skip to main content


Title: Confidence intervals for Markov chain transition probabilities based on next generation sequencing reads data
Background

Markov chains (MC) have been widely used to model molecular sequences. The estimations of MC transition matrix and confidence intervals of the transition probabilities from long sequence data have been intensively studied in the past decades. In next generation sequencing (NGS), a large amount of short reads are generated. These short reads can overlap and some regions of the genome may not be sequenced resulting in a new type of data. Based on NGS data, the transition probabilities of MC can be estimated by moment estimators. However, the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.

Methods

In this study, we present the asymptotic distributions of several statistics related to MC based on NGS data. We show that, after scaling by the effective coverageddefined in a previous study by the authors, these statistics based on NGS data approximate to the same distributions as the corresponding statistics for long sequences.

Results

We apply the asymptotic properties of these statistics for finding the theoretical confidence regions for MC transition probabilities based on NGS short reads data. We validate our theoretical confidence intervals using both simulated data and real data sets, and compare the results with those by the parametric bootstrap method.

Conclusions

We find that the asymptotic distributions of these statistics and the theoretical confidence intervals of transition probabilities based on NGS data given in this study are highly accurate, providing a powerful tool for NGS data analysis.

 
more » « less
NSF-PAR ID:
10478126
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Quantitative Biology
Volume:
8
Issue:
2
ISSN:
2095-4689
Format(s):
Medium: X Size: p. 143-154
Size(s):
["p. 143-154"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Modeling and drawing inference on the joint associations between single‐nucleotide polymorphisms and a disease has sparked interest in genome‐wide associations studies. In the motivating Boston Lung Cancer Survival Cohort (BLCSC) data, the presence of a large number of single nucleotide polymorphisms of interest, though smaller than the sample size, challenges inference on their joint associations with the disease outcome. In similar settings, we find that neither the debiased lasso approach (van de Geer et al., 2014), which assumes sparsity on the inverse information matrix, nor the standard maximum likelihood method can yield confidence intervals with satisfactory coverage probabilities for generalized linear models. Under this “largen, divergingp” scenario, we propose an alternative debiased lasso approach by directly inverting the Hessian matrix without imposing the matrix sparsity assumption, which further reduces bias compared to the original debiased lasso and ensures valid confidence intervals with nominal coverage probabilities. We establish the asymptotic distributions of any linear combinations of the parameter estimates, which lays the theoretical ground for drawing inference. Simulations show that the proposedrefineddebiased estimating method performs well in removing bias and yields honest confidence interval coverage. We use the proposed method to analyze the aforementioned BLCSC data, a large‐scale hospital‐based epidemiology cohort study investigating the joint effects of genetic variants on lung cancer risks.

