caa a22 4500 605519919 CHVBK 20210128100732.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9374-3 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9374-3 Detection of Significant Genomic Alterations via Simultaneous Minimal Sojourns at a State by Independent Continuous-time Markov Chains [Elektronische Daten] [Stéphane Robin, Valeri Stefanov] 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. Springer Science+Business Media New York, 2013 Birth-and-death process nationallicence Genomic alteration nationallicence Laplace transform nationallicence Markov jump process nationallicence Robin Stéphane INRA, UMR 518 MIA, 16, rue C. Bernard, 75005, Paris, France aut Stefanov Valeri Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 479-487 1387-5841 17:2<479 2015 17 11009 https://doi.org/10.1007/s11009-013-9374-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9374-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Robin Stéphane INRA, UMR 518 MIA, 16, rue C. Bernard, 75005, Paris, France aut NATIONALLICENCE 700 1- Stefanov Valeri Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 479-487 1387-5841 17:2<479 2015 17 11009