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# A Causally Formulated Hazard Ratio Estimation through Backdoor Adjustment on Structural Causal Model

*Proceedings of the 5th Machine Learning for Healthcare Conference*, PMLR 126:376-396, 2020.

#### Abstract

Identifying causal relationships for a treatment intervention is a fundamental problem in health sciences. Randomized controlled trials (RCTs) are considered the gold standard for identifying causal relationships. However, recent advancements in the theory of causal inference based on the foundations of structural causal models (SCMs) have allowed the identification of causal relationships from observational data, under certain assumptions. Survival analysis provides standard measures, such as the hazard ratio, to quantify the effects of an intervention. While hazard ratios are widely used in clinical and epidemiological studies for RCTs, a principled approach does not exist to compute hazard ratios for observational studies with SCMs. In this work, we review existing approaches to compute hazard ratios as well as their causal interpretation, if it exists. We also propose a novel approach to compute hazard ratios from observational studies using backdoor adjustment through SCMs and do-calculus. Finally, we evaluate the approach using experimental data for Ewing’s sarcoma.