Modeling metastatic progression from cross-sectional cancer genomics data.

MOTIVATION: Metastasis formation is a hallmark of cancer lethality. Yet, metastases are generally unobservable during their early stages of dissemination and spread to distant organs. Genomic datasets of matched primary tumors and metastases may offer insights into the underpinnings and the dynamics of metastasis formation. RESULTS: We present metMHN, a cancer progression model designed to deduce the joint progression of primary tumors and metastases using cross-sectional cancer genomics data. The model elucidates the statistical dependencies among genomic events, the formation of metastasis, and the clinical emergence of both primary tumors and their metastatic counterparts. metMHN enables the chronological reconstruction of mutational sequences and facilitates estimation of the timing of metastatic seeding. In a study of nearly 5000 lung adenocarcinomas, metMHN pinpointed TP53 and EGFR as mediators of metastasis formation. Furthermore, the study revealed that post-seeding adaptation is predominantly influenced by frequent copy number alterations. AVAILABILITY AND IMPLEMENTATION: All datasets and code are available on GitHub at https://github.com/cbg-ethz/metMHN.

Low-rank tensor methods for Markov chains with applications to tumor progression models.

Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The age of a tumor at diagnosis is typically unknown. Therefore, the quantity of interest is the time-marginal distribution over all possible genotypes of tumors, defined as the transient distribution integrated over an exponentially distributed observation time. It can be obtained as the solution of a large linear system. However, the sheer size of this system renders classical solvers infeasible. We consider Markov chains whose transition rates are separable functions, allowing for an efficient low-rank tensor representation of the linear system's operator. Thus we can reduce the computational complexity from exponential to linear. We derive a convergent iterative method using low-rank formats whose result satisfies the normalization constraint of a distribution. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.

Correcting for Observation Bias in Cancer Progression Modeling.

Tumor progression is driven by the accumulation of genetic alterations, including both point mutations and copy number changes. Understanding the temporal sequence of these events is crucial for comprehending the disease but is not directly discernible from cross-sectional genomic data. Cancer progression models, including Mutual Hazard Networks (MHNs), aim to reconstruct the dynamics of tumor progression by learning the causal interactions between genetic events based on their co-occurrence patterns in cross-sectional data. Here, we highlight a commonly overlooked bias in cross-sectional datasets that can distort progression modeling. Tumors become clinically detectable when they cause symptoms or are identified through imaging or tests. Detection factors, such as size, inflammation (fever, fatigue), and elevated biochemical markers, are influenced by genomic alterations. Ignoring these effects leads to "conditioning on a collider" bias, where events making the tumor more observable appear anticorrelated, creating false suppressive effects or masking promoting effects among genetic events. We enhance MHNs by incorporating the effects of genetic progression events on the inclusion of a tumor in a dataset, thus correcting for collider bias. We derive an efficient tensor formula for the likelihood function and apply it to two datasets from the MSK-IMPACT study. In colon adenocarcinoma, we observe a significantly higher rate of clinical detection for TP53-positive tumors, while in lung adenocarcinoma, the same is true for EGFR-positive tumors. Compared to classical MHNs, this approach eliminates several spurious suppressive interactions and uncovers multiple promoting effects.