Causal Direction Stability in Population Health Data: Bootstrap Uncertainty Quantification and Cross-Cycle Replication Using NHANES

Causal discovery methods applied to observational health data typically report a single direction decision without quantifying uncertainty or validating across independent cohorts. This paper addresses both gaps by applying three causal discovery algorithms — RESIT/ANM (Hoyer et al., 2009), DirectLiNGAM (Shimizu et al., 2006), and the CAM Score (Peters et al., 2014) — to three variable pairs in NHANES 2017–2018 (n = 5,856 adults): physical activity and depression (PHQ-9), sleep duration and BMI, and sleep duration and depression. Three methodological contributions are introduced: (i) confounder residualization removing age, sex, race/ethnicity, and poverty-income ratio before causal analysis; (ii) a 200-iteration bootstrap stability analysis reporting direction proportions per method; and (iii) the Causal Direction Stability Index (CDSI), a novel composite metric combining bootstrap majority agreement with variable non-Gaussianity. All three pairs returned uncertain or mixed direction decisions (CDSI range: 0.31–0.48), and no direction replicated in the independent NHANES 2013–2014 cohort. These null results are themselves informative: they demonstrate that current bivariate causal discovery methods cannot reliably recover causal direction from weak cross-sectional associations in population health data, and that CDSI provides a principled criterion for identifying when such analysis is likely to succeed or fail. To the author's knowledge, this is the first application of bootstrap-stabilised causal discovery with cross-cycle replication to NHANES data.