An EM algorithm to improve the estimation of the probability of clonal relatedness of pairs of tumors in cancer patients

• Main Authors: Audrey Mauguen, Venkatraman E. Seshan, Irina Ostrovnaya, Colin B. Begg
• Format: Article
• Language: English
• Published: BMC 2019-11-01
• Series: BMC Bioinformatics
• Subjects: Cancer; Clonality; EM algorithm; Tumor mutation; Parameter estimation; Random effect model
• Online Access: http://link.springer.com/article/10.1186/s12859-019-3148-z

Abstract Background We previously introduced a random-effects model to analyze a set of patients, each of which has two distinct tumors. The goal is to estimate the proportion of patients for which one of the tumors is a metastasis of the other, i.e. where the tumors are clonally related. Matches of mutations within a tumor pair provide the evidence for clonal relatedness. In this article, using simulations, we compare two estimation approaches that we considered for our model: use of a constrained quasi-Newton algorithm to maximize the likelihood conditional on the random effect, and an Expectation-Maximization algorithm where we further condition the random-effect distribution on the data. Results In some specific settings, especially with sparse information, the estimation of the parameter of interest is at the boundary a non-negligible number of times using the first approach, while the EM algorithm gives more satisfactory estimates. This is of considerable importance for our application, since an estimate of either 0 or 1 for the proportion of cases that are clonal leads to individual probabilities being 0 or 1 in settings where the evidence is clearly not sufficient for such definitive probability estimates. Conclusions The EM algorithm is a preferable approach for our clonality random-effect model. It is now the method implemented in our R package Clonality, making available an easy and fast way to estimate this model on a range of applications.