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Communication

Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio

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Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj, Romania
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Chemical Doctoral School, Babes-Bolyai University, 400028 Cluj-Napoca, Romania
Academic Editors: Sorana D. Bolboacă, Polychronis Kostoulas and David Carfì
Mathematics 2021, 9(19), 2506; https://doi.org/10.3390/math9192506
Received: 22 July 2021 / Revised: 29 September 2021 / Accepted: 4 October 2021 / Published: 7 October 2021
(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)
Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent could be what killed a patient. Sampling is usually done from a finite and discrete population and it follows a Bernoulli trial, leading to a contingency of two binomially distributed samples (better known as 2×2 contingency table). Current guidelines recommend reporting relative measures of association (such as the relative risk and odds ratio) in conjunction with absolute measures of association (which include risk difference or excess risk). Because the distribution is discrete, the evaluation of the exact confidence interval for either of those measures of association is a mathematical challenge. Some alternate scenarios were analyzed (continuous vs. discrete; hypergeometric vs. binomial), and in the main case—bivariate binomial experiment—a strategy for providing exact p-values and confidence intervals is proposed. Algorithms implementing the strategy are given. View Full-Text
Keywords: binomial distribution; confidence interval; contingency table; binomial proportion; excess ratio; odds ratio; relative risk binomial distribution; confidence interval; contingency table; binomial proportion; excess ratio; odds ratio; relative risk
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MDPI and ACS Style

Jäntschi, L. Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio. Mathematics 2021, 9, 2506. https://doi.org/10.3390/math9192506

AMA Style

Jäntschi L. Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio. Mathematics. 2021; 9(19):2506. https://doi.org/10.3390/math9192506

Chicago/Turabian Style

Jäntschi, Lorentz. 2021. "Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio" Mathematics 9, no. 19: 2506. https://doi.org/10.3390/math9192506

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