Methods in brief
A one-page, plain-language recap. The full theory, proofs, and implementation are in the paper and its Web Appendix.
The problem
Targeted maximum likelihood estimation (TMLE) pairs machine learning with semiparametric efficiency theory to estimate causal effects. Its standard theory assumes independent observations — but complex surveys (like NHANES) have stratification, clustering, and unequal selection. Treating survey data as i.i.d. gets both pieces wrong:
- ignoring the weights biases the point estimate (it targets a sample, not the population, quantity);
- ignoring the clustered design understates the variance, so confidence intervals are too narrow.
The estimator
We develop a survey-aware TMLE for the population average treatment effect. Its variance is obtained by Taylor-series linearization of the estimator’s influence function, treating the primary sampling unit (PSU) as the independent replication unit. Within explicit conditions, the estimator is asymptotically normal and the linearization variance is design-consistent under a stratified multistage design.
The central result: cross-fitting restores valid inference
With flexible machine-learning nuisances, valid variance turns on cross-fitting at the PSU level: among the estimators evaluated, only out-of-fold (cross-fitted) fitting keeps coverage valid. A single-fit survey TMLE can severely under-cover once the learners cross a complexity (Donsker) boundary — and internal cluster-aware cross-validation does not substitute for cross-fitting. The simulation shows this directly: coverage collapses at the interpolating rung for single-fit, while the cross-fitted arm stays near nominal.
The five arms
| Arm | Weights | Variance | Nuisance fitting |
|---|---|---|---|
| Non-Aware | ignored | i.i.d. | single-fit |
| Partially-Aware | used | i.i.d. | single-fit |
| Fully-Aware | used | design-based | single-fit |
| Fully-Aware-CV | used | design-based | internal cluster-CV |
| Fully-Aware-CF (recommended) | used | design-based | PSU-level cross-fitting |
Fully-Aware-CF is the arm the theory covers for machine-learning nuisances.