AbstractID: 6905 Title: A Bayesian approach to the problem of calculating the confidence limits of the
probability of success in animal experiments and clinical studies
Experiments in which outcomes of only two types can be observed are subject to
binomial statistics. Clinical studies and animal experiments in which the treatment results
are classified just as positive (success) or negative (failure) outcomes are typical
examples of such experiments. In these studies, the unknown parameter is the probability
of success, p.
In this paper a bayesian approach is proposed to the problem of defining and calculating
the confidence limits of p. The bayesian method is based on the construction of a
distribution function of p depending on the observed number of successes, k and number
of trials, n. An analytical expression of the distribution function is presented. On its basis
the most probable value of p together with its mean, variance and confidence limits are
calculated applying the usual definitions of these characteristics of a random variable
with a known distribution. A comparison with the confidence limits values calculated
using the normal approximation to the binomial distribution is done. A perfect
convergence is shown to exist in the range of validity of the normal approximation. At
the same time the commonly used confidence limits formulae show no convergence to
the normal approximation values. The bayesian method works for any number of trials
(large and small) and all possible values of number of successes, including k=0 and k=n,
providing exact formulae for the calculation of the confidence limits in all cases. A
Matlab code for the calculation of the confidence limits according to the proposed
method is provided.