The relative risk and odds ratios under classical statistics are applied under the assumption that all the observations in the data are certain and fail to respond when the data has some sort of vagueness, uncertainty, or indeterminacy, also called neutrosophic numbers. Neutrosophic numbers, the one form of fuzzy sets, contain incomplete, indeterminate and inconsistent information. Neutrosophic statistics is the generalization of classical statistics and can be      applied to the indeterminate, ambiguous or inexact observations in the population or sample data. In this paper, we propose the relative risk and odds ratios under the uncertainty environment, called neutrosophic relative risk and neutrosophic odds ratio. The proposed forms of relative risk and odds ratio are applied to two real data set examples taken from the medical sciences and found that the use of the proposed statistical measures provides better estimates under indeterminacy. The proposed methods will be more suitable to be  used in the fields of epidemiology and biostatistics. We present the relative risk and odds ratios under the uncertainty environment, called neutrosophic relative risk (NRR) and neutrosophic odds ratio (NOR). Therefore, the proposed NRR and NOR are the extensions of existing RR and OR and can be applied under an uncertain and indeterminate environment.

relative risk, odds ratio, fuzzy theory, neutrosophic statistics.

Received: December 21, 2023; Revised: October 11, 2024; Accepted: October 23, 2024; Published: November 7, 2024

How to cite this article: Rehan Ahmad Khan Sherwani, Wajiha Batool Awan, Maham Faheem, Azhar Ali Janjua, Mohammed Albassam and Muhammad Aslam, An application of neutrosophic statistics: extending relative risk and odds ratios to handle uncertainty in epidemiology and biostatistics, JP Journal of Biostatistics 25(1) (2025), 1-15. https://doi.org/10.17654/0973514325001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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