acute infection study. PLoS ONE
**2008**, 3, e1954. [Google Scholar] [CrossRef] - Rose, P.P.; Korber, B.T. Detecting hypermutations in viral sequences with an emphasis on g --> a hypermutation. Bioinformatics
**2000**, 16, 400–401. [Google Scholar] [CrossRef] - Los Alamos National Security, L. Hypermut: Analysis & detection of apobec-induced hypermutation. Available online: http://www.hiv.lanl.gov/content/sequence/HYPERMUT/hypermut.html (accessed on 28 February 2019).
- Abrahams, M.R.; Anderson, J.A.; Giorgi, E.E.; Seoighe, C.; Mlisana, K.; Ping, L.H.; Athreya, G.S.; Treurnicht, F.K.; Keele, B.F.; Wood, N.; et al. Quantitating the multiplicity of infection with human immunodeficiency virus type 1 subtype C reveals a non-poisson distribution of transmitted variants. J. Virol.
**2009**, 83, 3556–3567. [Google Scholar] [CrossRef] - Song, H.; Giorgi, E.E.; Ganusov, V.V.; Cai, F.; Athreya, G.; Yoon, H.; Carja, O.; Hora, B.; Hraber, P.; Romero-Severson, E.; et al. Tracking HIV-1 recombination to resolve its contribution to HIV-1 evolution in natural infection. Nat. Commun.
**2018**, 15, 1928. [Google Scholar] [CrossRef] - Konrad, B.P.; Taylor, D.; Conway, J.M.; Ogilvie, G.S.; Coombs, D. On the duration of the period between exposure to HIV and detectable infection. Epidemics
**2017**, 20, 73–83. [Google Scholar] [CrossRef] - Busch, M.P.; Satten, G.A. Time course of viremia and antibody seroconversion following human immunodeficiency virus exposure. Am. J. Med.
**1997**, 102, 117–124; discussion 125–116. [Google Scholar] [CrossRef] - Masciotra, S.; McDougal, J.S.; Feldman, J.; Sprinkle, P.; Wesolowski, L.; Owen, S.M. Evaluation of an alternative HIV diagnostic algorithm using specimens from seroconversion panels and persons with established HIV infections. J. Clin. Virol.
**2011**, 52 Suppl. 1, S17–S22. [Google Scholar] [CrossRef] - Owen, S.M.; Yang, C.; Spira, T.; Ou, C.Y.; Pau, C.P.; Parekh, B.S.; Candal, D.; Kuehl, D.; Kennedy, M.S.; Rudolph, D.; et al. Alternative algorithms for human immunodeficiency virus infection diagnosis using tests that are licensed in the United States. J. Clin. Microbiol.
**2008**, 46, 1588–1595. [Google Scholar] [CrossRef] - Giorgi, E.E.; Funkhouser, B.; Athreya, G.; Perelson, A.S.; Korber, B.T.; Bhattacharya, T. Estimating time since infection in early homogeneous HIV-1 samples using a poisson model. BMC Bioinformatics
**2010**, 11, 532. [Google Scholar] [CrossRef] - Mansky, L.M.; Temin, H.M. Lower in vivo mutation rate of human immunodeficiency virus type 1 than that predicted from the fidelity of purified reverse transcriptase. J. Virol.
**1995**, 69, 5087–5094. [Google Scholar] - Stafford, M.A.; Corey, L.; Cao, Y.Z.; Daar, E.S.; Ho, D.D.; Perelson, A.S. Modeling plasma virus concentration during primary hiv infection. J. Theoret. Biol.
**2000**, 203, 285–301. [Google Scholar] [CrossRef] - Markowitz, M.; Louie, M.; Hurley, A.; Sun, E.; Di Mascio, M.; Perelson, A.S.; Ho, D.D. A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo. J. Virol.
**2003**, 77, 5037–5038. [Google Scholar] [CrossRef] - Lee, H.Y.; Giorgi, E.E.; Keele, B.F.; Gaschen, B.; Athreya, G.S.; Salazar-Gonzalez, J.F.; Pham, K.T.; Goepfert, P.A.; Kilby, J.M.; Saag, M.S.; et al. Modeling sequence evolution in acute HIV-1 infection. J. Theoret. Biol.
**2009**, 261, 341–360. [Google Scholar] [CrossRef] [Green Version] - Sokal, R.R. A statistical method for evaluating systematic relationships. Uni. Kansas Scient. Bulletin
**1958**, 38, 1409–1438. [Google Scholar] - Langfelder, P.; Zhang, B.; Horvath, S. Dynamictreecut: Methods for Detection of Clusters in Hierarchical Clustering Dendrograms. R Package Version 1.63–1. Available online: https://CRAN.R-project.org/package=dynamicTreeCut 2016 (accessed on 28 February 2019).
- Sing, T.; Sander, O.; Beerenwinkel, N.; Lengauer, T. Rocr: Visualizing classifier performance in R. Bioinformatics
