The de-identified testing for Illumina deep sequencing at the CDC Malaria laboratory was determined as non-human subjects research by US CDC. The study protocols, from which field samples were obtained, were reviewed and approved by the Ethics Review Committee of the Kenya Medical Research Institute including blood sample collection and use of the samples for parasite genotyping.

The bioinformatics analysis pipeline developed in this study was to clean NGS data for consistent frequency calls at each SNP site across 12 chromosomes. Because 24 SNP barcodes differ from 16S metagenomics data in depth of coverage and amplicon diversity, an existing 16S bioinformatics pipeline was modified, and several additional data cleaning components were integrated as described below. This novel pathway, called B4Screening, involves four steps: initial adaptor trimming and cleaning, Bioconductor dada2 pathway, targeted removal of mismatched primers or probes, and a random forest classification of remaining reads. All steps are detailed below.

A previously developed mathematical algorithm, StrainRecon [17], was used for identifying haplotypes and enumerating strains based on frequency results of individual 24-SNP barcodes generated from NGS. Briefly, the basic StrainRecon algorithm accepts a vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{s}}$$\end{document}s of SNP frequencies as input and a parameter n denoting the anticipated number of strains. The output is twofold: a binary matrix M containing n reconstructed strain barcodes, and a vector v of strain mixtures. The strains found by the algorithm represent the maximum likelihood estimate of the original barcodes under three assumptions. First, the overall error from all steps of the pipeline can be modelled as normally distributed (Gaussian) noise. Second, noise values are independent between SNP sites. Third, the metric minimized to optimize the solution quality is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Mv - s_{2}$$\end{document}Mv-s2, called the misfit. (Here, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\| \cdot \right\|_{2}$$\end{document}·2 denotes the standard Euclidean L2-norm.) Both M and v are assumed to be completely unknown, making this a mathematical inverse problem. StrainRecon models the problem as a Bayesian maximum-a-posteriori (MAP) estimation problem, using block coordinate descent to quickly converge at a solution when the number of strains n is small. The algorithm further provides an average (and standard deviation) over the entire posterior distribution of candidate solutions, which can be used to illustrate confidence or ambiguity of each call the algorithm makes within a barcode or strain mixture fraction. In this paper, the StrainPycon 1.0 [27] implementation of the StrainRecon algorithm for Python 3.4.3 was used for analysis. Each sample was evaluated for barcode sequences given the assumption that field samples can include up to and including 6 strains.

StrainRecon allows discrimination of the pattern of haplotypes that are sufficiently prevalent in a sample relative to the experimental noise, as measured by misfit. The goal of this study was to create a tool that can further estimate the true number of parasite strain infections in a sample without the need for templates while being aware that extremely low-proportion strains in the sample are indistinguishable from noise. The method, therefore, takes each sample and runs the StrainRecon algorithm in a loop over number of strains n to determine the misfit of the MAP solution for each n. As the number of free parameters increases with n, the largest misfit will be found with n = 1, and the misfit decreases with larger n. In lay terms, it will always be possible to better fit the strains of a sample by imagining that it contained more haplotypes, but some of these haplotypes may be an artifact of introduced variation inherent in NGS sequencing. The approach used in this study for determining MOI was to set a threshold value, called T, on the misfit value and to return the lowest n whose MAP estimate had misfit below T. Together, the complete procedure is referred to as the STIM algorithm.

The upper bound of n is limited by noise levels in the analytical pipeline. In practice, when error rates are in the range of 1–3%, the upper bound of n that can be meaningfully processed is about 5–6 strains. Specifically, even under optimistic assumptions about mixture proportions for strain disambiguation (which is when mixture proportions are proportional to the first powers of 2), an inverse problem barring an informative Bayesian prior or a tailored noise model will be unable to differentiate more than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = - \log_{2} \left( \varepsilon \right)$$\end{document}n=-log2ε strains from noise level of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon > 0$$\end{document}ε>0. For example, at 1% error, this bound is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \le - \log_{2} \left( {0.01} \right) \approx 6.6$$\end{document}n≤-log20.01≈6.6. Within these constraints, the STIM method has the crucial advantage of estimating MOI while not depending on any template information, unlike DEploid [18], for example.

