# SNVHMM: predicting single nucleotide variants from next generation sequencing

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**Part of the following topical collections:**

## Abstract

### Background

The rapid development of next generation sequencing (NGS) technology provides a novel avenue for genomic exploration and research. Single nucleotide variants (SNVs) inferred from next generation sequencing are expected to reveal gene mutations in cancer. However, NGS has lower sequence coverage and poor SNVs detection capability in the regulatory regions of the genome. Post probabilistic based methods are efficient for detection of SNVs in high coverage regions or sequencing data with high depth. However, for data with low sequencing depth, the efficiency of such algorithms remains poor and needs to be improved.

### Results

A new tool SNVHMM basing on a discrete hidden Markov model (HMM) was developed to infer the genotype for each position on the genome. We incorporated the mapping quality of each read and the corresponding base quality on the reads into the emission probability of HMM. The context information of the whole observation as well as its confidence were completely utilized to infer the genotype for each position on the genome in study. Therefore, more probability power can be gained over the Bayes based methods, which is very useful for SNVs detection for data with low sequencing depth. Moreover, our model was verified by testing against two sets of lobular breast tumor and Myelodysplastic Syndromes (MDS) data each. Comparing against a recently published SNVs calling algorithm SNVMix2, our model improved the performance of SNVMix2 largely when the sequencing depth is low and also outperformed SNVMix2 when SNVMix2 is well trained by large datasets.

### Conclusions

SNVHMM can detect SNVs from NGS cancer data efficiently even if the sequence depth is very low. The training data size can be very small for SNVHMM to work. SNVHMM incorporated the base quality and mapping quality of all observed bases and reads, and also provides the option for users to choose the confidence of the observation for SNVs prediction.

## Keywords

Hide Markov Model Next Generation Sequencing Sequencing Depth Hide State State Transition Matrix## Background

In recent years, the advent of NGS technology has largely propelled the genomic research. NGS can generate millions of reads ranging from 30-350 base pairs (bp) based on the sequencing platform used. Continuous improvement in NGS technology brings the increasing of the throughput to a high extent and also lowers the cost [1]. With abundant reads aligned, many novel inferences can be made including regulatory element identification, mutation detection, gene expression estimation and detection of RNA splicing and fusion transcripts. NGS is expected to be a powerful tool for revealing genetic variations contributing to various complex diseases by providing sequence of a set of candidate genes, the whole exome or the whole genome. For example, whole genome sequencing can help in finding the frequency of tumor-specific point mutations for diseases such as multiple myeloma [2], while whole exome sequencing can be used to discover protein-coding mutation as well as small non-coding RNAs and aberrant transcriptional regulation that may contribute to diseases such as MDS [3].

The SNV calling algorithms can be divided into two categories. The first category includes threshold based commercial software packages such as Roche GSMapper and Lasergene, and the second category entails posterior probability based method including Maq [4], SOAPsnp [5], Varscan [6], Atlas-SNP2 [7] etc. For the threshold based prediction methods, a good threshold setting is difficult to obtain and relies heavily on the user experience [8].

In transcriptome based data, the number of reads representing a given transcript is highly variable across all genes making it difficult to determine a minimum depth. Moreover, the confidence for the prediction of each location is unavailable. Compared to the threshold based methods, posterior probability (Bayes) based methods achieve flexibility by considering the confidence of observation of each position on the genome. For the cancer genome sequencing data, sequencing errors, as well as the altered ploidy and tumor cellularity, are important factors affecting the accuracy of SNV calling. Although tools exist for SNVs discovery from NGS data, few are specifically suited to work with data from tumors. Recently, SNVMix [9] addressed this problem by incorporating the dependency of near-by genotypes and the posterior probability to improve the accuracy of SNVs prediction. However, the performance of SNVMix for data with low sequencing depth is not satisfactory compared to its performance with data having high sequencing depth. It has been observed that NGS provides lower sequence coverage in certain areas of genome including regulatory regions [10]. It is necessary to improve the performance of SNVs detection for tumor data with low sequencing depth. Moreover, SNVMix has achieved a relatively high sensitivity in the Bayesian framework, but the specificity is some low. The performance of specificity is needed to be improved further.

