Estimation of the correlation coefficient using the Bayesian approach and its applications for epidemiologic research

Background: The Bayesian approach is one alternative for estimating correlation coefficients in which knowledge from previous studies is incorporated to improve estimation. The purpose of this paper is to illustrate the utility of the Bayesian approach for estimating correlations using prior knowledge. Methods: The use of the hyperbolic tangent transformation (ρ = tanh ζ and r = tanh z) enables the investigator to take advantage of the conjugate properties of the normal distribution, which are expressed by combining correlation coefficients from different studies. Conclusions: One of the strengths of the proposed method is that the calculations are simple but the accuracy is maintained. Like meta-analysis, it can be seen as a method to combine different correlations from different studies.