     
    more » « less
  2. Obeid, Iyad Selesnick (Ed.)
    Electroencephalography (EEG) is a popular clinical monitoring tool used for diagnosing brain-related disorders such as epilepsy [1]. As monitoring EEGs in a critical-care setting is an expensive and tedious task, there is a great interest in developing real-time EEG monitoring tools to improve patient care quality and efficiency [2]. However, clinicians require automatic seizure detection tools that provide decisions with at least 75% sensitivity and less than 1 false alarm (FA) per 24 hours [3]. Some commercial tools recently claim to reach such performance levels, including the Olympic Brainz Monitor [4] and Persyst 14 [5]. In this abstract, we describe our efforts to transform a high-performance offline seizure detection system [3] into a low latency real-time or online seizure detection system. An overview of the system is shown in Figure 1. The main difference between an online versus offline system is that an online system should always be causal and has minimum latency which is often defined by domain experts. The offline system, shown in Figure 2, uses two phases of deep learning models with postprocessing [3]. The channel-based long short term memory (LSTM) model (Phase 1 or P1) processes linear frequency cepstral coefficients (LFCC) [6] features from each EEG channel separately. We use the hypotheses generated by the P1 model and create additional features that carry information about the detected events and their confidence. The P2 model uses these additional features and the LFCC features to learn the temporal and spatial aspects of the EEG signals using a hybrid convolutional neural network (CNN) and LSTM model. Finally, Phase 3 aggregates the results from both P1 and P2 before applying a final postprocessing step. The online system implements Phase 1 by taking advantage of the Linux piping mechanism, multithreading techniques, and multi-core processors. To convert Phase 1 into an online system, we divide the system into five major modules: signal preprocessor, feature extractor, event decoder, postprocessor, and visualizer. The system reads 0.1-second frames from each EEG channel and sends them to the feature extractor and the visualizer. The feature extractor generates LFCC features in real time from the streaming EEG signal. Next, the system computes seizure and background probabilities using a channel-based LSTM model and applies a postprocessor to aggregate the detected events across channels. The system then displays the EEG signal and the decisions simultaneously using a visualization module. The online system uses C++, Python, TensorFlow, and PyQtGraph in its implementation. The online system accepts streamed EEG data sampled at 250 Hz as input. The system begins processing the EEG signal by applying a TCP montage [8]. Depending on the type of the montage, the EEG signal can have either 22 or 20 channels. To enable the online operation, we send 0.1-second (25 samples) length frames from each channel of the streamed EEG signal to the feature extractor and the visualizer. Feature extraction is performed sequentially on each channel. The signal preprocessor writes the sample frames into two streams to facilitate these modules. In the first stream, the feature extractor receives the signals using stdin. In parallel, as a second stream, the visualizer shares a user-defined file with the signal preprocessor. This user-defined file holds raw signal information as a buffer for the visualizer. The signal preprocessor writes into the file while the visualizer reads from it. Reading and writing into the same file poses a challenge. The visualizer can start reading while the signal preprocessor is writing into it. To resolve this issue, we utilize a file locking mechanism in the signal preprocessor and visualizer. Each of the processes temporarily locks the file, performs its operation, releases the lock, and tries to obtain the lock after a waiting period. The file locking mechanism ensures that only one process can access the file by prohibiting other processes from reading or writing while one process is modifying the file [9]. The feature extractor uses circular buffers to save 0.3 seconds or 75 samples from each channel for extracting 0.2-second or 50-sample long center-aligned windows. The module generates 8 absolute LFCC features where the zeroth cepstral coefficient is replaced by a temporal domain energy term. For extracting the rest of the features, three pipelines are used. The differential energy feature is calculated in a 0.9-second absolute feature window with a frame size of 0.1 seconds. The difference between the maximum and minimum temporal energy terms is calculated in this range. Then, the first derivative or the delta features are calculated using another 0.9-second window. Finally, the second derivative or delta-delta features are calculated using a 0.3-second window [6]. The differential energy for the delta-delta features is not included. In total, we extract 26 features from the raw sample windows which add 1.1 seconds of delay to the system. We used the Temple University Hospital Seizure Database (TUSZ) v1.2.1 for developing the online system [10]. The statistics for this dataset are shown in Table 1. A channel-based LSTM model was trained using the features derived from the train set using the online feature extractor module. A window-based normalization technique was applied to those features. In the offline model, we scale features by normalizing using the maximum absolute value of a channel [11] before applying a sliding window approach. Since the online system has access to a limited amount of data, we normalize based on the observed window. The model uses the feature vectors with a frame size of 1 second and a window size of 7 seconds. We evaluated the model using the offline P1 postprocessor to determine the efficacy of the delayed features and the window-based normalization technique. As shown by the results of experiments 1 and 4 in Table 2, these changes give us a comparable performance to the offline model. The online event decoder module utilizes this trained model for computing probabilities for the seizure and background classes. These posteriors are then postprocessed to remove spurious detections. The online postprocessor receives and saves 8 seconds of class posteriors in a buffer for further processing. It applies multiple heuristic filters (e.g., probability threshold) to make an overall decision by combining events across the channels. These filters evaluate the average confidence, the duration of a seizure, and the channels where the seizures were observed. The postprocessor delivers the label and confidence to the visualizer. The visualizer starts to display the signal as soon as it gets access to the signal file, as shown in Figure 1 using the “Signal File” and “Visualizer” blocks. Once the visualizer receives the label and confidence for the latest epoch from the postprocessor, it overlays the decision and color codes that epoch. The visualizer uses red for seizure with the label SEIZ and green for the background class with the label BCKG. Once the streaming finishes, the system saves three files: a signal file in