Hidden Markov model (HMM) is widely used in many fields such as speech and handwriting recognition, text classification, as well as DNA and protein classification [11]. Recently, a HMM based program VARiD [12] was developed for SNVs prediction for data from multiple sequencing platforms. VARiD is mainly focused on color space sequence and does not fully consider the mapping and base quality of the aligned reads and corresponding bases on the aligned reads in the considered model. Moreover, this method is time consuming for whole genome analysis and has not been used on RNA-Seq or whole exome sequence analysis from tumor data so far.

In this paper we developed an algorithm SNVHMM, for SNVs prediction of tumor data obtained from NGS basing on a discrete HMM. Since non-SNVs are prevalent and continuous in the genome [13], point mutations in cancer data are relevant to certain genes and are concentrated in the corresponding area [14, 15], the contextual information, especially for the non-SNVs, can be considered and made full use of in addition to the information from the overall distribution of traditional Bayesian framework. So SNVHMM is expected to gain more probability power from the contextual information on the genome compared to traditional Bayesian framework, and obtain better performance for SNVs prediction. Moreover, with the contextual information added to the whole distribution information, SNVHMM is also expected to improve the statistical performance of Bayesian method for tumor data with low sequencing depth.

## Implementation

### Problem formulation and SNVHMM model specification

*L*. Given the aligned reads for the sequence in study, we can get the depth

*L*

_{ t }of the stated position

*t*on the genome. The quality of the reads covering position

*t*and the quality of corresponding bases on the reads are denoted as ${\left\{{r}_{i}^{t}\right\}}_{i=1}^{{L}_{t}}$ and ${\left\{{q}_{i}^{t}\right\}}_{i=1}^{{L}_{t}}$ respectively (Figure 1). We consider three genotypes for each stated position as {aa, ab, bb}, where {aa} denotes homozygous for the reference allele, {ab} denote heterozygous and {bb} denote homozygous for the non-reference allele. Our aim is to predict the genotype for each position on the genome, given the aligned reads.

We denote the number of the hidden states as *I*. The hidden state and observation for each position are noted as * S* = {

*s*

_{ t }}(

*t*= 1, 2, ⋯,

*L*) ∈ {

*v*

_{ i }}(

*i*= 1, 2, ⋯,

*I*) and

*= {*

**O**

**o**_{ t }}(

*t*= 1, 2, ⋯,

*L*) respectively, where ${\left\{{v}_{i}\right\}}_{i=1}^{I}$ are all states considered. The underlying genotypes of the sequenced genome are taken as the hidden states, which are interpreted as follows: (1) homozygous for normal; (2) heterozygous; (3) homozygous for mutation (Figure 2). These states are important in detecting single nucleotide polymorphism or point mutation for normal sample as well as cancer sample. The last two states are taken as SNV in our study. For simplicity, we note state {aa} as state 1, state {ab} as state 2 and state {bb} as state 3 in the following initial state distribution and state transition matrix.

*t*is taken as ${\mathit{o}}_{\mathit{t}}={\left\{{q}_{i}^{t},{r}_{i}^{t}\right\}}_{i=1}^{{L}_{t}}$. The emission probability ${b}_{{v}_{i}}\left({\mathit{o}}_{\mathit{t}}\right)$ is calculated as a conditional probability, given the hidden state:

where ${\left\{{u}_{i}\right\}}_{i=1}^{I}$ is the Binomial distribution parameter for each position on the genome and *P*_{ t } is the number of reads having the same base with reference allele at position *t*. The detailed derivation of (2) is given at the supplementary file. In this study, we only considered two types of nucleotides covering the stated position, which have the largest and second largest number at the stated position. In the case of rare third alleles, these reads are assumed to be errors. In this study, *u*_{ i } denotes the probability of occurrence for the allele having the largest number at the stated position.

