Standardization Methods
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What is Standardization?
Standardization (also called g-computation or the parametric g-formula) is one of the most fundamental methods for estimating causal effects from observational data. This approach, which Hernán and Robins discuss extensively in "What If" (Chapter 13), works by modeling the relationship between treatment, confounders, and outcome, then using this model to predict what would happen under different treatment scenarios.
Standardization is a method that estimates causal effects by:
- Fitting a model for the outcome conditional on treatment and confounders: E[Y|A,L]
- Using this model to predict outcomes for each individual under each treatment level
- Averaging these predictions across the entire population to obtain marginal (population-average) causal effects
The key insight behind standardization is that we can use the observed data to build a model that describes how outcomes depend on treatment and covariates, then leverage this model to answer counterfactual questions: "What would have happened if everyone had been treated?" versus "What would have happened if no one had been treated?"
In the NHEFS study, researchers wanted to estimate the causal effect of quitting smoking on weight change. Simply comparing weight change between quitters and non-quitters would be confounded by factors like baseline weight, age, and smoking intensity. Standardization allows us to model weight change as a function of quitting status and these confounders, then predict what weight change would look like if the entire population had quit versus if no one had quit.
The mathematical foundation comes from the g-formula (Robins, 1986):
For continuous confounders, the sum becomes an integral. In practice, we replace this with the sample average of predicted values, which gives us the standardized mean:
Standardization works by averaging over the actual confounder distribution in the study population. This is why it produces marginal (population-average) effects rather than conditional effects.
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