2.1. Ethics statement

All participants provided written informed consent for the study. Written assent and written parental consent were obtained for participants less than 18 years of age. The RCCS is administered by the Rakai Health Sciences Program (RHSP) and has received ethical approval from the Uganda Virus Research Institute’s Research and Ethics Committee (GC/127/08/12/137), the Uganda National Council for Science and Technology (HS450), and the Johns Hopkins School of Medicine (IRB00217467).

2.2. Study design and participants

The RCCS conducts population-based surveys every 18–24 months in agrarian, semi-urban trading, and Lake Victoria fishing communities in southern Uganda. Data in this study were collected over six RCCS survey rounds conducted between January 2010 and November 2020. As survey rounds occurred over more than a year, we herein refer to them by the median interview date. Communities that participated in the RCCS were categorized based on their geographic setting and primary economic activity (inland communities: agrarian/trading, Lake Victoria communities: fishing). These communities differ considerably in their HIV burden (HIV prevalence of  ∼ 14% [agrarian],  ∼ 17% [trading], and  ∼ 42% [fishing]) [36]. At each survey round, households were censused and all residents aged 15–49 who were able to provide consent (assent for those under 18) were invited to participate in a survey. Survey participants were eligible to participate exactly once in each survey round (“participant-visits”). As part of the survey, participants completed a detailed structured sociodemographic, behavioral, and health questionnaire. Specifically, participants were asked to self-report their sex, age, residency status (e.g. recent migration into a community), circumcision status (among males), occupation, occupation of sex partners in the year prior to the survey, and number of lifetime sex partners. As HIV is more prevalent among female sex and bar/restaurant workers [40,41], we generated a composite variable indicating reported sex or bar/restaurant work among women and sex with a sex or bar/restaurant worker among men to determine if these individuals were at higher risk of being multiply infected.

To account for the fact that the number of lifetime sex partners increases over the lifespan, we calculated the mean number of lifetime sex partners within population strata (s) defined by HIV serostatus, sex, age category in five year bins, and community type (inland/fishing) () to allow for standardization of the observed responses. Responses of no lifetime sex partners were treated as missing data as HIV transmission in this setting is predominantly heterosexual [42] and we therefore expected these individuals to have had at least one sexual encounter in order to acquire HIV, although we cannot rule-out perinatal transmission with available data. When calculating missing data was imputed to the mean value of a lognormal distribution fit to all numeric responses of  ≥ 1 lifetime sex partner within strata defined by HIV serostatus, sex, age category, and community type. Additionally, some RCCS participants provided categorical responses (“1–2” or “3+” lifetime sex partners). To calculate , we first imputed these values to a numeric response. Responses of “1–2” were imputed to the mean response among PLHIV reporting either one or two lifetime sex partners within strata. Similarly, responses of “3+” were imputed to the mean value of a lognormal distribution fit to all numeric responses of  ≥ 3 lifetime partners within strata as above.

In addition to completing the survey questionnaire, participants provided venous blood samples for HIV testing, viral load quantification, and viral deep sequencing. HIV serostatus was evaluated using a validated rapid test algorithm [43]. HIV viral load quantification was conducted using the Abbott real-time m2000 assay (Abbott Laboratories).

2.3. HIV deep sequencing and bioinformatic processing

HIV RNA deep-sequence data from plasma samples contributed by RCCS participants was generated through the Phylogenetics and Networks for Generalized HIV Epidemics in Africa consortium (PANGEA-HIV) [44–46]. The study sample included RCCS participants with HIV who were viremic ( ≥ 1 , 000 copies/mL) at one of their study visits between January 2010 and November 2020. To avoid biasing our inferences, for individuals that participated in multiple survey rounds we used only the data from the sample with the highest genome coverage or the highest viral load in the case of ties in our analyses of multiple infections. The study sample was further restricted to individuals in putative transmission networks and excluded individuals for who another phylogenetically close individual could not be identified over the entire study period [39]. All available sequence data for individuals in putative transmission networks was included in phylogenetic analyses.

Deep-sequencing was performed with two protocols (S1 Table), as previously described [39]. Briefly, for sequence data generated through the amplicon protocol, viral RNA was extracted from plasma samples on the QIAsymphony SP workstation with the QIAsymphony DSP Virus/Pathogen Kit. cDNA was generated through one-step reverse transcription PCR protocol using universal HIV-1 primers designed to generate four overlapping amplicons across the HIV-1 genome [34]. Deep-sequencing was conducted at the Wellcome Trust Sanger Institute core facility using the Illumina MiSeq and HiSeq platforms. To generate sequence data using the bait-capture protocol viral RNA was similarly extracted using the QIAsymphony DSP Virus/Pathogen Kit followed by library preparation according to the veSEQ-HIV protocol [33]. Library preparation was performed using the SMARTer Stranded Total RNA-Seq v2-PicoInputMammalian (Clontech, TakaRaBio) kit and double-stranded dual-indexed cDNA generated using in-house indexed primers. Libraries were pooled and cleaned with Agencourt AMPure XMP. Pooled libraries were hybridized to HIV-specific biotinylated 120-mer oligonucleotides (xGen Lockdown Probes, Integrated DNA Technologies) and isolated with streptavidin-conjugated beads. Captured libraries were PCR amplified prior to generation of 350-600 base pair (bp) paired-ends reads with the Illumina NovaSeq 6000 at the Oxford Genomic Centre.