### Prior distribution of HMM

*π*as Dirichlet distribution with hyper-parameter

*= (*

**δ***δ*

_{1},

*δ*

_{2},

*δ*

_{3}),

*= (*

**u***u*

_{1},

*u*

_{2},

*u*

_{3}) is taken conjugately according to a Beta distribution with hyper-parameter

*= (*

**α***α*

_{1},

*α*

_{2},

*α*

_{3}) and

*= (*

**β***β*

_{1},

*β*

_{2},

*β*

_{3}) as follows:

*= (1000, 100, 100) by assuming that most positions will be homozygous for the reference allele. We also set*

**δ***= (1000, 500, 1) and*

**α***= (1, 500, 1000) by assuming the probability of state {aa} occurring at the stated position is much larger than that it not occurring, vice versa for state {bb}. We also assume the probability of state {ab} occurring at the stated position is the same as that it not occurring. For the initial distribution of state transition matrix, we take the initial distribution of*

**β***A*

_{ i }as follows:

where we take **γ**_{ 1 } = (1000, 100, 100), **γ**_{ 2 } = (100, 1000, 100) and **γ**_{ 3 } = (100, 100, 1000)*.* Since the sum of elements in *A*_{ i } should be equal to probability 1, a normalization for ${\left\{{\mathit{A}}_{\mathit{i}}\right\}}_{i=1}^{I}$ is performed after each iteration of SNVHMM.

### Estimation of HMM parameters

*≜ (*

**λ***,*

**π***,*

**u***) and learn the unknown HMM by using EM algorithm and computing the maximum likelihood estimation when the observed data are incomplete [16]. The aim is to find the model parameter*

**A***λ*maximizing the observation probability i.e.

*L*(

*,*

**o***) ≜ P(*

**λ***|*

**o***) or log P(*

**λ***|*

**o***),where the later one is usually used when the length of the observation is large. We use a special case of EM algorithm, Baum-Welch algorithm [11], to learn the unknown parameters. For the training of HMM, we use the following auxiliary function $Q\left(\mathit{\lambda},\overline{\mathit{\lambda}}\right)$ as the objective function for the optimization of the HMM parameters.*

**λ***|*

**O***), i.e. $\frac{\text{max}}{\overline{\mathit{\lambda}}}Q\left(\mathit{\lambda},\overline{\mathit{\lambda}}\right)\to \mathrm{P}\left(\mathit{O}|\overline{\mathit{\lambda}}\right)>\mathrm{P}\left(\mathit{O}|\mathit{\lambda}\right)$[11]. Given model parameter set*

**λ***λ*, P(

*,*

**O***|*

**S***) can be calculated as:*

**λ***,*

**O***|*

**S***) in (6) with (7), (6) can be rewritten as:*

**λ***π*

_{ i }and

*a*

_{ ij }with constraints ${\sum}_{i=1}^{N}{\pi}_{i}}=1$ and ${\sum}_{j=1}^{N}{a}_{\mathit{ij}}}=1$ can be obtained by maximizing the first and second term of (8) with respect to

*π*

_{ i }and

*a*

_{ ij }respectively as follows:

The forward and backward algorithm [11] is used to update *π*_{ i } and *a*_{ ij }. In the implementation of Baum-Welch, the update of *u*_{ i } is used for the update of the emission probability. Finally, we use Viterbi algorithm [11] to infer the hidden states of the sequence in study.

## Results

### Dataset

Two types of tumor data are used to verify the effectiveness of our model. The first type is the lobular breast tumor data with two different sequencing depths, which includes 497 positions generated using the Illumina GA II platform and was validated by Sanger. These positions were sequenced using Sanger capillary-based technology and were predicted to be non-synonymous protein-coding. 305 of these positions were confirmed as SNV and are taken as positive (TP), while 192 were not confirmed and are taken as true negative (TN). We take these positions as ground truth for the computation of TP, false positive (FP), TN, false negative (FN). These data can be obtained from the supplementary dataset 2A and 2C [9] along with their corresponding ground truth for SNVs in supplementary dataset 2B and 2D. The depths of supplementary dataset 2A and 2C are 10X and 40X respectively. Moreover, we use these datasets to compare between SNVHMM and SNVMix2, which is more efficient than SNVMix1 [9]. For better training of SNVMix2, we also use the supplementary dataset 3A and 3C [9].

