A Statistical Test of the Hypothesis that Polyclonal Intestinal Tumors Arise by Random Collision of Initiated Clones

The random collision hypothesis is a mathematical idealization of intestinal tumor formation that can account for the polyclonal origin of tumors without requiring a mechanistic description of clonal interaction. Using data from recent polyclonality studies in mice, we develop a statistical procedure to test the random collision hypothesis. Elements from stochastic geometry and approximations due to Armitage (1949, Biometrika 36, 257-266) support a statistical model of tumor count data. Bayesian analysis yields the posterior distribution of the number of heterotypic tumors, from which p-values are computed to test random collision.