Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation

Area of Science:

• Statistics
• Causal Inference
• Epidemiology

Background:

• Doubly robust estimation methods are increasingly used in applied research.
• Misconceptions exist regarding the automatic doubly robust nature of combined propensity score and outcome modeling.
• Complex doubly robust estimators are sometimes misused.

Purpose of the Study:

• To introduce and explain the Inverse Probability of Treatment (Propensity Score) Weighted Generalized Linear Model (IPTW GLM) as a simple, doubly robust estimation method.
• To clarify why the IPTW GLM possesses the doubly robust property.
• To correct the misconception that combining propensity score weighting and outcome modeling guarantees a doubly robust estimator.

Main Methods:

• Utilizing canonical link generalized linear models (GLM).
• Fitting models via inverse probability of treatment (propensity score) weighted maximum likelihood estimation.
• Employing standardization (the Robins-Greenland-Robins formula) for average causal effect estimation.

Main Results:

• The IPTW GLM method is demonstrated to be a valid doubly robust estimator.
• The study clarifies that simply combining propensity score weighting and outcome adjustment does not generally yield a doubly robust estimator.
• Misconceptions about adjusting for residual confounding after propensity score weighting are addressed.

Conclusions:

• The IPTW GLM offers a straightforward and understandable approach to doubly robust estimation.
• Researchers should be cautious about the assumptions and application of doubly robust methods.
• The study provides practical R code and examples for reproducible research.