Bayesian Estimation of Relative Risk in Biomedical Research

The relative risk is an important parameter in certain epidemiological studies. It is given by the ratio of the rates of developing a certain disease between the exposed and the control group. This paper deals with the Bayesian estimation of the relative risk using: (a) uniform [0,1] priors; (b) restricted uniform priors; (c) beta priors. The appropriateness of such priors is discussed in the medical setting and analytical expressions are obtained for the distributions of the relative risk in the above three cases. Data taken from the Air Force Health study are analysed and 95 per cent confidence limits are presented for the three types of priors. Finally, for the Bayesian intervals, the estimated probabilities that the relative risk is greater than 1 are exhibited.