Background: Causal inference based on logically consistent mathematical methods requires suitable, high-quality data and a corresponding study design. However, the question of which aspects need a design of a study to consider in order to ensure the possibility to detect cause-effect relationships remains so far unanswered. Methods: In this article, we focus on the mathematical requirements of a study design of experimental or non-experimental studies whose aim is to identify causal relationship between events. Results: A relatively new proof of the relationship between study design and the possibility of causal inference has been provided. The possible relationship between relative risk, odds ratio and causality has been worked out. Conclusion: The mathematical proof described here is of use to improve the study design of experimental and non-experimental studies.

\href{https://doi.org/10.5281/zenodo.6299686}{Zenodo} \href{https://www.causation.eu/index.php/causation/article/view/47}{Causation}