Some results for maximum likelihood estimation of adjusted relative risks

Maximum likelihood (ML) estimation of relative risks via log-binomial regression requires a restricted parameter space. Computation via non linear programming is simple to implement and has high convergence rate. We show that the optimization problem is well posed (convex domain and convex objective) and provide a variance formula along with a methodology for obtaining standard errors and prediction intervals which account for estimates on the boundary of the parameter space. We performed simulations under several scenarios already used in the literature in order to assess the performance of ML and of two other common estimation methods.