which the sample frames are saved in the order they were streamed, a time segmented event (TSE) file with the overall decisions and confidences, and a hypotheses (HYP) file that saves the label and confidence for each epoch. The user can plot the signal and decisions using the signal and HYP files with only the visualizer by enabling appropriate options. For comparing the performance of different stages of development, we used the test set of TUSZ v1.2.1 database. It contains 1015 EEG records of varying duration. The any-overlap performance [12] of the overall system shown in Figure 2 is 40.29% sensitivity with 5.77 FAs per 24 hours. For comparison, the previous state-of-the-art model developed on this database performed at 30.71% sensitivity with 6.77 FAs per 24 hours [3]. The individual performances of the deep learning phases are as follows: Phase 1’s (P1) performance is 39.46% sensitivity and 11.62 FAs per 24 hours, and Phase 2 detects seizures with 41.16% sensitivity and 11.69 FAs per 24 hours. We trained an LSTM model with the delayed features and the window-based normalization technique for developing the online system. Using the offline decoder and postprocessor, the model performed at 36.23% sensitivity with 9.52 FAs per 24 hours. The trained model was then evaluated with the online modules. The current performance of the overall online system is 45.80% sensitivity with 28.14 FAs per 24 hours. Table 2 summarizes the performances of these systems. The performance of the online system deviates from the offline P1 model because the online postprocessor fails to combine the events as the seizure probability fluctuates during an event. The modules in the online system add a total of 11.1 seconds of delay for processing each second of the data, as shown in Figure 3. In practice, we also count the time for loading the model and starting the visualizer block. When we consider these facts, the system consumes 15 seconds to display the first hypothesis. The system detects seizure onsets with an average latency of 15 seconds. Implementing an automatic seizure detection model in real time is not trivial. We used a variety of techniques such as the file locking mechanism, multithreading, circular buffers, real-time event decoding, and signal-decision plotting to realize the system. A video demonstrating the system is available at: https://www.isip.piconepress.com/projects/nsf_pfi_tt/resources/videos/realtime_eeg_analysis/v2.5.1/video_2.5.1.mp4. The final conference submission will include a more detailed analysis of the online performance of each module. ACKNOWLEDGMENTS Research reported in this publication was most recently supported by the National Science Foundation Partnership for Innovation award number IIP-1827565 and the Pennsylvania Commonwealth Universal Research Enhancement Program (PA CURE). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the official views of any of these organizations. REFERENCES [1] A. Craik, Y. He, and J. L. Contreras-Vidal, “Deep learning for electroencephalogram (EEG) classification tasks: a review,” J. Neural Eng., vol. 16, no. 3, p. 031001, 2019. https://doi.org/10.1088/1741-2552/ab0ab5. [2] A. C. Bridi, T. Q. Louro, and R. C. L. Da Silva, “Clinical Alarms in intensive care: implications of alarm fatigue for the safety of patients,” Rev. Lat. Am. Enfermagem, vol. 22, no. 6, p. 1034, 2014. https://doi.org/10.1590/0104-1169.3488.2513. [3] M. Golmohammadi, V. Shah, I. Obeid, and J. Picone, “Deep Learning Approaches for Automatic Seizure Detection from Scalp Electroencephalograms,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York, New York, USA: Springer, 2020, pp. 233–274. https://doi.org/10.1007/978-3-030-36844-9_8. [4] “CFM Olympic Brainz Monitor.” [Online]. Available: https://newborncare.natus.com/products-services/newborn-care-products/newborn-brain-injury/cfm-olympic-brainz-monitor. [Accessed: 17-Jul-2020]. [5] M. L. Scheuer, S. B. Wilson, A. Antony, G. Ghearing, A. Urban, and A. I. Bagic, “Seizure Detection: Interreader Agreement and Detection Algorithm Assessments Using a Large Dataset,” J. Clin. Neurophysiol., 2020. https://doi.org/10.1097/WNP.0000000000000709. [6] A. Harati, M. Golmohammadi, S. Lopez, I. Obeid, and J. Picone, “Improved EEG Event Classification Using Differential Energy,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium, 2015, pp. 1–4. https://doi.org/10.1109/SPMB.2015.7405421. [7] V. Shah, C. Campbell, I. Obeid, and J. Picone, “Improved Spatio-Temporal Modeling in Automated Seizure Detection using Channel-Dependent Posteriors,” Neurocomputing, 2021. [8] W. Tatum, A. Husain, S. Benbadis, and P. Kaplan, Handbook of EEG Interpretation. New York City, New York, USA: Demos Medical Publishing, 2007. [9] D. P. Bovet and C. Marco, Understanding the Linux Kernel, 3rd ed. O’Reilly Media, Inc., 2005. https://www.oreilly.com/library/view/understanding-the-linux/0596005652/. [10] V. Shah et al., “The Temple University Hospital Seizure Detection Corpus,” Front. Neuroinform., vol. 12, pp. 1–6, 2018. https://doi.org/10.3389/fninf.2018.00083. [11] F. Pedregosa et al., “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011. https://dl.acm.org/doi/10.5555/1953048.2078195. [12] J. Gotman, D. Flanagan, J. Zhang, and B. Rosenblatt, “Automatic seizure detection in the newborn: Methods and initial evaluation,” Electroencephalogr. Clin. Neurophysiol., vol. 103, no. 3, pp. 356–362, 1997. https://doi.org/10.1016/S0013-4694(97)00003-9. 
    more » « less
  3. Abstract Long-read sequencing technology enables significant progress in de novo genome assembly. However, the high error rate and the wide error distribution of raw reads result in a large number of errors in the assembly. Polishing is a procedure to fix errors in the draft assembly and improve the reliability of genomic analysis. However, existing methods treat all the regions of the assembly equally while there are fundamental differences between the error distributions of these regions. How to achieve very high accuracy in genome assembly is still a challenging problem. Motivated by the uneven errors in different regions of the assembly, we propose a novel polishing workflow named BlockPolish. In this method, we divide contigs into blocks with low complexity and high complexity according to statistics of aligned nucleotide bases. Multiple sequence alignment is applied to realign raw reads in complex blocks and optimize the alignment result. Due to the different distributions of error rates in trivial and complex blocks, two multitask bidirectional Long short-term memory (LSTM) networks are proposed to predict the consensus sequences. In the whole-genome assemblies of NA12878 assembled by Wtdbg2 and Flye using Nanopore data, BlockPolish has a higher polishing accuracy than other state-of-the-arts including Racon, Medaka and MarginPolish & HELEN. In all assemblies, errors are predominantly indels and BlockPolish has a good performance in correcting them. In addition to the Nanopore assemblies, we further demonstrate that BlockPolish can also reduce the errors in the PacBio assemblies. The source code of BlockPolish is freely available on Github (https://github.com/huangnengCSU/BlockPolish). 
    more » « less
  4. Abstract Aim

