Overcoming Observation Bias for Cancer Progression Modeling

Abstract

Cancers evolve by accumulating genetic alterations, such as mutations and copy number changes. The chronological order of these events is important for understanding the disease, but not directly observable from cross-sectional genomic data. Cancer progression models (CPMs), such as Mutual Hazard Networks (MHNs), reconstruct the progression dynamics of tumors by learning a network of causal interactions between genetic events from their co-occurrence patterns. However, current CPMs fail to include effects of genetic events on the observation of the tumor itself and assume that observation occurs independently of all genetic events. Since a dataset contains by definition only tumors at their moment of observation, neglecting any causal effects on this event leads to the “conditioning on a collider” bias: Events that make the tumor more likely to be observed appear anti-correlated, which results in spurious suppressive effects or masks promoting effects among genetic events. Here, we extend MHNs by modeling effects from genetic progression events on the observation event, thereby correcting for the collider bias. We derive an efficient tensor formula for the likelihood function and learn two models on somatic mutation datasets from the MSK-IMPACT study. In colon adenocarcinoma, we find a strong effect on observation by mutations in TP53, and in lung adenocarcinoma by mutations in EGFR. Compared to classical MHNs, this explains away many spurious suppressive interactions and uncovers several promoting effects.The data, code, and results are available athttps://github.com/cbg-ethz/ObservationMHN.

Modeling metastatic progression from cross-sectional cancer genomics data

“…metMHN extends the Mutual Hazard Network (MHN) framework, originally introduced by Schill et al in 2020 [33] and further developed by Schill et al in 2023 [34], which models the progression of primary tumors. We first establish the notation employed by MHNs and then introduce metMHN.…”

“…Therefore the rate of observation should be dependent on the state of the tumor. In [34], the observation of a tumor was introduced as a separate event with its own set of parameters . The observation of a state x happens at a rate , where Ω j is a multiplicative effect of the presence of event j on the rate of observation.…”

“…States where the observation occurred are thus absorbing states of the Markov chain. Then the probability distribution at observation is equal to the stationary distribution p ( ∞ ) and given by with and Q and p (0) defined as in Equation (3) [34].…”

“…We are interested in the distribution of the full system at the time of first observation, which can be triggered by either primary tumor or metastasis. We calculate this analogously to [34] as the stationary distribution on the extended state space 𝒮 D where each of the observation events halts the progression of the entire system. Each state where either observation occurred becomes an absorbing state.…”

“…Following [34] we model the observation of tumors explicitly as events. Since we model two tumors that at some point evolve independently and can also be observed separately, we have to include two distinct observation events.…”