In a randomized, controlled trial, a ctDNA-guided approach to the postsurgical treatment of stage II colon cancer reduced adjuvant chemotherapy use without compromising recurrence-free survival.
Determining the etiologic basis of the mutations that are responsible for cancer is one of the fundamental challenges in modern cancer research. Different mutational processes induce different types ...of DNA mutations, providing 'mutational signatures' that have led to key insights into cancer etiology. The most widely used signatures for assessing genomic data are based on unsupervised patterns that are then retrospectively correlated with certain features of cancer. We show here that supervised machine-learning techniques can identify signatures, called SuperSigs, that are more predictive than those currently available. Surprisingly, we found that aging yields different SuperSigs in different tissues, and the same is true for environmental exposures. We were able to discover SuperSigs associated with obesity, the most important lifestyle factor contributing to cancer in Western populations.
The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a ...stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations.
Cancer treatments are often more successful when the disease is detected early. We evaluated the feasibility and safety of multicancer blood testing coupled with positron emission tomography-computed ...tomography (PET-CT) imaging to detect cancer in a prospective, interventional study of 10,006 women not previously known to have cancer. Positive blood tests were independently confirmed by a diagnostic PET-CT, which also localized the cancer. Twenty-six cancers were detected by blood testing. Of these, 15 underwent PET-CT imaging and nine (60%) were surgically excised. Twenty-four additional cancers were detected by standard-of-care screening and 46 by neither approach. One percent of participants underwent PET-CT imaging based on false-positive blood tests, and 0.22% underwent a futile invasive diagnostic procedure. These data demonstrate that multicancer blood testing combined with PET-CT can be safely incorporated into routine clinical care, in some cases leading to surgery with intent to cure.
Learning nonparametric systems of Ordinary Differential Equations (ODEs) x˙=f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel ...Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator. Experiments are provided for the FitzHugh–Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art.
Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot x = f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel ...Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator and provide experimental comparisons with the state-of-the-art.
Learning a nonparametric system of ordinary differential equations (ODEs) from \(n\) trajectory snapshots in a \(d\)-dimensional state space requires learning \(d\) functions of \(d\) variables. ...Explicit formulations scale quadratically in \(d\) unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach to learning using the implicit formulation provided by vector-valued Reproducing Kernel Hilbert Spaces. By rewriting the ODEs in a weaker integral form, which we subsequently minimize, we derive our learning algorithm. The minimization problem's solution for the vector field relies on multivariate occupation kernel functions associated with the solution trajectories. We validate our approach through experiments on highly nonlinear simulated and real data, where \(d\) may exceed 100. We further demonstrate the versatility of the proposed method by learning a nonparametric first order quasilinear partial differential equation.
Cancer is driven by the sequential accumulation of genetic and epigenetic changes in oncogenes and tumor suppressor genes. The timing of these events is not well understood. Moreover, it is currently ...unknown why the same driver gene change appears as an early event in some cancer types and as a later event, or not at all, in others. These questions have become even more topical with the recent progress brought by genome-wide sequencing studies of cancer. Focusing on mutational events, we provide a mathematical model of the full process of tumor evolution that includes different types of fitness advantages for driver genes and carrying-capacity considerations. The model is able to recapitulate a substantial proportion of the observed cancer incidence in several cancer types (colorectal, pancreatic, and leukemia) and inherited conditions (Lynch and familial adenomatous polyposis), by changing only 2 tissue-specific parameters: the number of stem cells in a tissue and its cell division frequency. The model sheds light on the evolutionary dynamics of cancer by suggesting a generalized early onset of tumorigenesis followed by slow mutational waves, in contrast to previous conclusions. Formulas and estimates are provided for the fitness increases induced by driver mutations, often much larger than previously described, and highly tissue dependent. Our results suggest a mechanistic explanation for why the selective fitness advantage introduced by specific driver genes is tissue dependent.
108 Background: Previous results of the DYNAMIC study demonstrated that a ctDNA-guided approach versus standard management in stage II colon cancer (CC) reduced adjuvant chemotherapy (ACT) use ...without compromising 2-year recurrence-free survival (RFS). MMR status defines two distinct subsets of stage II CC. Here, we report the impact of ctDNA burden, end of ACT (EOT) ctDNA, and updated survival data including overall survival (OS). Methods: DYNAMIC is a multi-center randomized phase II trial. Eligible patients (pts) had resected stage II CC and were suitable for ACT. Pts were randomly assigned 2:1 to ctDNA-guided management or standard management (clinician-guided based on conventional criteria). For ctDNA-guided management, a ctDNA-positive result at 4 or 7 weeks after surgery with a tumor-informed assay prompted oxaliplatin-based or fluoropyrimidine ACT; ctDNA-negative pts were not treated. Between Aug 2015 and Aug 2019, 302 received ctDNA-guided and 153 standard management. The primary endpoint was RFS, with a non-inferiority margin of 8.5%. Pre-specified key secondary endpoints were ACT use and OS, with an additional secondary endpoint of ctDNA clearance rate. Results: With a median follow-up of 59.6 months (IQR 55.0–61.5), 5-year RFS were 88% and 87% with ctDNA-guided and standard management, respectively (difference 1.1%, 95% confidence interval, -5.8% to 8.0%). 5-year OS for ctDNA-guided treatment was 93.8% and standard management 93.3% (HR 1.05; 95% CI, 0.47 to 2.37; P = 0.887). 5-year OS was significantly worse in treated ctDNA-positive versus untreated ctDNA-negative pts (85.6% vs 95.3%, HR 3.30; 95% CI, 1.02 to 9.05; P = 0.014). The 5-year OS for ctDNA-negative T3 and T4 disease were 96.0% and 90.6%, respectively (HR 2.45; 95% CI, 0.65 to 9.25; P = 0.171). For treated ctDNA-positive pts, ctDNA clearance was observed at EOT in 35/40 (87.5%). The 5-year RFS for EOT ctDNA clearance vs ctDNA persistence were 85.2% and 20.0%, respectively (HR 15.4; 95% CI, 3.91 to 61.0; P < 0.001). Pts with ≥ 0.38 (the median) mutant tumor molecules (MTM/mL) had a lower ctDNA clearance rate and worse RFS than pts with < 0.38 MTM/mL (ctDNA clearance 75% vs 100%, P = 0.047; 5-year RFS 58.9% vs 95.2%, HR 10.62, P = 0.005). Post-op ctDNA was detected in 5/59 (8.5%) of dMMR and 40/235 (17%) of pMMR cases. In an exploratory analysis, ctDNA clearance was observed in 3/4 (75%) and 32/36 (89%) of dMMR and pMMR cases, respectively. Conclusions: Mature outcome data confirms the previous finding of non-inferiority of RFS with a ctDNA-guided approach to ACT for stage II CC. For ctDNA-positive pts, the post-surgery mutation burden provides additional prognostic information, as does the EOT ctDNA result. Additional data is needed to define any differential impact of ACT by MMR status. This data supports a role for ctDNA analysis, including serial sampling, in the management of stage II CC. Clinical trial information: ACTRN12615000381583 .
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