Bayesian Estimation of Relative Risk in Biomedical Research

Abstract

SUMMARYThe 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 con®dence 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.

An Empirical Bayes Method for Multivariate Meta-analysis with an Application in Clinical Trials

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Harmonisation Of Transmissible disease Interpretation in the EU (HOTLINE)

“…Depending on the sampling designs for the various sources, the estimations of risk ratios may be performed directly from the collected data (e.g. through a logistic regression), or using various indirect methods, including the use of a Bayesian approach (Gupta et al, 1997;Hora and Kelley 1983;Bobb et al, 2011).…”

Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables

“…Hashemi, Nandrum, and Goldberg (1997) and Nurminen and Mutanen (1987) gave integral expressions for these posterior distributions. Equivalent expressions using finite sums were provided by Latorre (1982) for the odds ratio, Hora and Kelley (1983) for the odds ratio and relative risk, Weisberg (1972), Aitchison and Bacon‐Shone (1981), and Gupta et al (1997) for the relative risk (the latter authors also used uniform priors over restricted ranges), and Pham‐Gia and Turkkan (1993) for the difference of proportions (see also Walters, 1986 for uniform priors). It is relatively simple to evaluate numerically these posterior distributions.…”