**2005**, 21, 3940–3941. [Google Scholar] [CrossRef] - Mullins Lab. Divein. Available online: https://indra.mullins.microbiol.washington.edu/DIVEIN/insites.html (accessed on 28 February 2019).
- Deng, W.; Maust, B.S.; Nickle, D.C.; Learn, G.H.; Liu, Y.; Heath, L.; Kosakovsky Pond, S.L.; Mullins, J.I. Divein: A web server to analyze phylogenies, sequence divergence, diversity, and informative sites. Biotechniques
**2010**, 48, 405–408. [Google Scholar] [CrossRef] - Dempster, A.P. The Dempster–Shafer calculus for statisticians. Int. J. Approx. Reason.
**2008**, 48, 365–377. [Google Scholar] [CrossRef] - Geisser, S. Predictive inference; Chapman and Hall: New York, NY, USA, 1993. [Google Scholar]
- Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Second Edition); Springer Series in Statistics; Springer Science+Business Media, LLC: New York, NY, USA, 2009. [Google Scholar]
- Tibshirani, R. Regression shrinkage and selection via the lasso. J. Royal Statist. Society Series B-Methodolog.
**1996**, 58, 267–288. [Google Scholar] [CrossRef] - Gottlieb, G.S.; Heath, L.; Nickle, D.C.; Wong, K.G.; Leach, S.E.; Jacobs, B.; Gezahegne, S.; van’t Wout, A.B.; Jacobson, L.P.; Margolick, J.B.; et al. HIV-1 variation before seroconversion in men who have sex with men: Analysis of acute/early HIV infection in the Multicenter AIDS Cohort study. J. Infect. Dis
**2008**, 197, 1011–1015. [Google Scholar] [CrossRef] - Haaland, R.E.; Hawkins, P.A.; Salazar-Gonzalez, J.; Johnson, A.; Tichacek, A.; Karita, E.; Manigart, O.; Mulenga, J.; Keele, B.F.; Shaw, G.M.; et al. Inflammatory genital infections mitigate a severe genetic bottleneck in heterosexual transmission of subtype A and C HIV-1. PLoS Pathog.
**2009**, 5, e1000274. [Google Scholar] [CrossRef] - Keele, B.F.; Giorgi, E.E.; Salazar-Gonzalez, J.F.; Decker, J.M.; Pham, K.T.; Salazar, M.G.; Sun, C.; Grayson, T.; Wang, S.; Li, H.; et al. Identification and characterization of transmitted and early founder virus envelopes in primary HIV-1 infection. Proc. Natl. Acad. Sci. USA
**2008**, 105, 7552–7557. [Google Scholar] [CrossRef] [Green Version] - LeDell, E.; Petersen, M.L.; van der Laan, M.J. Computationally efficient confidence intervals for cross-validated area under the roc curve estimates (in review). Available online: https://biostats.bepress.com/ucbbiostat/paper304 (accessed on 28 February 2019).
- Los Alamos National Laboratory. Available online: http://www.hiv.lanl.gov/. (accessed on 28 February 2019).
- Matsen Group at Fred Hutchinson Cancer Research Center. Available online: https://matsen.fhcrc.org/research.html. (accessed on 28 February 2019).
- Donnell, D.; Ramos, E.; Celum, C.; Baeten, J.; Dragavon, J.; Tappero, J.; Lingappa, J.R.; Ronald, A.; Fife, K.; Coombs, R.W.; et al. The effect of oral preexposure prophylaxis on the progression of HIV-1 seroconversion. AIDS
