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Relative risk regression using a log-link binomial generalized linear model (GLM) is an important tool for the analysis of binary outcomes. However, Fisher scoring, which is the standard method for fitting GLMs in statistical software, may have difficulties in converging to the maximum likelihood estimate due to implicit parameter constraints. logbin is an R package that implements several algorithms for fitting relative risk regression models, allowing stable maximum likelihood estimation while ensuring the required parameter constraints are obeyed. We describe the logbin package and examine its stability and speed for different computational algorithms. We also describe how the package may be used to include flexible semi-parametric terms in relative risk regression models.