Methods and challenges in timing chromosomal abnormalities within cancer samples

Motivation: Tumors acquire many chromosomal amplifications, and those acquired early in the lifespan of the tumor may be not only important for tumor growth but also can be used for diagnostic purposes. Many methods infer the order of the accumulation of abnormalities based on their occurrence in a large cohort of patients. Recently, Durinck et al. (2011) and Greenman et al. (2012) developed methods to order a single tumor's chromosomal amplifications based on the patterns of mutations accumulated within those regions. This method offers an unprecedented opportunity to assess the etiology of a single tumor sample, but has not been widely evaluated. Results: We show that the model for timing chromosomal amplifications is limited in scope, particularly for regions with high levels of amplification. We also show that the estimation of the order of events can be sensitive for events that occur early in the progression of the tumor and that the partial maximum likelihood method of Greenman et al. (2012) can give biased estimates, particularly for moderate read coverage or normal contamination. We propose a maximum-likelihood estimation procedure that fully accounts for sequencing variability and show that it outperforms the partial maximum-likelihood estimation method. We also propose a Bayesian estimation procedure that stabilizes the estimates in certain settings. We implement these methods on a small number of ovarian tumors, and the results suggest possible differences in how the tumors acquired amplifications.