The second dataset that came from MDS tumor data comprises of 7 MDS samples including 5 samples from RNA-Seq having depth <20 and 2 samples from whole exome sequencing having depth >150. These data are all from our lab and 4 mutated MDS genes were validated by PCR, along with other 23 common mutated MDS genes [14, 15] were also checked by SNVHMM for point mutation detection on these genes.

### Statistical metrics

where $\mathit{\text{Precision}}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$ and $\mathit{\text{Recall}}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$, are the proportion of true SNVs being predicted among the total predicted positives and the total true positives respectively.

### Statistical performance

**Comparison of statistical performance of SNVHMM with SNVMix2 with different mapping quality (MQ) and base quality (BQ) threshold for 10X data**

Model | MQ | BQ | TP | FP | TN | FN | Sensitivity(%) | Specificity(%) | Accuracy(%) | F-score |
---|---|---|---|---|---|---|---|---|---|---|

SNVHMM | 50 | 20 | 247 | 59 | 133 | 58 | 80.98 | 69.27 | 76.46(MVC = 4) | 0.8085 |

40 | 20 | 254 | 66 | 126 | 51 | 83.28 | 65.63 | 76.46(MVC = 4) | 0.8128 | |

30 | 20 | 256 | 70 | 112 | 49 | 83.93 | 65.54 | 76.05(MVC = 4) | 0.8114 | |

30 | 10 | 236 | 63 | 129 | 69 | 77.38 | 67.19 | 73.44(MVC = 5) | 0.7815 | |

20 | 10 | 273 | 111 | 81 | 32 | 89.51 | 42.19 | 71.23(MVC = 3) | 0.7925 | |

10 | 5 | 273 | 110 | 82 | 32 | 89.51 | 42.71 | 71.43(MVC = 2) | 0.7936 | |

SNVMix2_TI | 50 | 20 | 303 | 160 | 32 | 2 | 99.34 | 16.67 | 67.40 | 0.7891 |

40 | 20 | 305 | 174 | 18 | 0 | 100 | 9.38 | 64.99 | 0.7781 | |

30 | 20 | 305 | 174 | 18 | 0 | 100 | 9.38 | 64.99 | 0.7781 | |

30 | 10 | 305 | 173 | 19 | 0 | 100 | 9.89 | 65.19 | 0.7791 | |

20 | 10 | 305 | 191 | 1 | 0 | 100 | 0.52 | 61.56 | 0.7615 | |

10 | 5 | 305 | 192 | 0 | 0 | 100 | 0 | 61.37 | 0.7606 | |

SNVMix2_TO | 50 | 20 | 245 | 75 | 117 | 60 | 80.32 | 60.94 | 72.84 | 0.7840 |

40 | 20 | 261 | 88 | 104 | 44 | 85.57 | 54.17 | 73.44 | 0.7982 | |

30 | 20 | 266 | 90 | 102 | 39 | 87.21 | 53.13 | 74.04 | 0.8048 | |

30 | 10 | 274 | 92 | 100 | 31 | 89.83 | 52.08 | 75.25 | 0.8167 | |

20 | 10 | 283 | 125 | 67 | 22 | 92.78 | 34.90 | 70.42 | 0.7938 | |

10 | 5 | 290 | 134 | 58 | 15 | 95.08 | 30.21 | 70.02 | 0.7956 |

**Comparison of statistical performance of SNVHMM with SNVMix2 with different mapping quality (MQ) and base quality (BQ) threshold for 40X data**