Of the 23.48 million Prinseq-cleaned, paired reads in the 108 laboratory-generated samples, 21.47 million reads remained prior to evaluating with the RF classifier (see next subsection for development of RF classifier). The number of unique amplicons assigned (across all 24 loci) in the laboratory strain dataset dropped from 9901 following the standard dada2 pipeline to 360 following additional filtering for primer mismatch and probe mismatch. Potential unique amplicon numbers per SNP target location in this screened set were varied, with a minimum of 2 (SNP14, SNP18) and a maximum of 70 (SNP11).

Of these 360 unique amplicons, 51 were retained following RF classification, and represented the expected SNPs at the target locations (Fig. 1) and several additional SNPs at different locations in the amplicon. The final number of unique amplicons per SNP target location ranged from 1 to 3 in the laboratory strain data. Overall, 21.35 million (90.9%) reads remained following exclusion of spurious amplicons via the RF classifier (see Additional file 1: Fig. S1). For each location, unique amplicons retained after RF classification were summed by target SNPs to generate frequencies for StrainRecon.Fig. 1

Distribution of unique amplicons in laboratory strains. Red bar represents number of unique amplicons following dada2 Bioconductor processing steps of B4Screening and additional matching-based steps, and green bar shows number of unique amplicons following RF classifier B4Screening steps, separated by SNP target location

There were 5193 unique datapoints for classifier development in the laboratory strain dataset, accounting for 2576 of the 2592 potential SNP sites among all 108 samples (not all SNPs had > 500 reads in each sample). If the classifier was trained with 75% of the total data selected, 3881 data values were used for training and 1312 for testing.

In the 1312 test set, all 1161 positively coded unique amplicons were correctly identified and all 151 negative unique amplicons as initially coded were also correctly identified. Alternatively, if a single mixed combination C was withheld as a test set rather than a random selection of unique amplicons across all data, to protect against inadvertent data leakage, 3369 data-samples combinations were used for training and 1824 for testing. In this case 1587 out of 1624 positively coded unique amplicons were correctly classified (sensitivity: 97.7%) while 197 of 200 (specificity: 98.5%) negatively coded unique amplicons were correctly classified. Overall, the amplicons classified for removal were low copy number relative to the total representation of the target region (see Additional file 1: Fig. S1).

When the field samples from western Kenya were processed, the same RF classifier was used to screen viable amplicons.

The proportion of samples retaining sufficient read depth across all SNP locations following RF classification was evaluated. A cut-off of 500 reads was selected to ensure that precision would not be influenced by read depth. With a minimum coverage depth of 500 reads post-processing, SNP 16 was absent in 16 of laboratory samples (15%). No laboratory strain samples had fewer than 16 total SNPs represented, and while the fifth percentile number of SNPs present within a sample was 21, 78 of 108 samples had all 24 SNPs present. With a cut-off of 500 reads, individual SNP read depth was lowest for SNP18 (2090 median read depth), and highest for SNP10 (17,630 median read depth) (see Additional file 2: Fig. S2).

Multivariable models assessed the relationship between sample characteristics and read depth. Neither proportion of strains in a mixture (p = 0.43), nor specific strain mixture (p = 0.67) was associated with read depth (Fig. 2a). Figure 2a also showed a low variability among three different processing pipelines. Parasite concentration was non-linearly associated with average read depth [(10² = 5500, 10³ = 6170, 10⁴ = 8310, 10⁵ = 8310 reads/site), p < 0.0001]. Samples with 10² and 10³ parasite concentration did not differ from each other, nor did samples with 10⁴ versus 10⁵ parasite concentrations. However, comparisons among other pairs were significant (emmeans, Tukey correction, p < 0.01) (Fig. 2b). Read depth did not significantly differ between pre-amplified and non-pre-amplified samples [(6460 vs. 7410 average reads/site), p = 0.053] (Fig. 2b). Both DBS and frozen blood plates yielded sufficient reads in each SNP location.Fig. 2

