Disclaimer: While this is a very important question to address, we don't think this is the major contribution of Canopy, but rather a by-product of our program. There are other methods that specifically focus on clustering mutations, e.g., SciClone, PyClone, etc.

A multivariate binomial mixture clustering step can be applied to the SNAs before MCMC sampling. We show in our paper via simulations that this pre-clustering method helps the Markov chain converge faster with smaller estimation error (especially when mutations show clear cluster patterns by visualization). This clustering step can also remove likely false positives before feeding the mutations to the MCMC algorithm.

Demo code for clustering can be found at binomial_EM.R. Detailed methods can be found in the supplements of our paper under section Binomial mixture clustering. BIC is used for model selection. 2D (two longitudinal/spatial samples) or 3D (three samples) plots are generated for visualization.

Below is a toy example, where three bulk tumor samples were in silico simulated from a tree of 4 clones/leaves. The 5 tree segments (excluding the leftmost branch, which corresponds to the normal clone) separate 200 mutations into 5 mutation clusters. The top panel shows BIC across different number of cluster. The bottom panels are for post-clustering visualization where different colors correpond to different mutation clusters. The code can be found here (top part); the dataset is stored in the R package and can be used via

data(toy3)

Below is real dataset from Ding et al. (Nature 2012), where a leukemia patient was sequenced at two timepoints -- primary tumor (sample 1) and relapse genome (sample 2). The real dataset is noisier and can potentially contain false positives for somatic mutations. We thus include in the mixture a multivariate uniform component on the unit interval, which corresponds to mutations that have high standard errors during sequencing or that are likely to be false positives. The code can be found here (bottom part); the dataset is stored in the R package and can be used via

data(AML43)

Canopy uses the pre-clustering results to initialize the MCMC procedure, and then fine tunes the individual mutations within each cluster later in the MCMC run, which also adjusts for the clustering uncertainty. An alternative is to generate pseudo-SNA corresponding to each mutation cluster. The read depth can be taken as the median across all mutations within the mutation cluster; the observed MAFs are just the estimated centroid from the EM algorithm, from which the number of mutant reads can be obtained.

Code for MCMC sampling after Binomial mixture clustering can be found here.