Deep learning has shown remarkable results for image analysis and is expected to aid individual treatment decisions in health care. Treatment recommendations are predictions with an inherently causal interpretation. To use deep learning for these applications in the setting of observational data, deep learning methods must be made compatible with the required causal assumptions. We present a scenario with real-world medical images (CT-scans of lung cancer) and simulated outcome data. Through the data simulation scheme, the images contain two distinct factors of variation that are associated with survival, but represent a collider (tumor size) and a prognostic factor (tumor heterogeneity), respectively. When a deep network would use all the information available in the image to predict survival, it would condition on the collider and thereby introduce bias in the estimation of the treatment effect. We show that when this collider can be quantified, unbiased individual prognosis predictions are attainable with deep learning. This is achieved by (1) setting a dual task for the network to predict both the outcome and the collider and (2) enforcing a form of linear independence of the activation distributions of the last layer. Our method provides an example of combining deep learning and structural causal models to achieve unbiased individual prognosis predictions. Extensions of machine learning methods for applications to causal questions are required to attain the long-standing goal of personalized medicine supported by artificial intelligence.