**2017**, 31, 2007–2016. [Google Scholar] [CrossRef] - Sivay, M.V.; Li, M.; Piwowar-Manning, E.; Zhang, Y.; Hudelson, S.E.; Marzinke, M.A.; Amico, R.K.; Redd, A.; Hendrix, C.W.; Anderson, P.L.; et al. Characterization of HIV seroconverters in a TDF/FTC prep study: HPTN 067/adapt. J. Acquir. Immune Defic. Syndr.
**2017**, 75, 271–279. [Google Scholar] [CrossRef] - Chaillon, A.; Samleerat, T.; Zoveda, F.; Ballesteros, S.; Moreau, A.; Ngo-Giang-Huong, N.; Jourdain, G.; Gianella, S.; Lallemant, M.; Depaulis, F.; et al. Estimating the timing of mother-to-child transmission of the human immunodeficiency virus type 1 using a viral molecular evolution model. PLoS ONE
**2014**, 9, e90421. [Google Scholar] [CrossRef] - Giorgi, E.E.; Li, H. Estimating the timing of early SHIV infections: A comparison between Poisson Fitter and Beast. Bioinformatics
**2019**. manuscript in preparation. [Google Scholar] - Gottlieb, G.S.; Nickle, D.C.; Jensen, M.A.; Wong, K.G.; Grobler, J.; Li, F.; Liu, S.L.; Rademeyer, C.; Learn, G.H.; Karim, S.S.; et al. Dual HIV-1 infection associated with rapid disease progression. Lancet
**2004**, 363, 619–622. [Google Scholar] [CrossRef] - Herbeck, J.T.; Rolland, M.; Liu, Y.; McLaughlin, S.; McNevin, J.; Zhao, H.; Wong, K.; Stoddard, J.N.; Raugi, D.; Sorensen, S.; et al. Demographic processes affect HIV-1 evolution in primary infection before the onset of selective processes. J. Virol.
**2011**, 85, 7523–7534. [Google Scholar] [CrossRef] - Janes, H.; Herbeck, J.T.; Tovanabutra, S.; Thomas, R.; Frahm, N.; Duerr, A.; Hural, J.; Corey, L.; Self, S.G.; Buchbinder, S.P.; et al. HIV-1 infections with multiple founders are associated with higher viral loads than infections with single founders. Nat. Med.
**2015**, 21, 1139–1141. [Google Scholar] [CrossRef] [Green Version] - Rossenkhan, R.; Novitsky, V.; Sebunya, T.K.; Musonda, R.; Gashe, B.A.; Essex, M. Viral diversity and diversification of major non-structural genes vif, vpr, vpu, tat exon 1 and rev exon 1 during primary HIV-1 subtype C infection. PLoS ONE
**2012**, 7, e35491. [Google Scholar] [CrossRef] [PubMed] - Li, H.; Bar, K.J.; Wang, S.; Decker, J.M.; Chen, Y.; Sun, C.; Salazar-Gonzalez, J.F.; Salazar, M.G.; Learn, G.H.; Morgan, C.J. High multiplicity infection by HIV-1 in men who have sex with men. PLoS Pathog.
**2010**, 6, e1000890. [Google Scholar] [CrossRef] [PubMed] - Bar, K.J.; Li, H.; Chamberland, A.; Tremblay, C.; Routy, J.P.; Grayson, T.; Sun, C.; Wang, S.; Learn, G.H.; Morgan, C.J. Wide variation in the multiplicity of HIV-1 infection among injection drug users. J. Virol.
**2010**, 84, 6241–6247. [Google Scholar] [CrossRef] [PubMed] - Novitsky, V.; Wang, R.; Margolin, L.; Baca, J.; Rossenkhan, R.; Moyo, S.; van Widenfelt, E.; Essex, M. Transmission of single and multiple viral variants in primary HIV-1 subtype C infection. PLoS ONE
**2011**, 6, e16714. [Google Scholar] [CrossRef] [PubMed] - Chaillon, A.; Gianella, S.; Little, S.J.; Caballero, G.; Barin, F.; Kosakovsky Pond, S.; Richman, D.D.; Smith, D.M.; Mehta, S.R. Characterizing the multiplicity of HIV founder variants during sexual transmission among MSM. Virus Evol.
**2016**, 2, vew012. [Google Scholar] [CrossRef] [Green Version] - Zanini, F.; Brodin, J.; Thebo, L.; Lanz, C.; Bratt, G.; Albert, J.; Neher, R.A. Population genomics of intrapatient HIV-1 evolution. Elife.
**2015**, 4, e11282. [Google Scholar] [CrossRef] - Grebe, E.; Facente, S.N.; Bingham, J.; Pilcher, C.D.; Powrie, A.; Gerber, J.; Priede, G.; Chibawara, T.; Busch, M.P.; Murphy, G.; et al. Interpreting HIV diagnostic histories into infection time estimates: Analytical framework and online tool. bioRxiv
**2018**. [Google Scholar] [CrossRef]