Relationship between read depth and sample characteristics in laboratory strain mixes. a Reflects log₁₀ total reads by plates that contain 3 different strain mixtures A: D10/D6/V1-S, B: D6/RO33/W2, C: 7G8/V1-S/RO33 respectively, as cited in Methods. b Reflects impact of pre-amplification (PA) and non-pre-amplification (NOPA), separated by parasite concentration as not all parasite concentration/pre-amplification combinations exist in the data. The groups that are significantly different in read depth by original parasite concentration are indicated by “g1”and “g2” symbol, respectively

SNP frequency calls for unique strains must be consistent within a single sample to ensure consistent barcode calls. Boxplots for frequencies across all parasite concentrations, pre-amplification and sample types (Fig. 3) show the full range and central tendency for unique-strain SNP frequencies across all conditions in laboratory strain data. A single site (SNP23) in Combination A mix was excluded from this analysis as the high proportion template appears to have both potential SNPs present in the original source material (see Additional file 3: Fig. S3).Fig. 3

Frequencies of unique SNPs across all parasite concentrations, pre-amplification and sample types from laboratory strain mixes. Red is values with no unique strains at given SNP location, green is where the highest proportion strain is unique, teal where the intermediate proportion strain is unique and purple where the lowest proportion strain is unique. The estimated SNP frequency for each strain as generated in restriktor is represented in black dot. Combinations (A, B, C) were listed with proportions (1, 2, 3) as cited in Methods

Using SNP frequency calls, StrainRecon’s MAP estimates of 108 laboratory strain samples were calculated, varying the parameter n of the number of strains to be reconstructed (anticipated MOI) between 1 and 5. The reconstructed barcodes for each sample were compared to ground truth barcodes intended to be mixed, counting the number of reference/alternate matches at SNP sites with read depth of at least 500.

The 72 samples from Combinations B and C contain three strains. The dominant strain in the 36 samples from Combination A consistently generated two distinct reads at SNP23 (see Additional file 3: Fig. S3), indicating a likely presence of mutation. These two distinct reads at SNP23 were reconstructed independently, and Combination A samples were therefore characterized as containing four strains (33% of samples).

Table 1 shows that over 98.5% of the base pairs in the dominant “high” strains (target proportion range of 88–97.5%) were identified correctly, even when the algorithm is configured to identify more strains (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \le 5$$\end{document}n≤5) than are truly mixed in the samples [17]. The “intermediate” strains (target proportion range of 2–10%) were reconstructed at 77.5–89.3% accuracy, and the “low” strains in the mixtures (target proportion range of 0.5–2%) were reconstructed at 47.1–64.6% accuracy. Among these, when using parameter n = 3 (true mixtures in samples), the accuracy for “high” strains, “intermediate” strains, and “low” strains were 98.7, 89.3 and 64.6%, respectively. Total DNA template material affected the ability to reconstruct barcodes, with percentage of correct SNP calls in the three true strains at 75.0% among all mixtures at 10² parasites/µl, 80.6% at 10³ parasites/µl, 88.4% at 10⁴ parasites/µl, and 90.6% at 10⁵ parasites/µl.Table 1

Barcode reconstruction quality with StrainRecon, varying the number of strains to be found

It is noted that larger n provides more free parameters, thus allowing solutions to have a better fit to the SNP frequency vector than smaller n, even when n exceeds the true number of strains in a sample. In this latter case, the algorithm “overfits” and attempt to explain experimental noise in the data with extra low-frequency strains to score a lower misfit value (see Additional file 4: Fig. S4 and Additional file 5: Fig. S5 with detailed information using individual sample examples). However, the third strain (and mutated fourth strain for Combination A samples) in all mixtures had very small proportion, even less than the estimated noise level of the experiment (≤ 5%), which deteriorates the barcode reconstruction.