Kraken v.0.10.5-beta [47] with a custom database of human, bacterial, archael, viral, and fungal genomes was used to isolate reads of viral and unknown origin which were trimmed of adaptors and low-quality bases using trimmomatic [48] v.0.36/0.39. Trimmed reads were de novo assembled into contigs using SPAdes [49] and metaSPAdes [50] v.3.10. Shiver v.1.5.7 [51] was used to align reads to a reference sequence constructed for each sample using these contigs.

2.4. Inference of within-host deep-sequence phylogenetic trees

To improve the computational efficiency of our within-host deep-sequence phylogenetic analyses we first clustered participants with HIV into putative transmission networks as previously described (S1 File) [39,52], and then grouped putative networks into batches for deep-sequence phylogenetic analyses.

Deep-sequence data belonging to participants in each batch were further processed with phyloscanner [38] v.1.8.1 to infer within-host phylogenetic trees in 287 sliding windows of length 250 bp with a step size of 25 across the HIV genome as in [39]. As suggested in [38], this window-size was chosen to be long enough to capture sufficient within-host diversity to provide phylogenetic signal but no longer than the target read length and short enough to minimize within-window recombination. Windows spanning env gp120 were excluded as genetic diversity in the variable loop regions [53] led to poor sequence alignment and unreliable within-host phylogenetic trees. In addition to deep-sequence data from RCCS participants, we included as phylogenetic background 113 consensus sequences from representative subtypes and circulating forms and 200 near full-length consensus sequences from Kenya, Uganda, and Tanzania (Los Alamos National Laboratory HIV Sequence Database, http://www.hiv.lanl.gov, S2 File). Within phyloscanner, MAFFT v.7.475 [54] with iterative refinement and iterative re-alignment using consistency scores was used to align sequencing reads and IQ-TREE v.2.0.3 with the GTR+F+R(Free-Rate)6 substitution model was used for phylogenetic inference [55,56]. Phylogenetic branch lengths within phyloscanner were adjusted to account for varying substitution rates across the HIV genome as described in [57] (S3 File). Adjusted distances can be interpreted as average distances expected in the pol gene. The genomic coordinates of input sequence data were standardized to the coordinates of the HIV-1 HXB2 reference genome (GenBank: K03455.1).

For each participant, phyloscanner was used to estimate the number of genetically distinct phylogenetic lineages (subgraphs) in each genome window using a modified parsimony algorithm. In each window, for each participant, the given phylogenetic tree was pruned to include only tips from the given participant and the specified outgroup (here, the subtype H consensus sequence). Ancestral nodes in the pruned tree were assigned to one of two states: either that of the participant or an unsampled “unassigned” state (to which the outgroup and root of the phylogeny was assigned), representing the lineages that are evolutionarily ancestral to the lineages that initiated a given host’s infection. To accurately assign nodes without relying on patterns of phylogenetic clustering with reference sequences, we employed a modified Sankoff minimum parsimony algorithm for ancestral state reconstruction as described in [38,58] (in particular, see Supplementary Information 1.2 and Supplementary Fig 1 in [38]). This algorithm assigns a cost (c(n, h)) to a state change along a lineage ending at ancestral node n that is proportional to the sum of the branch lengths descendant from that node that give rise to tips form host h (l(n, h)). As tips from all other subjects with the exception of the outgroup were pruned from the tree prior to this procedure (“single-host tree”), this is equivalent to the sum of the total branch length of the subtree with node n as its root. Specifically, this cost was calculated as:

(1)

where k is a tuneable constant that controls the penalty associated with fewer host h subgraphs. Traditional parsimony is recovered when k = 0 which will always assign all tips in a single-host tree to a single subgraph, regardless of the phylogenetic branch length captured within that subgraph. As k → ∞, each tip belonging to host h will be assigned to a unique subgraph. Here, we parameterized k with the goal of distinguishing evolution that occurred within a given host from evolution that occurred prior to HIV acquisition, in the case of multiple infection. In the case of single infection, all tips in a single-host tree will be closely related (e.g. Fig 1A) and therefore we want the ancestral reconstruction that minimizes c(n, h) to assign all tips to a single subgraph. In the case of a multiple infection the tips will be expected to fall into ( ≥ )2 clades with relatively small within-subgraph distances but large between-subgraph distances and we seek to parameterize k such that the ancestral reconstruction minimizing c(n, h) differentiates these clades into distinct subgraphs. We conservatively used a k value of 15 such that , which is greater than the 99th percentile of the pairwise genetic distances between epidemiologically confirmed HIV transmission pairs [57] and comparable to within-subtype HIV genetic diversity within Rakai [7].