**Figure 1.**Prediction errors of the Center of Bounds, PrankenBeast, Poisson Fitter, and modified Poisson Fitter estimators of infection time before (

**a**–

**d**) and after (

**e**–

**h**) calibration for mutation rate after fitting a linear model with terms for log

_{10}plasma viral load (lPVL), the interaction of the estimator with lPVL, the last negative date, the interaction of the estimator with the last negative date and an intercept. Predictions were made on held out data in a leave-on-out cross-validation scheme (see Methods). The sequences used for prediction were: (

**a**), (

**e**): RV217 (NFLG) 1-2 months; (

**b**), (

**f**): CAPRISA 002 (V3) 1-2 months; (

**c**), (

**g**): RV217 ~6 months; (

**d**), (

**h**): CAPRISA 002 ~6 months. The median difference between the predicted and gold-standard values is shown as the center line of each box; the solid box boundaries illustrate the 25th and 75th percentiles (interquartile range, IQR). The leftmost entry (“Gold standard”) depicts the (zero) “prediction” error if the true days since infection values are known. Values depicted in parentheses indicate the root mean squared error, which is an estimate of the standard error when the fitted predictor is applied to future samples, and the bias is shown above these. The whiskers extend to the most extreme data point within 1.5 times the IQR from the box boundaries; points outside of this range are plotted as outlier points. NFLG, near full-length genome.

**Figure 2.**Multiplicity AUC of estimators of multiple-founder infections. Bar plots show areas under the receiver operating characteristic (ROC) curve (AUC) for uncalibrated (red) and calibrated (turquoise) predictors of multiplicity when evaluating predictions on held-out values during leave one-out cross-validation, using the LASSO procedure to select and fit a logistic regression model. Uncalibrated predictors include the method used in the past HVTN sieve analyses, two values computed by the Poisson Fitter software to evaluate a fit to a star-like phylogenetic model, and variants of these using preprocessed inputs (see Methods). Calibrated versions of these predictors are made using models trained using all available data, except for the one participant held out at a time (LOOCV). AUC values of 1.0 indicate a perfect predictor, and values of 0.5 indicate a predictor that is no better than random chance. The sequences used for prediction were: (

**a**): RV217 NFLG 1–2 months; (

**b**): CAPRISA 002 V3 1–2 months; (

**c**): NFLG ~6 months; (

**d**): V3 ~6 months.

Study Feature | RV 217 (ECHO) | CAPRISA 002 |
---|---|---|

HIV-1 subtype(s) | CRF01_AE (MSM); A1/D/C and Recombinants (WSM) | C (WSM) |

Sequencing strategy | Single genome amplification and sequencing | Next generation sequencing (Illumina w/PrimerID) |

