A comparison of optimization solvers for log binomial regression including conic programming

Abstract Relative risks are estimated to assess associations and effects due their ease of interpretability, e.g., in epidemiological studies. Fitting log-binomial regression models allows use the coefficients directly infer relative risks. The estimation these models, however, is complicated because constraints which have be imposed on parameter space. In this paper we systematically compare different optimization algorithms obtain maximum likelihood estimates for regression. We first establish under conditions guaranteed finite unique, identify exclude problematic cases. simulation studies using artificial data performance optimizers including solvers based augmented Lagrangian method, interior-point methods a conic optimizer, majorize-minimize algorithms, iteratively reweighted least squares expectation-maximization algorithm variants. demonstrate that emerge as preferred choice reliability, lack requirement tune hyperparameters speed.