STATISTICALLY MOTIVATED SEARCH FOR CLUSTERS OF EVENTS IN SEQUENCES AND ANALYSIS OF BIOMEDICAL DATA

The task of searching for clusters in sequences arises when analyzing various medical and biological data. This may be searching for clusters of events (outbreaks of events) in epidemiology, searching for areas of increased mutation frequency in a nucleotide sequence, etc. For the case of continuous time, the search for condensations and rarefactions in the event flow was considered by us earlier. In this publication, the problem of finding clusters is solved for discrete time. The independent trials model and the homogeneous two-state Markov chain model are considered as null hypotheses assuming the absence of clusters. Events that are separated from each other by less than some fixed distance are combined into components, each of which is characterized by two numbers — the total number of events that make it up and compactness, measured by the total number of moments in time when there were no events (the number of empty cells). The critical region is constructed on the plane — (number of points, compactness) taking into account multiple comparisons, and too large or too compact components are recognized as significant clusters. The proposed method is compared with the scanning statistics method popular in epidemiology and with the method common in bioinformatics based on the hidden Markov chain model and the Viterbi algorithm. Unlike the scanning statistics method, the proposed method can search for several clusters. The efficiency of the proposed method is comparable to the Viterbi method, but its important advantage is that there is no need to estimate the parameters of the hidden Markov chain, which can only be done with a very large training sample.