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

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 2x2 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.

Automated summary

Medical studies often compare two outcomes from samples, with the importance placed on the probability and confidence in the findings. Current guidelines recommend reporting both relative and absolute measures of association, but the exact confidence interval for these measures poses a mathematical challenge due to the discrete distribution. In order to address this issue, algorithms implementing a strategy for providing exact p-values and confidence intervals have been proposed.