NHANES applications

Four contemporary questions in NHANES (2007–2018), chosen to span exposure prevalence and overlap. Each estimand is the population average treatment effect on the risk-difference scale, estimated under all five design-awareness arms; the primary arm is Fully-Aware-CF (emphasized in the forest).

The four questions: E1 short sleep → obesity · E2 food insecurity → depression · E3 e-cigarette use → hypertension · E4 gestational-diabetes history → hypertension.

Note

The cross-example forest and five-arm table now report the \(m=40\) multiple-imputation estimates, matching the paper’s Table 3 and Figure 2.

Cross-example overview

Forest

The point estimate is broadly stable across arms; what shifts is the uncertainty (and, in E3, whether the interval excludes zero — it does for the naive Non-Aware arm but not for the design-aware arms). The primary Fully-Aware-CF arm is drawn larger.

Table

Design, overlap, and covariate-set robustness

Domain size, exposure/outcome prevalence, and single-fit (_fa) versus cross-fitted (_cf) propensity ranges. Poor overlap (E3, E4) is where the single-fit propensity approaches the boundary.

The conclusions are largely stable across alternative adjustment sets: E1, E2, and E4 are unchanged. The exception is E3, where dropping BMI — a strong predictor of the outcome — turns the e-cigarette → hypertension null borderline-significant. Consistent with the paper’s over-adjustment reading, the fully-adjusted design-aware estimate (which covers zero) remains the primary one (see the E3 tab and Web Appendix F).

Sample descriptions

Survey-weighted characteristics of each analytic domain by exposure group, with standardized mean differences (SMD). These are the per-example Table 1s in Web Appendix E.

E1

Balance (SMD)

Table 1

E2

Balance (SMD)

Table 1

E3

Balance (SMD)

Table 1

E4

Balance (SMD)

Table 1

By question

Each tab collects everything available for that question. The cross-example forest above shows all four side by side.

E1: Short sleep → obesity

Common exposure, excellent overlap: all arms agree and the design-aware interval is roughly a third wider than the naive one.

E2: Food insecurity → depression

Ignoring the weights understates the association, though both intervals exclude zero — the weights change the magnitude, not the qualitative finding.

E3: E-cigarette use → hypertension

The naive Non-Aware analysis returns an apparently significant association, but survey-weighting alone moves the estimate to an interval covering zero — the apparent association is removed at the weighting step, not by cross-fitting.

E4: GDM history → hypertension

Rare exposure: the single-fit propensity reaches 0.003 (a near-violation of positivity) while the cross-fitted propensities are held at or above the 0.05 floor, and the primary risk difference is near zero.