Recall that the StrainRecon method takes the number of anticipated strains n as input and then determines what barcodes and mixture vectors of n strains produce the best fit (lowest misfit) by minimizing noise. A natural approach for estimating the true number of strains is then to place a threshold on the acceptable fitness level and determine how many strains n StrainRecon needs to produce barcodes and mixture vector with sufficiently low misfit. This algorithm is called STIM. The STIM estimation method was first evaluated on synthetic data produced by generating 1000 barcode matrices M and mixture vectors v uniformly at random for each specific number of strains n and calculating the dot-product Mv. Following the StrainRecon framework [17], Gaussian noise with a known standard deviation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upgamma }$$\end{document}γ, corresponding to the amalgam of errors and reads in the laboratory pipeline, is added to the dot-product before the resulting vector is reconstructed. Figure 4 (left) varies the threshold value T on the horizontal axis, showing that lower noise levels give rise to misfit thresholds where MOI can be discerned for a wider range of strain counts. For comparison, Fig. 4 (right) shows how well STIM performs when, mathematically, the proportion of each strain in the mixture (vector v) is ideally separated from others (by being proportional to powers of 2 as can be shown through mathematical analysis). The noise on the mixture values is normally distributed around a mean of 0 with standard deviation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upgamma }$$\end{document}γ of either 0.05 (top row) or 0.01 (bottom row). Since normally distributed variables fall within two standard deviations from the mean 95% of the time, these \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upgamma }$$\end{document}γ values correspond to hypothetical pipelines whose accuracy for SNP reads are expected to lie with within 10 and 2%, respectively, of their true values at least 95% of the time. The black vertical bar shows the threshold value suggested by Morozov’s discrepancy principle, a point below which data are effectively best explained by noise. The results show that STIM is sensitive to noise levels: lower underlying error rate (standard deviation of 0.01) allows differentiation of strain count between 1 and 5 at some thresholds, whereas high underlying noise (standard deviation of 0.05) is more restrictive.Fig. 4

STIM estimation method on synthetic data. The data was generated by creating uniformly random barcodes and mixture vectors and adding Gaussian noise (top: std.dev = 0.05, bottom: std.dev = 0.01) to create input vectors for StrainRecon. The graph shows the percentage of synthetic samples for which the MOI was correctly identified by choosing the lowest number of strains that go below the misfit threshold on the horizontal axis. The plots on the left show regular performance, whereas on the right StrainRecon is provided with the correct value of the mixture vector. The black vertical lines show lowest misfit threshold permitted by Morozov’s discrepancy principle (here the expression simplifies to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{SNPs}{2} = 12$$\end{document}SNPs2=12), below which any signal is effectively better explained by noise [17]

The assumption of Gaussian noise works well for in silico, but a rigorous model for experimental noise in practice is lacking. To adapt STIM for field data the first step was to calculate the MOI threshold T for laboratory strain mixture data (108 samples) while simultaneously calibrating MOI values that are analytically predetermined. To tolerate error in the pipeline and the noise-to-signal uncertainty in StrainRecon, the threshold T was varied while conservatively measuring whether samples from the laboratory strain experiment were called at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 3 \pm 1$$\end{document}n=3±1 strains. The case for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 2$$\end{document}n=2 accounts for mixture proportions that were so low (0.5–1%) relative to noise so that the corresponding samples effectively have two strains. Conversely, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 4$$\end{document}n=4 accommodates the Combination A samples in mixtures that had a mutation in SNP23 in one of the laboratory strains, thus creating 4-strain combinations (Additional file 3: Fig. S3). In STIM, the calibrated threshold of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = 1.8 \times 10^{ - 7}$$\end{document}T=1.8×10-7 provided MOI within \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 3 \pm 1$$\end{document}n=3±1 strains for 101 out of 108 laboratory-mixed samples (93.6%). Overestimation (n = 5) was observed in 7 out of 108 laboratory samples (7.4%). The results are delineated in Table 2. To account for any potential inaccuracy in the threshold choice determination, the final step evaluated the field results across a range of threshold values (see Fig. 6).Table 2

