Statistical Inference for Functionals in Epidemiology using the Delta Method and Influence Functions: An Applied and Reproducible Tutorial
Author
Miguel Angel Luque-Fernandez
This repository introduces the use of the functional delta-method and its link to the Influence Curve (IC) in Epidemiology from a practical perspective including boxes with code in R statistical software (R Foundation for Statistical Computing, Vienna, Austria) allowing readers learning by doing. We provide reproducible R-code to derive the 95% confidence intervals for the most common epidemiological measures of association using the Delta Method in an Rmarkdown document. In section two we introduce some basic notation for the delta-method and derive the SE for a multivariable sample mean. In section three we derive the SE for the classical epidemiological measures of association. In section four we introduce an empirical example to derive the SE for a single proportion, the conditional odds ratio and relative risk, and finally a marginal causal risk ratio estimated using the augmented inverse probability of treatment weights estimator. Then, in section five we contrast the functional delta-method with the bootstrap approach and finish the article in section five with some applied conclusions.
We invite readers to fork and clone our repository and use it for taeching purposes (master students in epidemiology). Furthermore, readers can practice the use of GitHub as a collaborative tool for reproducible science (http://migariane.github.io/DeltaMethodEpiTutorial.nb.html).
Keywords:
Epidemiology, Computing, Delta Method, Causal Inference, Reproducible Science
Please cite this repository as follows:
Miguel Angel Luque-Fernandez (2019). Educational Note: Statistical Inference for Functionals in Epidemiology using the Delta Method and Influence Functions: An Applied and Reproducible Tutorial. GitHub Repository: http://migariane.github.io/DeltaMethodEpiTutorial.nb.html
Acknowledgment: Miguel Angel Luque Fernandez is supported by the Spanish National Institute of Health, Carlos III Miguel Servet I Investigator Award (CP17/00206).