Quality filtering of inferred within-participant phylogenetic trees was performed with phyloscanner. Specifically, within each window, subgraphs with less than three reads or less than 1% of reads from a particular participant were marked as putative contaminants and removed from the analysis. To mask regions with insufficient data for reliable phylogenetic inference any window with less than 30 reads from a given participant after aforementioned filter was also removed from the analysis. After filtering we identified the subgraphs with data from the deep-sequenced reads from each sequenced sample for a given participant.

2.5. Bayesian model to identify multiple infections

We developed a Bayesian statistical model to identify samples harboring multiple infections and estimate the prevalence of multiple infections in a set of deep-sequencing reads that were processed with phyloscanner. We refer to this model as the the deep-phylo multiple infection model (deep-phyloMI). We first summarized the phyloscanner output for each sample and each genomic window in terms of two binary variables, (presence/absence of sequencing reads from sample i in window w following phyloscanner contamination filtering) and (presence/absence of multiple subgraphs for sample i in window w) where n is the number of sequenced samples. To simplify notation below, when we set . We further summarized the data for sample i into two quantities, and where is the number of genome windows.

2.5.1. Base model accounting for partial sequencing success of infecting variants.

We first developed a base model that accounts for partial sequencing success across the HIV genome in giving rise to the observed and . Working from first principles, we first derived a likelihood model for observing the pair of counts (, ) for the unobserved groups of samples with true multiple infection () and single infection (), and subsequently marginalise out the unknown true multiple infection status (either or ). Among samples from multiply infected individuals (), we assumed that the probability of sequencing each of the infecting variants in window w was given by for each sample i. The probability of sequencing at least one variant in each window is therefore and the probability of sequencing both variants given at least one was sequenced is therefore . Assuming sequencing success was independently and identically distributed for each sample, we obtained(2a)(2b)where represents the 0-truncated Binomial distribution as we only consider data from individuals with phyloscanner output in at least one genomic window, and is the total number of genomic windows. This model implicitly accounts for the presence of windows in which only a single variant was present in the phyloscanner output due to incomplete sequencing success. For samples from individuals infected with only a single variant (), we obtained analogously

(3a)(3b)

Taken together, the joint likelihood of observing the count pair (, ) conditional on latent multiple infection status is given by

(4)

Thus, aggregating over the two unknown possible multiple infection states for each sample in a finite mixture model framework, we have

(5)

One of our primary inferential targets was the individual-level probability of harboring multiple infection not conditional on observed and , which we denoted with . Making this target explicit in the joint likelihood, we have

(6a)(6b)(6c)

and so the log posterior distribution of the parameters , for all the data under our model is

(7)

where we use f to denote posterior and prior densities.

2.5.2. Base model prior densities.

In the base model, prior to observing data, we modelled the individual-level probability of multiple infection as identical for all i with the prior density,

(8)

with diffuse variance [59]. Given the known log-linear dependency of sequencing success on log viral load [33], known differences in sequencing success rates by sampling protocol [39], and other factors, we specified the prior on the individual-level sequencing probability through a logistic mixed effects model. Specifically, we modeled with

(9a)(9b)(9c)(9d)(9e)(9f)(9g)(9h)

where and are indicator variables for whether sample i was sequenced using the amplicon or bait capture approach respectively and , , and are the sample log₁₀ copies/mL values standardized to have mean zero and standard deviation 1 among all samples and among only the amplicon () and bait capture () samples, respectively. To maintain identifiability we constrain  +   +  by specifying their joint prior distributions with a zero-mean multivariate normal with a particular variance-covariance matrix described in [59], such that all marginal distributions are standard normal, e.g. and , which we represent with the notation stz-MVN. To maintain marginal priors with standard deviation , we adopt a non-centered parameterisation and post-multiply the sum-to-zero random variables with . Finally, denotes an individual-level random effect.

2.5.3. Modelling false-negative and false-positive phylogenetic observations.

We extended the base model to account for possible false-negative and false-positive phylogenetic observations, accounting for incomplete removal of false-positive observations through phyloscanner, and/or incomplete phylogenetic identification of multiple infections due to insufficient phylogenetic background. First, among samples from individuals in which we accounted for the scenario in which both variants are successfully sequenced in a given window but were identified as a single phylogenetic clade by phyloscanner, i.e. false-negative observations, by modifying our data-generating model to

(10)

where λ represents the false-negative rate. We analogously accounted for the scenario in which only a single variant was sequenced but phyloscanner spuriously assigned multiple subgraphs in a given window, i.e. false-positive observations, through a false-positive rate ε in the model. We modeled false-positives among samples lacking multiple infection and among windows in multiply infected samples in which only a single variant was sequenced, which occurs with probability when , but was spuriously assigned to two subgraphs. Note that because we did not differentiate between windows with exactly 2 and >2 subgraphs, we do not consider the scenario where both variants are sequenced in a true multiple infection and the two sequenced variants are spuriously assigned to 3 or 4 subgraphs. Our data generating model was updated to account for false-positives and false-negatives as:

(11a)(11b)

with additional prior densities

(12a)(12b)

where [,2.2] represents that logit ( λ )  was constrained to be <2.2 and all other components of the model remaining as above.

