Confidence limits of the probability of success in animal experiments and clinical studies: A Bayesian approach

Abstract 

Purpose

To determine from the number of trials, n, and the number of observed successes, k the most probable value, the variance and the confidence limits of the probability of success, p, in animal experiments and clinical studies subject to binomial statistics.

Method

In such experiments the probability of success is an unknown parameter. The Bayesian approach to the problem is advocated, based on constructed distribution of the probability of success.

Results

A simple Matlab code for the calculation of the confidence limits according to the proposed method is provided. The most probable, the mean, the variance and the confidence limits are calculated applying the usual definitions of these characteristics.

Conclusion

The proposed method works for any number of trials – large and small and all possible values of the number of successes, including k=0 and k=n, providing exact formulae for the calculation of the confidence limits in all cases.

Keywords: Binomial confidence limits, Binary data