Am J Epidemiol. 2014 Jan 15;179(2):252-60. doi: 10.1093/aje/kwt245. Epub 2013 Oct 29.
The method of maximum likelihood is widely used in epidemiology, yet many epidemiologists receive little or no education in the conceptual underpinnings of the approach. Here we provide a primer on maximum likelihood and some important extensions which have proven useful in epidemiologic research, and which reveal connections between maximum likelihood and Bayesian methods. For a given data set and probability model, maximum likelihood finds values of the model parameters that give the observed data the highest probability. As with all inferential statistical methods, maximum likelihood is based on an assumed model and cannot account for bias sources that are not controlled by the model or the study design. Maximum likelihood is nonetheless popular, because it is computationally straightforward and intuitive and because maximum likelihood estimators have desirable large-sample properties in the (largely fictitious) case in which the model has been correctly specified. Here, we work through an example to illustrate the mechanics of maximum likelihood estimation and indicate how improvements can be made easily with commercial software. We then describe recent extensions and generalizations which are better suited to observational health research and which should arguably replace standard maximum likelihood as the default method.
最大似然法在流行病学中被广泛应用，但许多流行病学家在该方法的概念基础方面接受的教育很少或根本没有。在这里，我们提供了一个关于最大似然法的入门读物，以及一些在流行病学研究中已被证明有用的重要扩展，这些扩展揭示了最大似然法和贝叶斯方法之间的联系。对于给定的数据集和概率模型，最大似然法找到使观察到的数据具有最高概率的模型参数值。与所有推理统计方法一样，最大似然法基于一个假设的模型，并且不能解释模型或研究设计未控制的偏倚源。尽管如此，最大似然法还是很受欢迎，因为它在计算上简单直观，并且在（主要是虚构的）模型正确指定的情况下，最大似然估计具有理想的大样本性质。在这里，我们通过一个例子来说明最大似然估计的力学，并指出如何通过商业软件轻松地进行改进。然后，我们描述了最近的扩展和推广，这些扩展更适合观察性健康研究，并且应该可以取代标准的最大似然法作为默认方法。
