When both models are imperfect.
Compare TMLE and IPW as you change treatment- and outcome-model errors.
TMLE
Outcome + treatment model
IPW
Treatment model only
Estimate − true effect · outcome units
Shared by both maps · range changes with pattern
Select a square in either map, or move the sliders. The population stays fixed.
What changed in the models?
| Population group | True treatment probability | Distorted probability |
True outcome means Untreated / treated |
Initial distorted means Untreated / treated |
|---|
Two equally common groups have treatment effects of 1 and 3. Exact treatment proportions remove sampling variation. Outcome means here are continuous values, not probabilities.
Why do the errors interact?
TMLE updates the outcome predictions using the treatment model. Its remaining population error involves a weighted product of treatment-model error and outcome-model error after targeting.
Here, either correct model gives the correct effect. When both are wrong, the direction and location of their errors matter. A zero fitted residual correction alone does not establish accuracy.
This is a controlled population illustration, not a repeated-study estimate of bias or precision. It uses linear continuous-outcome TMLE and normalized (Hájek) IPW, with the same 0.02–0.98 propensity bounds. No probabilities are clipped in these grids. These results do not guarantee that TMLE is better in other populations.