Five Facts About Influence Functions

Epidemiologists rely on statistical approaches to estimate parameters of interest, like the prevalence of exposure or the incidence of disease. Influence functions are a powerful statistical concept that may be used for the development and application of quantitative methods in epidemiology and more broadly. The influence function quantifies the impact that individual observations have on the estimator and is broadly useful for obtaining consistent variance estimators. Influence functions are relevant for many quantitative methods used by epidemiologists, providing a unifying framework to obtain variance estimates for ordinary least squares, generalized estimating equations, and inverse probability weighting. Further, they are pivotal for deriving methods such as augmented inverse probability weighted and targeted maximum likelihood estimators. Here we describe some basic facts about influence functions and detail two simple examples.