Average treatment effect in the overlap can be a tricky causal estimand. Why?

The ATO is a little different than other estimands.

Often, it's not well defined before the analysis.

This is because there are many ways to define the population.

Instead, it's based on the statistical method.

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It can be tempting to think of propensity scores as a prediction problem. This is problematic. Why?

In prediction models, any variable that helps can be included.

In causal inference, this can cause bias, e.g., collider bias.

Instead, use a directed acyclic graph (DAG) for variable selection.

For IPTW which causal estimand was it? If it was ATE, then it's estimating something different from PSM.

The causal estimand impacts several area. It's important to keep in mind.

PS: There are four estimands:
- ATE
- ATT
- ATU
- ATO

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Choosing a causal estimand is important. Why?

To make sure the research question is answered!

Certain methods can only estimate specific estimands. This is important when comparing methods.

Let's use an example.

Imagine we want to compare two methods:

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Nominal coverage helped me with confidence intervals:

If you repeat an analysis 1,000 times, nominal coverage is the % of intervals that capture the true effect.

For 95% CIs, we'd expect ~950/1,000 to include the true value. It's a long-run frequency idea, not a guarantee for any single interval!

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We can then use IPCWs for things such as Kaplain-Meier Curves