Model | MQ | BQ | TP | FP | TN | FN | Sensitivity(%) | Specificity(%) | Accuracy(%) | F-score |
---|---|---|---|---|---|---|---|---|---|---|

SNVHMM | 50 | 20 | 281 | 77 | 115 | 24 | 92.13 | 59.89 | 79.68(MVC = 7) | 0.8477 |

40 | 20 | 283 | 83 | 109 | 22 | 92.78 | 56.77 | 78.87(MVC = 6) | 0.8435 | |

30 | 20 | 273 | 77 | 115 | 32 | 89.51 | 59.89 | 78.07(MVC = 9) | 0.8336 | |

30 | 10 | 289 | 79 | 113 | 16 | 94.75 | 58.85 | 80.88(MVC = 9) | 0.8588 | |

20 | 10 | 279 | 86 | 106 | 26 | 91.47 | 55.21 | 77.46(MVC = 8) | 0.8328 | |

10 | 5 | 281 | 87 | 105 | 24 | 92.13 | 54.69 | 77.67(MVC = 7) | 0.8351 | |

SNVMix2_TI | 50 | 20 | 291 | 109 | 83 | 14 | 95.40 | 43.23 | 75.25 | 0.8255 |

40 | 20 | 294 | 113 | 79 | 11 | 96.39 | 41.14 | 75.05 | 0.8258 | |

30 | 20 | 294 | 115 | 77 | 11 | 96.39 | 40.10 | 74.65 | 0.8235 | |

30 | 10 | 295 | 113 | 79 | 10 | 96.72 | 41.15 | 75.25 | 0.8275 | |

20 | 10 | 294 | 117 | 75 | 11 | 96.39 | 39.06 | 74.25 | 0.8212 | |

10 | 5 | 295 | 118 | 74 | 10 | 96.72 | 38.54 | 74.25 | 0.8217 | |

SNVMix2_TO | 50 | 20 | 283 | 86 | 106 | 22 | 92.79 | 55.21 | 78.27 | 0.8398 |

40 | 20 | 287 | 93 | 99 | 18 | 94.10 | 51.56 | 77.67 | 0.8380 | |

30 | 20 | 287 | 96 | 96 | 18 | 94.10 | 50.00 | 77.06 | 0.8343 | |

30 | 10 | 284 | 105 | 87 | 21 | 93.11 | 45.31 | 74.65 | 0.8184 | |

20 | 10 | 291 | 105 | 87 | 14 | 95.40 | 45.31 | 76.06 | 0.8302 | |

10 | 5 | 291 | 104 | 88 | 14 | 95.41 | 45.83 | 76.26 | 0.8314 |

### Implementation and robust analysis

The proposed algorithm is implemented in C and supports both Maq [4] and SAMtools [17] pileup format. Running SNVHMM on the lobular breast cancer data with sequencing depth 40X takes 1 ~ 2 seconds and it needs ~20 seconds for the lobular breast cancer data including 14649 locations with sequencing depth 40X on 64 bit Linux Ubuntu 3.0.0. SNVHMM is robust under different MQ and BQ threshold settings. The standard deviations of accuracy and F-score are between 0.001 and 0.003 respectively for both 10X and 40X lobular breast cancer data.

The software is available online at https://sites.google.com/site/snvhmm4/. The initial setting and trained parameters are also available for the lobular breast cancer data and MDS data.

### Performance of SNVHMM on MDS sample

**Number of point mutations found in 5 MDS RNA-Seq data and 2 whole exome data for SNVHMM**

Type | RNA-Seq | Whole exome | |||||
---|---|---|---|---|---|---|---|

Sample | RS_1 | RS_2 | RS_3 | RS_4 | RS_5 | WE_1 | WE_2 |

Number | 10645(91.6%) | 33354(93.3%) | 13881(91.5%) | 4777(94.2%) | 6951(92.6%) | 58803(94.8%) | 61344(93.7%) |

