Oncogenetic graphical models are crucial for understanding cancer progression by analyzing the accumulation of genetic events. These models are used to identify statistical dependencies and temporal order of genetic events, which helps design targeted therapies. However, existing algorithms do not account for temporal differences between samples in oncogenetic analysis. This paper introduces Timed Hazard Networks (TimedHN), a new statistical model that uses temporal differences to improve accuracy and reliability. TimedHN models the accumulation process as a continuous-Time Markov chain and includes an efficient gradient computation algorithm for optimization. Our simulation experiments demonstrate that TimedHN outperforms current state-of-The-Art graph reconstruction methods. We also compare TimedHN with existing methods on a luminal breast cancer dataset, highlighting its potential utility.
