Fig. 1.

Directed Acyclic Graph describing the data-generating mechanism for the simulations. Signs indicate positive or negative associations. Rectangle shaped variables are image variables, dashed variables are unobserved. Tumor aggressiveness and patient fitness cannot be directly measured. $x,z$ represent biological processes, causing the outcome and image patterns. We cannot directly observe these biological processes, but $x^{\prime },z^{\prime }$ are noisy views of these variables that are measurable from the image. $x$ is a collider since it is the child of $u_1$ and $u_2$. Conditioning on $x$ will induce an artificial association between $u_1$ and $u_2$, thereby inducing a confounding path between treatment and survival, that only exists when conditioning on the collider.