  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.