2.5.4. Estimating risk factors of multiple infection.

We further extended the model described above to model the probability of multiple infection as dependent on potential clinical, behavioral, and/or epidemiological risk factors through a logistic regression approach. Specifically, we modeled the logit of the individual-level multiple infection prior probabilities as a linear predictor of fixed effects,

(13a)(13b)(13c)

where are dimensional row vectors for each of putative multiple infection predictive covariates and are dimensional column vectors of fixed effect coefficients. For all categorical j in with levels, we model the corresponding fixed effects with the sum-to-zero joint multivariate normal prior defined above to maintain identifiability.

We also considered a fixed effects model with Horseshoe-type shrinkage priors [60,61] on the effect sizes to handle correlated individual-level covariates. To maintain desirable sum-to-zero properties, we define a global non-negative shrinkage parameter τ ∈ [ 0 , ∞ ) , and for each categorical j with levels non-negative local shrinkage parameters , and the diagonal matrix . We then specify sum-to-zero shrinkage effects through a joint zero-mean multivariate normal distribution with variance covariance matrix  −  , such that and the induced marginal distributions of each are , which we refer to . We incorporated the global shrinkage parameter in non-centered parameterisation through post-multiplication as in Eq 9. Therefore, we have:

(14a)(14b)(14c)(14d)(14e)

where we modelled the with t-distributions with 2 degrees of freedom instead of Cauchy distributions to ease numerical sampling.

As above, the number of lifetime sex partners included missing and ambiguous responses (e.g. “3+”), and these values were estimated as additional random variables in the Bayesian inference, assuming they were missing at random within sex, age, and community type, using lognormal prior distributions specific to these strata defined by the non-missing responses as above. Imputed values for missing responses were limited to the range [1,60] and responses of “3+” were limited to the range [3,60].

2.5.6. Generated quantities.

Based on the estimated parameter distributions of the models described above, we generated a number of quantities to aid in interpretation of our results.

2.5.6.1. Posterior probabilities of individual-level multiple infection.

We computed the posterior probabilities of individual-level multiple infection directly from Monte Carlo samples of the joint posterior density via

(15)

by taking for each individual i all Monte Carlo samples of the posterior density of , evaluating according to:

(16)

and calculating the expectation across these.

2.5.6.2. Prevalence of multiple infection in the study sample.

Following from prior work on Bayesian latent class models with covariates [66–71], under the base model the posterior estimate of the prevalence of multiple infection in the study sample is given by:

(17)

where is from the joint posterior density of the model defined by Eqs 8, 9, 11, and 12. In the presence of modeled risk factors, the prevalence of multiple infections in the study sample will vary based on sub-groups s defined by X^risk. In the case where contains only the covariates used to define s:

(18)

Finally, we estimated the prevalence in a target population (e.g. the entire sample of sequenced viremic RCCS participants) through post-stratification:

(19)

where are the number of sampled individuals in each of the S sub-populations s and are the sub-group specific prevalence estimates from Eq 18.

2.5.6.3. Prevalence and risk ratios of harboring multiple infection associated withepidemiological covariates.

We calculated a posterior estimate for the prevalence risk ratio (PRR) of multiple infections in epidemiological strata s^* as compared to strata s as

(20)

In the case where contained additional covariates beyond those used to define s^* from s we estimated a multivariate risk ratio (RR) associate with the covariate(s) that distinguish s^* from s by calculating the ratio of the estimated risk of multiple infection for person i as if they belonged to strata s^* divided by the risk of multiple infection of the same person i as if they belonged to strata s, while holding all other covariates at their observed values (based on the design matrices and , respectively):

(21)

2.5.6.4. Post-stratification adjustments.

Finally, because sequence data was not available for all viremic participants with HIV in our study population, we employed post-stratification based on prevalence estimates in epidemiological sub-groups s to estimate the prevalence of multiple infections in the population under study (viremic study participants) [72]. Specifically, we calculated

(22)

where is the estimated population size or estimated relative population size of sub-group s. The population prevalence ratio between two non-overlapping composite sub-groups can therefore be calculated as in Eq 20. We performed post-stratification based on the total number of participant-visits from viremic PLHIV stratified by age ((14, 24], (24, 34], and (34, 49] years), sex, and community type. Because viral load measurements were not routinely conducted for all PLHIV in the 2010 and 2012 survey rounds we calculated population-sizes using only participant-visits in the 2014-2019 survey rounds.

