Individual treatment effect estimation in the presence of unobserved confounding based on a fixed relative treatment effect

In healthcare, treatment effect estimates from randomized controlled trials are often reported on a relative scale, for instance as an odds-ratio for binary outcomes. To weigh potential benefits and harms of treatment this odds-ratio has te be translated to a difference in absolute risk, preferably on an individual patient level. Under the assumption that the relative treatment effect is fixed, it is possible that treatments have widely varying effects on an absolute risk scale. We demonstrate that if this relative treatment effect is known a-priori, for example from randomized trials, it is possible to estimate the treatment effect on an absolute scale on an individualized basis, even in the presence of unobserved confounding. We use this assumption both on a standard logistic regression task and on a task with real-world medical images with simulated outcome data, using convolutional neural networks. On both tasks the method performs well.