A Primer on Large-Sample Statistical Inference for Epidemiologists

Statistical theory forms a foundation for how epidemiologists learn about populations in public health and medical studies and is fundamental for the understanding of more advanced epidemiological methods (e.g., in causal inference and machine learning). Textbooks provide in-depth coverage of probability and statistical theory, but with such comprehensive coverage that it can be easy to miss the forest for the trees. Here, we provide a summary of fundamental concepts from large-sample statistical theory to allow for more focused understanding tailored to epidemiologists and health science researchers. This primer aims to promote appropriate understanding and application of statistical methods in epidemiologic research. We clarify several often-confused statistical topics and provide a motivation for the application of large-sample inferential methods to data from population health and medical studies. Assumptions underlying commonly used statistical methods that must be considered for valid inference are also discussed. These ideas are contextualized with an example from the Women's Interagency HIV Study.