Distribution of MOI estimates by STIM on 108 laboratory-mixed samples using the threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = 1.8 \times 10^{ - 7}$$\end{document}T=1.8×10-7

The StrainRecon and STIM algorithms with a threshold of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = 1.8 \times 10^{ - 7}$$\end{document}T=1.8×10-7 were used to evaluate field samples from 4 cross-sectional surveys conducted in Kenya. A Kruskal–Wallis H-test (non-parametric one-way analysis of variance that extends the Mann–Whitney U test) on the MOI differing among smear-positive samples from 1996, 2001, 2007, and 2012 surveys was significant (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H = 29.7$$\end{document}H=29.7, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 2 \times 10^{ - 6}$$\end{document}p<2×10-6). The result suggests that the distribution of MOI in at least one of the years stochastically dominated another.

To determine the differences in MOI between years, the Conover-Imam test was carried out to compare pairwise stochastic dominance for all pairs. False discovery rate (FDR) was controlled for using the two-stage step-up method of Benjamini, Krieger, and Yekutieli (BKR), which improves the power of the well-known Benjamini and Hochberg (BH) FDR mitigation method without making additional assumption [28]. The results with the FDR-corrected p values (q values) are shown in Table 3. The comparisons showed significant decrease in MOI (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q < 0.02$$\end{document}q<0.02) between every pair of survey years between 1996 and 2012 with the exception of 2007 and 2012 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q = 0.15$$\end{document}q=0.15). In best fitting results from STIM, all samples contained either 5 or fewer strains and no sample contained 6 (or more) strains above the 5% noise level resolution of STIM. Notably, strains of low proportions (≤ 5%) in samples are indistinguishable from pipeline noise in the MOI estimates. The STIM results thus suggest a decline from an average of 4.32 strains per infected person in 1996 to 4.01, 3.56, and 3.35 in the years 2001, 2007, and 2012, respectively (Fig. 5c). Figure 5d also shows that the fraction of samples with one strain increased from 3% in 1996 to 17% in 2012 while the fraction of samples with 5 strains reduced from 57% in 1996 to 18% in 2012. The FDR-adjusted statistical test results for STIM are robust to changes in the misfit threshold parameter T (Fig. 6) except between 2007 and 2012 which straddles the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q = 0.05$$\end{document}q=0.05 boundary.Table 3

Difference in MOI across years in the Kenyan field samples

In addition to MOI, all barcodes with at least 5% proportion that StrainRecon reconstructed from the samples across all years were unique, 878 distinct strains in total. This finding suggests a lack of clonality in the Asembo Bay area.

Since the surveys 2007 and 2012 comprised individuals up to 20 years of age, a potential influence of age on MOI was further examined. There were no significant correlations between MOI and age, comparing children of 5 years and below with older ages, in 2007 (q = 0.07) or 2012 (q = 0.24) surveys, respectively.

In summary, the validation using field samples from Kenya suggests that the approach developed in this study could be used on the field samples for reliably reconstructing strains in individual samples and for detecting changes in MOI over time.

Multiplex PCR is a fast and cost-saving approach for pathogen diagnosis and genotyping [29, 30]. Three multiplex PCRs covering all 24 barcode SNPs identified by Daniels et al. [19] within the P. falciparum genome were developed in this study. The 24 short target regions needed to be amplified with comparable efficiency in multiplex PCRs to ensure generation of sufficient SNP coverage at each location via NGS. The 3 optimal multiplex PCRs were developed through a series of optimizations and pilot testing.

