Unsupervised detection of fragment length signatures of circulating tumor DNA using non-negative matrix factorization

Sequencing of cell-free DNA (cfDNA) is currently being used to detect cancer by searching both for mutational and non-mutational alterations. Recent work has shown that the length distribution of cfDNA fragments from a cancer patient can inform tumor load and type. Here, we propose non-negative matrix factorization (NMF) of fragment length distributions as a novel and completely unsupervised method for studying fragment length patterns in cfDNA. Using shallow whole-genome sequencing (sWGS) of cfDNA from a cohort of patients with metastatic castration-resistant prostate cancer (mCRPC), we demonstrate how NMF accurately infers the true tumor fragment length distribution as an NMF component - and that the sample weights of this component correlate with ctDNA levels (r=0.75). We further demonstrate how using several NMF components enables accurate cancer detection on data from various early stage cancers (AUC = 0.96). Finally, we show that NMF, when applied across genomic regions, can be used to discover fragment length signatures associated with open chromatin.


Sample-size estimation
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Replicates
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Statistical reporting
• Statistical analysis methods should be described and justified • Raw data should be presented in figures whenever informative to do so (typically when N per group is less than 10) • For each experiment, you should identify the statistical tests used, exact values of N, definitions of center, methods of multiple test correction, and dispersion and precision measures (e.g., mean, median, SD, SEM, confidence intervals; and, for the major substantive results, a measure of effect size (e.g., Pearson's r, Cohen's d) • Report exact p-values wherever possible alongside the summary statistics and 95% confidence intervals. These should be reported for all key questions and not only when the p-value is less than 0.05.
Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission: (For large datasets, or papers with a very large number of statistical tests, you may upload a single table file with tests, Ns, etc., with reference to sections in the manuscript.)

Group allocation
• Indicate how samples were allocated into experimental groups (in the case of clinical studies, please specify allocation to treatment method); if randomization was used, please also state if restricted randomization was applied • Indicate if masking was used during group allocation, data collection and/or data analysis Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission: Additional data files ("source data") • We encourage you to upload relevant additional data files, such as numerical data that are represented as a graph in a figure, or as a summary table • Where provided, these should be in the most useful format, and they can be uploaded as "Source data" files linked to a main figure or table • Include model definition files including the full list of parameters used • Include code used for data analysis (e.g., R, MatLab) • Avoid stating that data files are "available upon request" Please indicate the figures or tables for which source data files have been provided: We do not report any p-values in the manuscript. To quantify the correlations displayed in fig2d and fig2e, we calculate Pearson's r. Spearman's rho was used to quantify correlations in fig 3e.

N/A
The inferred fragment length histograms for the prostate cancer data is uploaded as supplementary table 1. For a both figure2 and figure3 we have uploaded a zip file containing the R script used to generate the figure as well as source data for the figures. We have also uploaded a zip file with scripts used in the analysis of the delfi data. Software used for other parts of analysis can be found at https://github.com/grenaud/cinch.