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Detection of Significant Genomic Alterations via Simultaneous Minimal Sojourns at a State by Independent Continuous-time Markov Chains

Author

Listed:
  • Stéphane Robin

    (UMR 518 MIA
    UMR 518 MIA)

  • Valeri T. Stefanov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

Abstract

The connection between a disease and some genetic disorders can be studied by looking for recurrent alterations in genomic profiles of humans affected by the disease. Modeling each patient profile as a 2-state jump Markov process, we define a recurrent alteration in terms of a sojourn time of a cumulated process. The cumulated process happen to be a birth-and-death process. We provide the exact Laplace transforms of relevant hitting times associated with the latter. Based on this exact results, we derive an upper bound of a sojourn time probability of interest. Our upper bound is exactly equal to the p-value nominated in all earlier literature where an attempt is made for an assessment of the significance of genomic alterations. Moreover, that p-value has never been evaluated exactly in previous works. Finally, we give abaques which are useful for the assessment of recurrent genomic alterations for a variety of realistic alteration frequencies and lengths.

Suggested Citation

  • Stéphane Robin & Valeri T. Stefanov, 2015. "Detection of Significant Genomic Alterations via Simultaneous Minimal Sojourns at a State by Independent Continuous-time Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 479-487, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9374-3
    DOI: 10.1007/s11009-013-9374-3
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    References listed on IDEAS

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    1. Franck Rapaport & Christina Leslie, 2010. "Determining Frequent Patterns of Copy Number Alterations in Cancer," PLOS ONE, Public Library of Science, vol. 5(8), pages 1-10, August.
    2. S. Robin & V. T. Stefanov, 2009. "Simultaneous Occurrences of Runs in Independent Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 267-275, June.
    3. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
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