2.6. Simulation study

We used simulations to validate our inference model. For all simulations, we simulated data for genome windows in n = 2 , 000 samples which were assigned a normalized log₁₀ viral load () with random draws from a N(0,1) distribution. For all samples, was drawn from a N(0,1) distribution and calculated as  +   +  with and . Under these parameters, we generated three simulated data sets as described below.

2.6.1. Base simulation.

(23a)(23b)(23c)(23d)(23e)

where represents a vector of x repeated n times and  ⊕  represents concatenation of two vectors.

2.6.2. Full simulation.

(24a)(24b)(24c)(24d)(24e)(24f)(24g)

Additional simulations from this simulation model were generated with all other parameters held constant except (A): , (B): λ = 0 . 10 , 0 . 20 , 0 . 40, and (C): ε = 0 , 0 . 005 , 0 . 05.

2.6.3. Extended simulation.

(25a)(25b)(25c)(25d)(25e)(25f)(25g)

where represents the entry in the ith row and jth column of the design matrix and shuffle(v) denotes shuffling the elements of v.

2.7. Data analysis and visualization

All data analysis was conducted in R v.4.4.1 [73] using the tidyverse [74] with dplyr v.1.1.4 [75], tibble v.3.2.1 [76], and tidyr v.1.3.1 [77]. Haven v.2.5.4 [78] was used to parse a subset of input data files. Visualization of data and results was done using ggplot2 v.3.5.1 [79] with bayesplot v.1.11.1 [80,81], cowplot v.1.1.3 [82], and patchwork v.1.2.0. [83]. Phylogenetic trees were manipulated and visualized using ape v.5.8 [84], ggtree v.3.12.0 [85–89], phytools v.2.1.-1 [90], and tidytree v.0.4.6 [85]. Highest posterior density intervals were calculated with HDInterval v.0.2.4 [91] and convergence statistics were assessed with posterior v.1.6.0 [92]. Preliminary analyses and model fitting was performed using fitdistrplus v.1.1-11 [93].

3.1. Phylogenetic signatures of multiple infection in population-based pathogen surveillance

Between 2010 and 2020, 50,967 participants contributed to the RCCS in 109,608 visits over six survey rounds. Overall, 8,841 participants were HIV seropositive and 3,586 were viremic (plasma viral load  ≥  1,000 copies/mL) at one of their visits (S2 and S3 Tables). Of these, 2 ,029 individuals were sampled between January 2010 and November 2020, had HIV RNA deep-sequence data available at minimum quality criteria for deep-sequence phylogenetic analysis, and were identified as a member of a putative transmission network (Tables 1 and S4 and S1 File.). Availability of sequence data among viremic participants was generally higher among men, from residents of fishing communities, and from participants aged 25-34 years.

We next inferred within-host phylogenies from deep-sequencing reads in twenty-nine 250 bp non-overlapping genomic windows using phyloscanner (S4 File.), which captured evolutionary relationships of HIV variants within individual participants. Sequencing coverage varied significantly between samples (median [interquartile range (IQR)]: 5000 [4250] bp, S1A Fig) but was generally higher among bait capture sequenced samples and samples with higher viral load. Across the genome, sequencing success was highest in gag (Figs 1F and S1B), likely due to differential amplification efficiency of the primers used in the amplicon sequencing approach [94].

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Table 1. Characteristics of the study sample obtained from population-level HIV deep-sequence surveillance in the Rakai Community Cohort Study, 2010-2020, stratified by availability of deep-sequence data.

https://doi.org/10.1371/journal.ppat.1013065.t001

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Fig 1. Empiric phylogenetic multiple infection signatures from 2,029 samples from people with viremic HIV in the Rakai Community Cohort Study, 2010-2020.

(A) Representative within-host phylogenetic tree lacking evidence of multiple phylogenetic subgraphs. (B) Representative within-host phylogenetic tree with two subgraphs as indicated by the green and blue shading of the tips. (C) Distribution of branch length distance between the MRCAs of the two subgraphs with the most sequencing reads in all genome windows windows with  ≥ 2 subgraphs from all samples. Bins are shaded according to the 95th and 50th percentile. Vertical dotted line indicates median value. Binwidth is calculated such that there are approximately 50 bins across the range of observed values. (D) Per-sample number of non-overlapping genome windows with sequence data versus the number of non-overlapping genome windows with multiple subgraphs. Samples with at least one window with multiple subgraphs are shown in purple. Points have been jittered along both the X and Y axes for visual clarity. Dotted line shows modeled prediction in the absence of false-positive or false-negative multiple subgraph windows. Marginal densities are shown at right and above the scatter-plot. (E) Schematic of the HIV genome based on the coordinates from HXB2 (Genbank: K03455.1). (F) Number of samples with sequence data in each of the 29 non-overlapping genome windows. (G) Number of samples with evidence of multiple subgraphs in each of the 29 non-overlapping genome-windows.

