Fig. 1

Cohort A data and feature extraction. a Fragment length distributions of cfDNA from 41 patient samples grouped by tumour content estimated from panel-sequencing data. Per group, the median profile is shown banded by the interquartile range, with the y-axis on a logarithmic scale. b Residuals of second-degree polynomial regression models fitted in the range 81–141 bp. The discrete Fourier transform was applied to each set of residuals. c The Daubechies wavelet filter was used to extract features in a data-driven fashion across the full range of 81–336 bp. d Biplot of PCA based on the features chosen separately by stability selection (based on cohort B, not shown). Variable loadings are illustrated by green arrows with purple labels where ‘Wx_y’ denotes the wavelet coefficient on scale x at location y, and ‘Fz’ refers to the absolute value of the zth Fourier coefficient. e Coefficient paths of beta boosting applied to the selected features. The dotted vertical line indicates the optimal number of iterations, as determined by cross-validation