A |
Modeling |
A1 |
Rudiments of causal analysis: motivating examples from analysis of vaccine efficacy trials and HIV prevention. Rudiments of causal analysis based on directed acyclic graphs |
A2 |
The parameter of interest: Introducing the parameter of interest, motivated by a causal quantity (the causal effect of a two-level treatment). Viewing the parameter of interest as the value of a functional defined on the statistical model at the law of the data. |
A3 |
Regularity: Discussing the regularity/smoothness of the above functional, based on the notion of fluctuation (merely, a finite-dimensional model through a given law). |
A4 |
Double-robustness: Discussing a remarkable property that the functional enjoys and that we fully exploit. Defining the so-called remainder term. |
B |
Inference |
B1 |
A simple inferential strategy: Introducing and discussing the Inverse-Probability of Treatment Weighting (IPTW) estimator. |
B2 |
Nuisance parameters: An algorithmic stance on the estimation of nuisance parameters that one must carry out to infer the parameter of interest. Why machine learning? How? Formalizing and applying machine learning, through the use of SuperLearner and caret R packages. |
B3 |
Two naive plug-in estimators: More on the IPTW estimator, and introducing and discussing the so-called G-COMP estimator. |
B4 |
Standard analysis of plug-in estimators |
B5 |
One-step correction: introduction and discussing the one-step correction principle (Le Cam 56, Pfanzagl 82). |
B6 |
Targeted minimum loss estimation: introducing and discussing the targeted minimum loss estimation methodology. |
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