https://doi.org/10.1371/journal.ppat.1013065.g001

To characterise phylogenetic signatures of multiple infection, we used phyloscanner to identify distinct co-circulating variants among participants with viremic HIV (Materials and methods and Fig 1A and 1B). We tabulated the number () of genome windows in which distinct phylogenetic lineages (phylogenetic subgraphs) were observed. The median genetic distance between the most recent common ancestors of subgraphs in genome windows with multiple subgraphs was 0.19 [IQR: 0.17] substitutions/site (Figs 1C and S2), which is consistent with contemporary circulating genetic diversity within Rakai [7,57]. Empirically, 181 (8.92%) samples had multiple subgraphs in at least one of the 29 non-overlapping windows (Fig 1D). Among these, the proportion of sequenced windows in which multiple subgraphs were observed varied considerably, but was generally relatively rare (median [IQR] 11.11 [19.14]% of sequenced windows for each sample, 2 [3] windows total). We observed a clear dependence of the ability to identify multiple subgraphs on sequencing success as quantified by genome coverage in the phyloscanner output. Of those samples with sequence data in all genome windows, 12.26% (52/424) had at least one window with multiple subgraphs compared to 8.04% (129 / 1605) among the remaining samples. Multiple subgraph windows were more common in the genome windows corresponding to gag, env, and nef, likely reflecting circulating genetic diversity in these regions with higher substitution rates [95]. Previous studies of HIV multiple infection in this setting have used amplicon-based deep-sequencing of two regions in p24 (1427–1816) and gp41 (7941–8264) regions [2,29,30]. Of 1,742 sequenced participants with data in windows spanning these regions (S4 File.), 75 (4.31%) had multiple subgraphs in one of the regions.

3.2. Bayesian model to identify multiple infections from pathogen deep-sequencedata

The observed dependence between phylogenetically identified samples with multiple infection and successful genome sequencing implies it is difficult to deduce the underlying prevalence of multiple infections from the empirical data without a statistical model that accounts for partial sequencing success, false-positive multiple subgraphs, and false-negative unique subgraphs within hosts. Specifically, because identification of multiple infection requires successful sequencing of both variants and genetic divergence between those variants, there is inherently more uncertainty in multiple infection status when sequencing success is poor or when infecting variants are genetically related in the sequenced region of the genome. Further, contamination or sequencing errors may give rise to spurious within-host genetic diversity and thereby inflate the estimated prevalence of multiple infection.

Therefore, we constructed a Bayesian model accounting for partial sequencing success to estimate the probabilities that each individual harbors a multiple infection, prevalence of multiple infection among deep-sequenced viremic participants, and risk factors for multiple infection (Materials and methods). We first verified that we were able to accurately estimate model parameters on simulated test data in the presence of incomplete sequencing success (S5 Table.). Next, we investigated the impact of false-positive and false-negative observations, as empiric analyses of RCCS deep-sequence data indicated that false-negative rates were likely substantial in that among samples with , the observed values for a given number of sequenced windows () was less than expected based on our model (S1 File. and Fig 1D). We found that failing to account for these errors led to an overestimation of the prevalence of multiple infections on simulated data (Fig 2A and S6 Table.). This prompted us to explicitly include false-positive and false-negative detection rates in our model as free parameters. With this, we found that model parameters could be accurately estimated on simulated data (Fig 2B–2H and S7 Table.). Model performance was robust across simulations covering a range of reasonable values of the prevalence of multiple infections as well as false-positive and false-negative rates of multiple subgraph observation(S3, S4, and S5 Figs).

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Fig 2. Verification of model accuracy for estimating multiple infection prevalence on simulated data with incomplete sequencing success and false-negative and false-positive observations.

(A) Number of windows with sequence data (x-axis) v. number of windows with multiple subgraphs (y-axis) for each simulated sample. Data from multiply infected samples is highlighted in red. Marginal distributions are shown at right and above. (B) Estimated posterior probability of multiple infection for each sample. Confidence bounds represent the 95% highest posterior density. Data for each sample is shaded as in (A). (C-H) Posterior distributions of the baseline sequencing success (, C), dependence of sequencing success on viral load (log copies/mL) standardized to mean = 0 and standard deviation = 1. (, D), standard deviation of per-individual sequencing success random effect (, E), the multiple subgraph false-negative rate (λ, F), the multiple subgraph false-positive rate (ε, G), and the population prevalence of multiple infections (, H). Posterior distributions in (C-H) bins are shaded according to the 95% and 50% HPD. Histogram bin width is calculated such that there are approximately 50 bins over the range of the plotted values. True values are shown as vertical dotted lines.

https://doi.org/10.1371/journal.ppat.1013065.g002

To identify risk factors for multiple infection among people living with HIV, we formulated an extended model in which individual-level prior multiple infection probabilities are described with a logit linear predictor of putative risk factors. On simulated data, this model accurately estimated the true risk ratio associated with a covariate leading to a two-fold higher probability of harboring a multiple infection (risk ratio (RR) median [95% HPD] 1.74 [1.08–2.48]) in the context of four additional background null covariates (S8 Table.).

