Spatial statistical tools for genome-wide mutation cluster detection under a microarray probe sampling system

Mutation cluster analysis is critical for understanding certain mutational mechanisms relevant to genetic disease, diversity, and evolution. Yet, whole genome sequencing for detection of mutation clusters is prohibitive with high cost for most organisms and population surveys. Single nucleotide polymorphism (SNP) genotyping arrays, like the Mouse Diversity Genotyping Array, offer an alternative low-cost, screening for mutations at hundreds of thousands of loci across the genome using experimental designs that permit capture of de novo mutations in any tissue. Formal statistical tools for genome-wide detection of mutation clusters under a microarray probe sampling system are yet to be established. A challenge in the development of statistical methods is that microarray detection of mutation clusters is constrained to select SNP loci captured by probes on the array. This paper develops a Monte Carlo framework for cluster testing and assesses test statistics for capturing potential deviations from spatial randomness which are motivated by, and incorporate, the array design. While null distributions of the test statistics are established under spatial randomness via the homogeneous Poisson process, power performance of the test statistics is evaluated under postulated types of Neyman-Scott clustering processes through Monte Carlo simulation. A new statistic is developed and recommended as a screening tool for mutation cluster detection. The statistic is demonstrated to be excellent in terms of its robustness and power performance, and useful for cluster analysis in settings of missing data. The test statistic can also be generalized to any one dimensional system where every site is observed, such as DNA sequencing data. The paper illustrates how the informal graphical tools for detecting clusters may be misleading. The statistic is used for finding clusters of putative SNP differences in a mixture of different mouse genetic backgrounds and clusters of de novo SNP differences arising between tissues with development and carcinogenesis.