    Disturbances such as fire operate against a backdrop of constraints imposed by climate and soils to influence grass–woody plant abundance. However, little is known of how these factors interact to determine the upper limits of woody cover and stature in grasslands, in which shrub/tree abundance has been increasing globally.

    Location

    Kansas, Oklahoma, Texas, USA.

    Time period

    2004–2014.

    Major taxa studied

    Angiosperms and gymnosperms.

    Methods

    Using a database of 1,466 sites and quantile regression to derive precipitation‐based upper limits to woody cover and height within grasslands of the central/southern Great Plains, USA, we assessed how soil texture and climate‐related fire probabilities [two groups; low fire probability, P(Flow), versus high fire probability, P(Fhi)] might influence realization of the climate potential.

    Results

    Soil texture had no substantive influence on regional‐scale woody cover, but taller plants were predicted on sandy soils. Woody plant height potential increased linearly with increasing annual precipitation, becoming asymptotic atc. 800 mm for both the P(Flow) and the P(Fhi) fire groups, after which P(Flow) areas were predicted to support taller plants. Potential woody cover also increased linearly with annual precipitation untilc. 800 mm, after which predictions of maximum % cover were similar under both fire groups.

    Main conclusions

    Precipitation was the overriding factor constraining potential woody cover and height, particularly in drier regions, with fire playing a minor role at these regional scales. In contrast to height potential, cover potential remained similar for both P(Flow) and P(Fhi) sites. Dynamic adjustments in woody plant architecture and allocation to foliage and stems, wherein areal cover is maintained when height is suppressed has implications for remote sensing, primary production and biogeochemical processes. Our analyses indicate drier grasslands [< 800 mm mean annual precipitation (MAP)] undergoing woody plant encroachment have the potential to become shrublands (e.g. short woody plants, low cover), whereas wetter areas have the potential to become woodland or forest (taller woody plants, high cover).

     
    more » « less
  5. Abstract Motivation

    Reconstructing the full-length expressed transcripts (a.k.a. the transcript assembly problem) from the short sequencing reads produced by RNA-seq protocol plays a central role in identifying novel genes and transcripts as well as in studying gene expressions and gene functions. A crucial step in transcript assembly is to accurately determine the splicing junctions and boundaries of the expressed transcripts from the reads alignment. In contrast to the splicing junctions that can be efficiently detected from spliced reads, the problem of identifying boundaries remains open and challenging, due to the fact that the signal related to boundaries is noisy and weak.

    Results

    We present DeepBound, an effective approach to identify boundaries of expressed transcripts from RNA-seq reads alignment. In its core DeepBound employs deep convolutional neural fields to learn the hidden distributions and patterns of boundaries. To accurately model the transition probabilities and to solve the label-imbalance problem, we novelly incorporate the AUC (area under the curve) score into the optimizing objective function. To address the issue that deep probabilistic graphical models requires large number of labeled training samples, we propose to use simulated RNA-seq datasets to train our model. Through extensive experimental studies on both simulation datasets of two species and biological datasets, we show that DeepBound consistently and significantly outperforms the two existing methods.

    Availability and implementation

    DeepBound is freely available at https://github.com/realbigws/DeepBound.

     
    more » « less