3.3. Prevalence of HIV multiple infections among sequenced participants

We next considered estimating the prevalence of multiple infection in the sequenced sample of 2,029 participants living with viremic HIV. In a model accounting for partial sequencing success and false-positive and false-negative observations of multiple subgraphs we estimate that 92 (4.53%) of the sequenced viremic PLHIV had a median posterior probability of multiple infection greater than 50% when allowing the probability of multiple infection () to vary by age, sex, and community type (Figs 3A, 3B, and S6). Our empirical analyses above demonstrated that the number of genome windows with multiple subgraphs is less than would be expected in the absence of false-negatives (Fig 1D). In line with this observation, the model estimated a high false-negative rate (median [95% HPD] 57.63% [53.27%–61.99%], S9 Table.), implying that empirical phylogenetic signatures of multiple infection under-estimate the true infection status of individuals in any single HIV genomic window. It was therefore essential to have whole-genome data from a subset of participants (Fig 1) to estimate false-negative detection rates. Further, informed by the 91.08% of samples with no multiple subgraph windows, we estimated the false-positive rate to be low (0.32% [0.26%–0.4%]). However, we note that even a low absolute rate will likely give rise to spurious multiple subgraph observations in a large sample size, which warrants consideration in our statistical framework.

In this model, the estimated prevalence of multiple infections in the study sample was 5.86% [4.65%–7.21%] (S9 Table.). Relaxing our minor subgraph frequency-based filtering step resulted in only a slightly higher prevalence of multiple infections in the study sample (6.1% [4.86%–7.39%], S10 Table.). When considering only genome windows spanning the p24 and gp41 regions as in previous studies (e.g. [2,29,30]), we were unable to estimate with suitably high effective sample size (ESS) values as there were at most two regions of data for each sample. We therefore fixed based on the whole-genome analysis (S9 Table.) and found that that the sample prevalence of multiple infections based on p24 and gp41 was considerably lower as compared to the whole-genome analysis (2.31% [0.71%–4.94%], S11 Table.), highlighting the utility of incorporating whole-genome data into our inference. Finally, after adjusting for slight biases in the availability of sequence data among viremic participants (Table 1) using post-stratification based on age, sex, and community type (S4 Table), the prevalence of multiple infections among viremic PLHIV in the RCCS was estimated to be slightly lower than the prevalence in the sequenced sample (4.09% [2.95%–5.45%], Fig 3C).

We next used our model to identify individuals with likely multiple infection based on their within-host phylogenetic trees and our modeling framework. Classification was based on the inferred, posterior multiple infection probabilities, and therefore our model-based approach accounted for individual-level factors associated with sequencing success and population-level false-postive and false-negative rates. We determined a binary classification cut-off above which individuals were classified as having a likely multiple infection such that the total number of identified individuals was consistent with the estimated prevalence in the sample, which resulted in a cut-off of 3.5%. Using this threshold, we estimated there were 118 individuals with a likely multiple infection (Fig 3B).

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Fig 3. Individual-level estimates and population-level characteristics of HIV multiple infection in people with viremic HIV in the Rakai Community Cohort Study, 2010-2020.

(A) Estimated posterior probability of multiple infection for each participant. Confidence bounds represent the 95% highest posterior density. Participants with at least one multiple subgraph window are shown in purple. (B) Number of participants with multiple infection as a function of the threshold used to dichotomize the probability of multiple infection. Central estimate uses the median estimated prevalence of multiple infections and shading uses 95% and 50% HPD. Horizontal dotted line plotted at the number of participants needed to match the estimated population prevalence of multiple infection. (C) Posterior distribution of the prevalence of multiple infections among viremic participants in the RCCS after accounting for sampling biases. Bins are shaded according to the 95% and 50% HPD. Histogram width is calculated such that there are approximately 50 bins over the range of the plotted values.