## Discussion

We introduced a new algorithm SNVHMM for SNVs prediction of tumor data from next generation sequencing, which generally yield data with low sequencing depth due to sequencing errors, as well as the altered ploidy and tumor cellularity. SNVHMM was conceived to circumvent the shortcomings of existing algorithms that cannot efficiently predict SNVs for data with low sequencing coverage. In this algorithm, we considered three genotypes concerned as the hidden states of HMM, and incorporated the confidence of the observation into the emission probability in HMM. The performance of SNVHMM was compared with a recently published method SNVMix2. Compared to SNVMix2, SNVHMM considered the relation of state from near-by locations in addition to their distribution. Moreover, SNVHMM predicted the hidden states by maximizing the posterior probability in condition of the whole observation while SNVMix2 predicted the genotype basing on maximizing the posterior probability in condition of the observation from single location. So SNVHMM gained more probability power for prediction from the same dataset. It was shown by experiment from the lobular breast cancer data sequenced with lower depth that SNVHMM improved the performance of SNVMix2 by only using much smaller size of training data. It was also observed that SNVHMM even exceeded the performance of SNVMix2 trained by much larger datasets. If looking into the performance of SNVHMM and SNVMix2_TI for lobular cancer data, we found that SNVHMM corrected 42% ~ 75% and 26% ~ 33% false positives to true negatives for sequencing depth 10X and 40X respectively, with more than 85% of them to have coverage less than 20. For SNVHMM and SNVMix2_TO, SNVHMM also corrected 10% ~ 17% and 2% ~ 8% false positives to true negatives for sequencing depth 10X and 40X respectively, with more than 80% of them to have coverage less than 20. So SNVHMM improved the performance of SNVMix2 for low-coverage sequencing data or at the low depth area of genome by improving the true negative rate largely. This verified the effectiveness of SNVHMM in utilizing the contextual information of non-SNVs by improving the specificity largely while remaining a relatively high sensitivity.

For experiments on MDS samples, SNVHMM could detect the point mutations efficiently. More than 95% of the point mutations detected by both SNVHMM and SNVMix2 are obvious mutation as most of the covered reads have the same non-reference base. From the common mutated 27 genes list of MDS, most of the mutated genes can be found in majority of the samples by SNVHMM. We also examined the region of the genes not detected to find no non-reference bases covered or insufficient non-reference bases covered with low quality.

*π*differs largely from the initial value for the lobular breast cancer data. It is not surprising as

*π*indicates the proportion of three kinds of bases on the genome, and it is observed from the ground truth of the lobular breast cancer data that majority of the bases have the state “ab”. It is also observed that majority parameters of the trained

*u*and

*A*changed significantly. The initial setting of

*u*and

*A*seems to be some close to the true parameters of these data. For the MDS data, the trained

*π*and

*A*changed largely compared with the initial setting while

*μ*also changed but not as much as

*π*and

*A*. We check the raw data to find that the SNVs are sparse and state “aa” dominates the whole distribution, so it is reasonable that the first value in

*π*increased largely while the second and the third value in

*π*decreased. It is also not surprising that all the states have a large transition probability to state “aa”. All the trained parameters for different thresholds of lobular breast cancer data and MDS data are provided at https://sites.google.com/site/snvhmm4/.

**Comparison of the parameters of SNVHMM before and after training on lobular breast cancer (LBC) data and MDS RNA_seq data for threshold of mapping quality 50 and base quality 20**

Parameter | LBC_10X | LBC_40X | MDS_RNA_Seq | |
---|---|---|---|---|

| initial | (0.904233 0.499051 0.090499) | (0.904233 0.499051 0.090499) | (0.904233 0.499051 0.090499) |

trained | (0.001199 0.984717 0.014086) | (0.000001 0.999831 0.000170) | (0.988258 0.011743 0.000001) | |

| initial | (0.999023 0.508543 0.000123) | (0.999023 0.508543 0.000123) | (0.999023 0.508543 0.000123) |

trained | (0.904833 0.466663 0.151255) | (0.897743 0.509801 0.165214) | (0.904233 0.544121 0.090499) | |