The most important and challenging issue was how to uniformly call the 24 barcode SNP frequencies based on NGS data and assign these frequencies to haplotypes. The second, interlinked, challenge was to determine how many strains were represented in each sample. To resolve these challenges, the StrainRecon mathematical algorithm for strain disambiguation [17] from different chromosomes and different SNPs [19] was leveraged in this study. It is important to point out that the consistency of SNP frequency calls at targeted SNP locations determines the ability of the StrainRecon and thus STIM to successfully assign these frequencies to haplotypes and disentangle the multiple strains within a sample and MOI estimation.

To maximize the consistency of SNP frequency calls from NGS data for haplotype assignment and strain reconstruction, the unique bioinformatics pipeline with B4Screeining pathway developed in this study first removed spurious amplicons introduced by sequencing. Initial data trimming and cleaning steps, by CutAdapt and Prinseq and data quality visualization via FaQCs prior to entry into the Bioconductor pipeline, ensured only sufficient quality, trimmed reads were processed. Without proper screening of noise, the extraneous element could erroneously generate orders of magnitude more sequences than truly exist in the data. There were numerous low copy number amplicons that did not reflect true diverse amplicons removed at population level using the novel and sensitive RF classifier developed in this study.

While this novel bioinformatics pipeline currently applies to the described 24-SNP malaria barcoding scheme, the implications of data cleaning steps here indicate the importance of careful evaluation of NGS output in any non-template-driven systems, such as whole genome multi locus sequence typing (wgMLST) or other barcoding approaches. The majority of unique amplicons (yet minority of total reads) generated in the laboratory and subsequently removed by routine bioinformatics processing did not reflect intended targets. In addition, chimerism between multiplex PCR targets was substantial in raw data. Therefore, leaving primers that are clearly distinct between sites on reads during the processing allowed a quick screen for chimeras. Incorporating this step prior to primer trimming also improves data quality and efficiency of analysis.

In the bioinformatics pipeline, where only information regarding known specific SNP sites (binary) was incorporated, the finding of multiple distinct point mutations per amplicon was not utilized. This latter information (category) can be incorporated in future work not only to enhance 24 SNP frequency calls but also to be useful for amplicon deep sequencing data analysis.

Although laboratory or clinical samples can have high parasite densities, field samples from population-based community surveys are collected largely from asymptomatic individuals who tend to have low parasite densities. In addition, in high and medium transmission areas, a minor proportion of parasite strains in a sample is often undetectable using conventional molecular technologies [31]. Both low parasite density samples and low proportion of parasite strains in a sample could increase difficulty in producing consistent frequencies across all SNP locations due to the limited DNA template availability. In this study, the impact of pre-amplification, parasite concentration and strain proportion on consistency of 24 SNP frequency calls were evaluated. It showed that SNP frequencies were not influenced by parasite concentration within the currently tested range or by pre-amplification, but differed by strain proportion. It is easy to envision that SNP frequency calls are entirely based on original DNA template diversity when noise and spurious amplicons from NGS are minimized using the unique bioinformatics developed in this study. Most importantly, the results have practical applications. First, it allows evaluation of field samples with a range of parasite densities, with and without pre-amplification. Second, pre-amplification allows evaluation of samples that have insufficient parasite concentration for analysis of diversity, but sufficient concentration to amplify without this step. Critically, NGS is sensitive for detection of low frequency SNPs in a sample [32, 33]. Compared to existing conventional molecular tools where minor parasite proportion below 10–30% in a sample were generally undetectable [9, 34–36], the tools developed in this study detected the barcodes of dominant strain with 98.5% accuracy and the proportion of parasite strains ranging from 2 to 10% in a sample with accuracy between 77.5 and 89.3%. Although the target lowest limit for minor strain detection was designed at 0.5 parasite/µl (see second subsection for laboratory assay development in Methods), this study did not attain such a fine level of resolution due to the inaccuracy observed at lower proportions (0.5–2%) of strains, specifically that as the strain proportion decreases, the ability to accurately detect the minor strain diminishes. This lower bound is influenced by both background noise level in the current analysis pipeline and the low DNA copy number of minor strains in the sample, decreasing expected precision. Nevertheless, the results from this study showed a substantial improvement in sensitivity for detecting minor parasite populations in a sample, particularly those above 5% proportion, with acceptable precision. While deep sequencing of individual targeted antigenic genes also provides ability to detect gene-specific minor variants in a sample, the estimates in the highly selected genes might not represent true genomic signatures of parasites [14, 15, 37] and may offer limited temporal and geographic discrimination between parasite populations [15].

