Abstract
BackgroundWe 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.ResultsIn 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.ConclusionsThe 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.
Highlights
We previously introduced a random-effects model to analyze a set of patients, each of which has two distinct tumors
Constructing the index these authors have focused solely on mutations that are shared between the two tumors, ignoring the information from mutations that occur in one tumor but not the other, evidence that argues against clonal relatedness
Motivated by a study of contralateral breast cancer that will be described in more detail we developed a random-effects model to simultaneously analyze each case for clonal relatedness and to obtain an estimate of how frequently this occurs [6]
Summary
We previously introduced a random-effects model to analyze a set of patients, each of which has two distinct tumors. Other authors have used the proportion of observed mutations that are shared as the index [3, 4], while Bao et al [5] formalized this idea by assuming that the matched mutations follow a binomial distribution. All of these approaches analyze each case independently. The approach we discuss in this article, improving upon Mauguen et al [6], is the only available method that models the data from all cases collectively to obtain parametric estimates of the proportion of cases in the population that are clonal. Our method relies heavily on the recognition of the fact that the probabilities of occurrence of the observed mutations
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