| initial | $\left(\begin{array}{ccc}\hfill 0.848400\hfill & \hfill 0.072800\hfill & \hfill 0.078800\hfill \\ \hfill 0.087570\hfill & \hfill 0.838210\hfill & \hfill 0.074300\hfill \\ \hfill 0.085100\hfill & \hfill 0.075600\hfill & \hfill 0.839300\hfill \end{array}\right)$ | $\left(\begin{array}{ccc}\hfill 0.848400\hfill & \hfill 0.072800\hfill & \hfill 0.078800\hfill \\ \hfill 0.087570\hfill & \hfill 0.838210\hfill & \hfill 0.074300\hfill \\ \hfill 0.085100\hfill & \hfill 0.075600\hfill & \hfill 0.839300\hfill \end{array}\right)$ | $\left(\begin{array}{ccc}\hfill 0.848400\hfill & \hfill 0.072800\hfill & \hfill 0.078800\hfill \\ \hfill 0.087570\hfill & \hfill 0.838210\hfill & \hfill 0.074300\hfill \\ \hfill 0.085100\hfill & \hfill 0.075600\hfill & \hfill 0.839300\hfill \end{array}\right)$ |

trained | $\left(\begin{array}{ccc}\hfill 0.567581\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.325414\hfill & \hfill 0.107006\hfill \\ \hfill 0.061140\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.864239\hfill & \hfill 0.074624\hfill \\ \hfill 0.044694\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.257290\hfill & \hfill 0.698019\hfill \end{array}\right)$ | $\left(\begin{array}{ccc}\hfill 0.412955\phantom{\rule{0.5em}{0ex}}\hfill & \hfill 0.476467\hfill & \hfill 0.110580\hfill \\ \hfill 0.159858\phantom{\rule{0.5em}{0ex}}\hfill & \hfill 0.723625\hfill & \hfill 0.116519\hfill \\ \hfill 0.112374\phantom{\rule{0.5em}{0ex}}\hfill & \hfill 0.323298\hfill & \hfill 0.564329\hfill \end{array}\right)$ | $\left(\begin{array}{ccc}\hfill 0.999064\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.000271\hfill & \hfill 0.000377\hfill \\ \hfill 0.986557\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.013444\hfill & \hfill 0.000001\hfill \\ \hfill 1.000000\phantom{\rule{1em}{0ex}}\hfill & \hfill 0.000001\hfill & \hfill 0.000001\hfill \end{array}\right)$ |

## Conclusions

We have proposed a new SNVs prediction tool SNVHMM for cancer data from NGS. SNVHMM can gain more probability power from the transition probability in additional to the posterior probability computation for the genotype distribution of whole observation. So SNVHMM is very efficient when the depth of NGS data is very low. Since NGS has lower sequence coverage and poor SNV detection capability in the regulatory regions of the genome, it is very helpful for SNV prediction for the low-depth area on the genome. SNVHMM outperformed an existing SNV prediction tool SNVMix by reducing its false positives and increasing its true negative. Moreover, SNVHMM needs much less data for training while obtaining a better performance than SNVMix. Finally, two types of MDS data with different coverage are tested, which shows the effectiveness of SNVHMM.

## Availability and requirements

** Project name:** SNVHMM: predicting single nucleo tide variants from next generation sequencing

**Project home page:** https://sites.google.com/site/snvhmm4/

**Operating system:** 64-bit Linux

**Programming language:** C

**Other requirements:** Linux Ubuntu 3.0.0 or higher

**License:** GNU GPL

**Any restrictions to use by non-academics:** license needed.

## Notes

### Acknowledgements

We would like to acknowledge the members of Translational Biosystems Lab in Cornell Medical School and Dr. Jing Su for his help with programming.

**Funding**

This work was supported by Funding: NIH R01LM010185-03 (Zhou), NIH U01HL111560-01 (Zhou), NIH 1R01DE022676-01 (Zhou), U01 CA166886-01 (Zhou).

## Supplementary material

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