Scan Statistics Applications in Genomics

The area of scan statistics encompasses a broad class of methods for detecting clusters of events. These methods have been applied to identify genomic regions containing nonrandom clusters of restriction sites, genetic markers, or specific word patterns since the early 1990s. Typically, the positions of these sites are modeled as independent and identically distributed random points on the unit interval or events in Bernoulli or Poisson processes. In the majority of the applications, the scan statistics are defined either as the maximum count of points contained in a scanning window of fixed length or the minimum aggregated spacing between a fixed number of consecutive points. In some applications, the underlying models are generalized to the two-dimensional unit square or graphs representing gene networks where the scan statistics are maximum likelihood ratios. Statistical significance can be evaluated by p-value calculations using asymptotic and other analytical approximations or permutation-based procedures. This chapter includes reviews of the DNA sequence analysis studies to identify clusters of the GATC tetranucleotide on E. coli DNA and palindromes in herpesvirus genomes. Some recent applications in finding clusters of chromosomal translocation breakpoints, viral DNA integration sites, and DNA variants associated with copy number variations are also presented. Identification of these clusters will help design better gene therapies and elucidate the mechanisms of diseases like leukemia, schizophrenia, and autism. As different types of genomics data are accumulating rapidly, the methodology of scan statistics is expected to play increasingly important roles in biomedical research.