  We devise a novel inference algorithm to effectively solve the cancer
progression model reconstruction problem. Our empirical analysis of the
accuracy and convergence rate of our algorithm, CAncer PRogression Inference
(CAPRI), shows that it outperforms the state-of-the-art algorithms addressing
similar problems.
  Motivation: Several cancer-related genomic data have become available (e.g.,
The Cancer Genome Atlas, TCGA) typically involving hundreds of patients. At
present, most of these data are aggregated in a cross-sectional fashion
providing all measurements at the time of diagnosis.Our goal is to infer cancer
progression models from such data. These models are represented as directed
acyclic graphs (DAGs) of collections of selectivity relations, where a mutation
in a gene A selects for a later mutation in a gene B. Gaining insight into the
structure of such progressions has the potential to improve both the
stratification of patients and personalized therapy choices.
  Results: The CAPRI algorithm relies on a scoring method based on a
probabilistic theory developed by Suppes, coupled with bootstrap and maximum
likelihood inference. The resulting algorithm is efficient, achieves high
accuracy, and has good complexity, also, in terms of convergence properties.
CAPRI performs especially well in the presence of noise in the data, and with
limited sample sizes. Moreover CAPRI, in contrast to other approaches, robustly
reconstructs different types of confluent trajectories despite irregularities
in the data.We also report on an ongoing investigation using CAPRI to study
atypical Chronic Myeloid Leukemia, in which we uncovered non trivial
selectivity relations and exclusivity patterns among key genomic events.