The STIM algorithm for assessing MOI based on SNP read frequencies relies crucially on noise levels. Highly variable input in a noisy pipeline may cause MOI to be overestimated by confusing noise with true signal in reconstruction. A threshold was placed on MOI misfit, and calibrated by balancing the false negative rate of the strain reconstruction quality of StrainRecon on the known laboratory samples to the false positive rate and number of strains estimated. The same threshold was then used for running STIM on field data under the assumption that most noise would be from the pipeline steps against which the threshold already accounted. Importantly, the trends and conclusions from the field continue to hold even if the true threshold for this was slightly shifted relative to the one determined by the laboratory strain setting. In other words, MOI value estimated by STIM is subject to noise, whereas temporal changes in MOI as estimated by STIM are resilient to such noise. A large study across geographic regions is ongoing to examine the robustness of the STIM method in the field as well as potential needs for further calibration of the proposed threshold with a richer set of artificial strain mixtures.

MOI has only recently been used as a metric for malaria transmission. Therefore, the EIR and malaria prevalence in children 5 years old and younger from same study area were obtained from 1995–1996 to 2012 (Fig. 5a, b, data extracted from both published [38] and unpublished KEMRI/CDC data) for side-by-side comparison with the MOI estimated from current study (Fig. 5c, d). The results show that the EIR sharply declined between 1995 and 2001 and remained low, even as malaria prevalence gradually decreased between 1996 and 2007, then reaching a plateau between 2007 and 2012. In comparison, the average MOI gradually declined over time and the percentage of samples with 5 strains dropped from 57% in 1996 to 18% in 2012 (during which period the proportion of one-strain samples increased). Since there was no correlation between MOI and age, the decline in MOI over time is unlikely to be confounded by host age [20]. Overall, the decreases in both average MOI and proportion of samples with 5 strains over time are in tandem with the decline in EIR and malaria prevalence; but the turning points are different. Specifically, MOI shows slow reduction, EIR has a sharp decline, and malaria prevalence stagnates from 2007 to 2012. This suggests a non-linear scaling relationship among the three malaria metrics [3]. The reasons behind the slow reduction in MOI are unclear; the large number of distinct strains detected in the area may play a role (878 distinct strains at least 5% proportion were detected in total and are reported in Results). Nevertheless, the MOI, which provides the information of strain numbers within a host, is a higher resolution parasite index compared with the malaria prevalence index and it might represent true transmission level. A further study of the parasite strain population size and strain relatedness is needed using this dataset.

The tools developed in this study advance both the estimation of number of strains within a host but also the number of strains at a population level, enhancing the resolution for MOI estimation. This advantage is particularly obvious compared to the original Taqman PCR 24 SNP barcode assay and COIL analysis for complexity of infection (COI) estimation in which monomorphic or polymorphic genotypes within each sample are estimated [19–21]. Taken together, the combined approach established in this study could be used for MOI estimation, particularly for temporal changes in MOI in regions with medium to high transmission levels. A large-scale validation study is being conducted using samples from different malaria countries/regions with heterogeneous transmission intensity.

Additional file 1: Figure S1. RF classification using laboratory strains. Figure shows proportion of each unique amplicon relative to all amplicons from the targeted region on a plate from all laboratory strain samples based on RF classifier (when random selection determined the training set). X axis is the log₁₀ count of SNP-specific reads in a Miseq run and y axis is log₁₀ count of unique amplicon-specific reads in that individual run. Red points are amplicons classified as negative (False) for exclusion while green points are amplicons classified as positive (True) for further SNP frequency analysis.