[Paper Review] Bivariate deconvolution for cancer detection after surgery

Nuria Senar, Stavros Makrodimitris+4 more|arXiv (Cornell University)|Mar 18, 2026

Cancer Genomics and Diagnostics0 citations

TL;DR

Introduces a bivariate deconvolution model to estimate post-surgery tumor fractions from cfDNA methylation, linking pre- and post-surgery measurements to improve minimal residual disease detection.

ABSTRACT

Detection of minimal residual disease (MRD) in cancer patients after surgery can provide an early marker for disease recurrence and guide subsequent treatment decisions. Accurate and sensitive estimation of tumour burden after cancer surgery may be obtained through liq- uid biopsies, measuring circulating tumour DNA (ctDNA) using, for example, mutation-based Variant Allele Frequency (VAF) values. However, to be applicable to all patients this ei- ther requires tumour-informed, patient-specific mutation panels or sensitive, tumour-agnostic genome-wide measurements. We propose a solution that accounts for patient-specific charac- teristics in genome-wide screens. For that, we introduce a bivariate deconvolution model to estimate tumour proportion from circulating cell-free DNA (cfDNA) methylation profiles of patients before and after surgery. The observations are modelled as a convolution of two bivariate latent variables, corresponding to tumour and background signals, mixed by the tumour proportion at each measurement. This bivariate approach links pre- and post-surgery measurements improving estimation of the tumour proportion after surgery, when the tumour signal is potentially very weak, or absent. We approximate likelihood of the convolution through a discretisation of the bivariate density for each latent variable into a two-dimensional grid for each pair of observations which allows for fast maximum likelihood estimation. We evaluate the predictive performance of the estimated post-surgery tumour proportions based on cfDNA methylation against available mutation-based VAF values in one-year recurrence-free survival.

Motivation & Objective

• Motivate the need for sensitive MRD detection after curative cancer surgery.
• Develop a bivariate deconvolution framework that jointly models pre- and post-surgery cfDNA methylation signals.
• Estimate patient-specific tumor fractions using a maximum likelihood approach with fast discrete convolution.

Proposed method

• Model observations as a convolution of two latent components (tumor and background) weighted by patient-specific tumor fractions.
• Assume bivariate log-normal distributions for tumor and background components with a feature-wise correlation parameter.
• Discretize the bivariate density into a 2D grid for fast likelihood evaluation and perform a three-step block coordinate ascent optimization.
• Use pre- and post-surgery measurements to inform post-surgery tumor fraction estimation and link to outcomes.
• Initialise parameters using tumour tissue and healthy cfDNA methylation profiles and enforce identifiability constraints pi^0_i > pi^1_i.

Figure 1 : Example of discretisation for $y^{1}=40$ and $y^{0}=30$ with $m=8$ bins. The midpoints of $C_{r}^{0}(C_{s}^{1})$ are represented by centred dots in each cell. For the left grid, the first row ( $r=1$ ) and column ( $s=1$ ) represent the intervals for which values of $\tilde{{T}}^{0}$ and

Experimental results

Research questions

• RQ1 Can a bivariate deconvolution model improve estimation of post-surgery tumor fractions from cfDNA methylation signals?
• RQ2 How does incorporating pre-surgery information and feature-wise correlations affect residual disease detection and its association with recurrence-free survival?
• RQ3 How does the bivariate approach compare to univariate deconvolution and mutation-based VAF in predicting one-year outcomes?
• RQ4 Is the method robust to initialization and to potential lack of correlation between measurements?

Key findings

• Simulation studies show the bivariate model yields more accurate post-surgery tumor fractions than the univariate version, particularly when signal is weak.
• Including feature-wise correlation parameters improves post-surgery tumor fraction estimation and its association with true tumor proportions.
• On real CRLM MeD-seq data (112 patients), post-surgery methylation-based tumor fractions significantly separated relapsed vs. non-relapsed groups and outperformed VAF-based post-surgery fractions in predicting one-year recurrence-free survival.
• Logistic regression and ROC analyses indicate the bivariate tumor fraction is a stronger predictor of relapse than the VAF-based measure.
• The approach remains robust when measurements are uncorrelated, showing no loss of power under that scenario.

Figure 2 : $\hat{\boldsymbol{\pi}}^{1}_{\text{VAF}}$ and $\hat{\boldsymbol{\pi}}^{1}$ .