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

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.