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

估计相对风险以评估关联和影响，因为它们易于解释，例如在流行病学研究中。拟合对数二项式回归模型允许使用估计的回归系数来直接推断相对风险。然而，由于必须对参数空间施加约束，这些模型的估计很复杂。在本文中，我们系统地比较了不同的优化算法，以获得对数二项式回归中回归系数的最大似然估计。我们首先确定在哪些条件下最大似然估计保证是有限和唯一的，这允许识别和排除有问题的情况。在使用人工数据的模拟研究中，我们比较了不同优化器的性能，包括基于增广拉格朗日方法的求解器、包括圆锥优化器在内的内点方法、主要化-最小化算法、迭代重新加权最小二乘法和期望最大化算法变体。我们证明了圆锥优化器因其可靠性、不需要调整超参数和速度而成为首选。