Targeted Maximum Likelihood for ATE, why not just GLM for ATE? I have been attempting to learn targeted maximum likelihood (TMLE), which is a struggle. The estimand of interest is often the average treatment effect. If we have an outcome $Y$, intervention $A$ and a set of covariates $W$ this is defined as,
$$ATE = $$
$$E_W( E(Y|A = 1, W) - E(Y | A = 0, W)) = $$
$$ E_W( E(Y|A = 1 ,W)) - E_W( E(Y|A = 0,W))$$
where $E_W$ denotes the expectation with respect to the distribution of the covariates. Why do we need targeted maximum likelihood here? For any GLM I can estimate $E_W( E(Y|A = 1,W))$ by first just finding $E(Y|A = 1,W)$ explicitly from the GLM (similarly for $E(Y|A = 0,W)$)  and marginalizing out over the distribution of my covariates. What is TMLE getting me here that traditional MLE of a GLM is not?

The answer is double robustness. Like all doubly-robust methods, with TMLE you get two chances to get the model correct and the treatment effect estimate is consistent if either is correct (or approach at a given rate). With g-computation using a GLM, you only get one chance to get the model right. If that model is wrong (and it almost certainly is), then your treatment effect estimate is not consistent. You can use flexible machine learning methods with TMLE that are more likely to approximate the true form of either the treatment and outcome model. Indeed, given the inability of an outcome model GLM to even plausibly capture the true outcome model, one should almost never use it to estimate treatment effect, whereas TMLE should be among your first choices.
