Bivariate deconvolution for cancer detection after surgery

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.

Figures (12)

• 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 $\tilde{{T}}^1$ are very small. The density displayed in cell $C_4^0(C_1^1)$ is the marginal density for $\tilde{{T}}^0$ and illustrates a case for which the midpoint approximation is likely inaccurate.. The shaded and striped cells belong to the same pair of proposals of $({\tilde{T}}, {\tilde{B}})$.
• Figure 2: $\hat{\boldsymbol{\pi}}^1_{\text{VAF}}$ and $\hat{\boldsymbol{\pi}}^1$.
• Figure 3: Kaplan-Meier curves for OS, in days.
• Figure A.1: Evaluation of small values of the weighted latent component with $p_{({\pi}, {\theta})}(\tilde{T}^{0} \in C^1_r, \tilde{T}^{1} \in C^0_s)$, where the numbers refer to the numbered elements in equation \ref{['eq:cumulative']}. Figure \ref{['fig:cuma']} represents the general example for computing equation \ref{['eq:cumulative']}. Figure \ref{['fig:cumb']} does the same for our case, where we only check the first row and columns of the grid ($s=1$), leaving elements $3$ and $4$ in equation \ref{['eq:cumulative']} equal to zero.
• Figure B.1: Distribution of simulation means, standard deviations and tumour proportions.