HIV-1 genomic region | Near full length genome (NFLG) | V3 variable loop of the gp120 envelope protein |

Median bases per HIV-1 sequence (min, IQR, max) | NFLG: 8813 (8624, 8753-8841, 8891); LH:5057 (5027, 5051-5063, 5209); RH:5061 (4898, 5040-5092, 5141) | 498 (495, 498-498, 501) |

Median HIV-1 sequences per participant after removing recombination and hypermutation (min, IQR, max) | 9.5 (2.6, 8.4-10, 11) NFLG: 10 (2, 8-10, 11) LH: 10 (2, 8-10,10) RH: 10 (3, 8-10, 11) | 352 (26, 142.3-640, 2764) |

Median HIV-1 sequences removed per participant (min, IQR, max) | 0 (0, 0-1, 8) NFLG: 0 (0, 0-1.3, 8) LH: 0 (0, 0-0, 4) RH: 0 (0, 0-1, 4) | 0 (0, 0-1, 356) |

Total number of participants | 36 | 21 |

Number of MSM | 17 | 0 |

Number of WSM | 19 | 21 |

N participants with 1-2M sample | 36 | 20 |

N participants with ~6M sample | 34 | 18 |

Mean Gold days 1-2M (SD) | 47 (4.3) | 62 (4.9) |

Mean Gold days ~6M (SD) | 184 (11.3) | 180 (12.1) |

N Gold isMultiple 1-2M (%) | 10 (28%) | 5 (25%) |

N Gold isMultiple ~6M (%) | 10 (29%) | 6 (33%) |

Median bounds width in days 1-2M (min, IQR, max) | 48 (20, 34-76, 308) | 54 (27, 41-70, 108) |

Median bounds width in days ~6M (min, IQR, max) | 146 (18, 91-195, 369) | 120 (30, 86-170, 183) |

Mean lPVL 1-2M (SD) | 4.5 (0.8) | 4.9 (0.7) |

Mean lPVL ~6M (SD) | 4.1 (1.0) | 4.5 (0.8) |

_{10}plasma viral load; SD, standard deviation; Gold = modified center of bounds (COB) timing estimate applied to previously unavailable acute tight diagnostic bounds (prior to the 1-2M sample date) and the agreed-upon gold standard is a multiple indicator, see Methods.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rossenkhan, R.; Rolland, M.; Labuschagne, J.P.L.; Ferreira, R.-C.; Magaret, C.A.; Carpp, L.N.; Matsen IV, F.A.; Huang, Y.; Rudnicki, E.E.; Zhang, Y.;
et al. Combining Viral Genetics and Statistical Modeling to Improve HIV-1 Time-of-Infection Estimation towards Enhanced Vaccine Efficacy Assessment. *Viruses* **2019**, *11*, 607.
https://doi.org/10.3390/v11070607

**AMA Style**

Rossenkhan R, Rolland M, Labuschagne JPL, Ferreira R-C, Magaret CA, Carpp LN, Matsen IV FA, Huang Y, Rudnicki EE, Zhang Y,
et al. Combining Viral Genetics and Statistical Modeling to Improve HIV-1 Time-of-Infection Estimation towards Enhanced Vaccine Efficacy Assessment. *Viruses*. 2019; 11(7):607.
https://doi.org/10.3390/v11070607

**Chicago/Turabian Style**

Rossenkhan, Raabya, Morgane Rolland, Jan P.L. Labuschagne, Roux-Cil Ferreira, Craig A. Magaret, Lindsay N. Carpp, Frederick A. Matsen IV, Yunda Huang, Erika E. Rudnicki, Yuanyuan Zhang,
and et al. 2019. "Combining Viral Genetics and Statistical Modeling to Improve HIV-1 Time-of-Infection Estimation towards Enhanced Vaccine Efficacy Assessment" *Viruses* 11, no. 7: 607.
https://doi.org/10.3390/v11070607