Maximum Likelihood Estimation of the Log-Binomial Model

Maximum likelihood estimation of prevalence ratios using the log-binomial model is problematic when the estimates are on the boundary of the parameter space. When the model is correct, maximum likelihood is often the method of choice. The authors provide a theorem, formulas, and methodology for obtaining maximum likelihood estimators of the log-binomial model and their estimated standard errors when the solution is on the boundary of the parameter space. Examples are given to illustrate the method.