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

Abstract

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the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.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 coverage d defined 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.

Graphical abstract

Keywords

Markov chains / next generation sequencing / transition probabilities / confidence intervals

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SUPPLEMENTARY MATERIALS

The supplementary materials can be found online with this article at https:// 10.1007/s40484-020-0200-y.

ACKNOWLEDGEMENTS

We thank Dr. Gesine Reinert of Oxford University for discussions and help related to the problems studied in this paper. LW is supported by NSFC grants (Nos.11571349 and 91630314), the National Key R&D Program of China under Grant 2018YFB0704304, NCMIS of CAS, LSC of CAS, and the Youth Innovation Promotion Association of CAS. JR and FS were supported by US National Science Foundation (NSF) (DMS-1518001) and National Institutes of Health (NIH) (R01GM120624, 1R01GM131407).

COMPLIANCE WITH ETHICS GUIDELINES

The authors Lin Wan, Xin Kang, Jie Ren and Fengzhu Sun declare that they have no conflict of interests.

This article does not contain any studies with human or animal subjects performed by any of the authors.

RIGHTS & PERMISSIONS

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