https://doi.org/10.1371/journal.ppat.1013065.g003

3.4. Risk factors of HIV multiple infection

In African contexts, HIV infection risk varies at the individual-level, such as by age, gender, sexual behaviour and circumcision status, and at the community-level [35,36,41]. We therefore next aimed to characterize individual and population-level risk factors for multiple infection with HIV. First, given the significantly higher prevalence of HIV and viremic HIV in Lake Victoria fishing communities [36,96], we investigated whether participants with viremic HIV in these communities had increased risk of multiple infection as compared to participants with viremic HIV in inland communities. Using the model described above with age, sex, and community type as predictors of the probability of multiple infection and accounting for sequencing biases through poststratificaiton we calculated the prevalence of multiple infections among viremic PLHIV in fishing and inland communities and found that multiple infections in fishing communities were 2.33 times (95% HPD 1.3–3.7)-times more frequent than in inland communities (with posterior median [95% HPD] prevalence of multiple infection of 7.42% [5.62%–9.31%]) and 3.14% [1.8%–4.74%] respectively, Fig 4A and S9 Table.). The estimated prevalence ratio for HIV multiple infection was therefore broadly comparable to the risk ratio of HIV prevalence and viremia in fishing as compared to inland communities (2.5-3)[36,96], consistent with the expectation that the risk of superinfection acquisition scales with the population prevalence of viremic HIV. Because participants from fishing communities are oversampled in our sequence data (Tables 1 and S4), this also explains the lower estimated prevalence of multiple infections in the population as compared to the sample.

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Fig 4. Risk factors of HIV multiple infection among people with viremic HIV in the Rakai Community cohort Study, 2010-2020.

(A) Posterior distribution of the prevalence of multiple infections stratified by community type, accounting for sampling biases, estimated in a multivariate model (age, sex, and community type) with diffuse priors (n =  2,029). Bins are shaded according to the 95% and 50% highest posterior density (HPD). Histogram width is calculated such that there are approximately 50 bins over the range of plotted values. (B) Predicted risk of multiple infection among men aged 25 to 29 years old as a function of lifetime sex partners and community type estimated in a bivariate model with diffuse priors (n =  997). Median of the posterior distribution is plotted as the central estimate and shading represents the 95% and 50% HPD. Colors are as in (A). (C) Logistic coefficients for the association between putative risk factors and the probability of harboring a multiple infection estimated with Bayesian shrinkage priors (n =  1,970). Sex and bar/rest. work variable includes female sex and bar/restaurant worker and men who report having sex with female sex and bar/restaurant workers. Median of the posterior distribution is plotted as the central estimate, horizontal bars extend to the 95% and 50% HPD. Colors are as in (A).

https://doi.org/10.1371/journal.ppat.1013065.g004

We additionally incorporated a binary feature describing the sequencing technology used to generate the deep-sequence data from each participant to assess the extent of technical bias in our inferences. In a univariate analysis, we estimated that multiple infections were less common among participants sequenced using the bait-capture protocol (RR median [95% HPD]: 0.64 [0.4–0.94], S12 Table.). However, 50.45% of bait-capture sequenced participants were residents of fishing communities compared to 76.02% of amplicon sequenced participants. Consequently, in a bivariate model with community type, the estimated magnitude of the dependence of multiple infection status on sequencing technology was considerably reduced and no longer considered to be significant at the 95% level. (multivariate RR median [95% HPD] 0.77 [0.48–1.12], S13 Table.).

Participants with HIV in fishing communities also reported having more lifetime sex partners (S7 Fig), so we next assessed whether the risk of harboring a multiple infection differed by the number of self-reported lifetime sex partners within each of the two community locations. As women tend to under-report their number of sex partners relative to men [97], we restricted this analysis to male participants. The number of lifetime sexual partners generally increases with age, and so we standardized responses relative to the age-specific mean number of lifetime sexual partners among participants separately for the inland and fishing communities (S8 Fig). Among 997 male participants included in this analysis, 516 reported an exact number of lifetime sex partners, 477 responded they had three or more lifetime partners, and 4 did not provide a response. We imputed ambiguous responses and missing data within our inference framework by assuming responses were missing at random between people with and without multiple infection (Materials and methods).

In a bivariate model with community type and number of lifetime sexual partners we did not find a statistically significantly higher risk of multiple infection in male participants with more lifetime sexual partners in the context of substantial missing data and sampling over potential missing values using age-specific prior distributions. However, we note that the posterior effect size translated into an estimated more than two-fold higher risk of multiple infection between men living with viremic HIV in fishing communities associated with having 30 lifetime sexual partners compared to one lifetime sexual partner (e.g. RR median [95% HPD] among 25-29 year olds 2.47 [0.7–5.61], Figs 4B and S9 for all age groups and S14 Table.). Very similar results were observed using a complete case analysis of the 516 men who provided an exact number of lifetime sex partners (S15 Table.).

We also performed a comprehensive discovery-based risk factor variable selection analysis over eight additive biological, behavioral and epidemic features, stratifying epidemiological and behavioral variables by community type to account demographic differences between the populations and excluding additional variable interactions. This analysis confirmed residency in fishing communities as a risk factor of multiple infection among sequenced participants, albeit with a wide credible interval, (multivariate RR median [95% HPD] 1.59 [0.92–2.85]), but did not identify any other variables that were associated with significantly higher or lower risk of multiple infection in our sample (Fig 4C and S16 Table.). Specifically, despite the fact that female bar/restaurant workers face a three-fold higher risk of incident HIV [41] we did not identify an increased risk of multiple infection among female bar/restaurant workers or men who have sex with bar/restaurant workers in either inland or fishing communities.