Bayesian approach to estimate 'Relative Excess Risk Due to Interaction'

This repository contains codes to fit Relative Excess Risk Due to Interaction estimated using Odds ratios as suggested by David B. Richardson, Jay S. Kaufman,American Journal of Epidemiology,2010. Haitao Chu, Stephen R Cole proposed Bayesian approach to the model for two binary exposures.

Briefly the model is, $$odds_{i} = exp(\alpha)*(1+\beta_{1}*x_{1,i} + \beta_{2}*x_{2,i} + \beta_{3}*x_{1,i}*x_{2,i})$$
$$P(y_{i} = 1) = \frac{odds_{i}}{1+odds_{i}}$$

With the following constrains on parameters $$ \beta_{1} , \beta_{2} >= -1 $$
$$ \beta_{3} >= -(1+\beta_{1} + \beta_{2})$$