Design-Aware Predictive and Causal Modeling of Cardiovascular Risk in Chronic Kidney Disease Using Penalized and Double Machine Learning Approaches

We develop a design-aware mathematical framework that unifies penalized prediction and causal inference for finite populations observed through complex survey designs. The framework integrates survey-weighted pseudo-likelihoods, $\ell_1$-penalized estimation, Neyman-orthogonal moment functions, and a design-consistent bootstrap that resamples primary sampling units within strata. Methodologically, the contribution is an explicit pipeline that preserves design consistency while separating predictive associations from structural causal effects in high-dimensional, clustered data. We illustrate the framework using data from the Chilean National Health Survey (ENS) 2016--2017 to study the relationship between chronic kidney disease (CKD) and high cardiovascular (CV) risk. In the ENS adult population, the survey-weighted prevalence of CKD was 3.1\% (95\% CI: 2.4--3.8), and the prevalence of high CV risk was 23.9\% (95\% CI: 21.5--26.3). High CV risk was markedly more frequent among individuals with CKD than among those without CKD (90.9\% versus 21.5\%). Predictive and associational analyses combined survey-weighted penalized logistic regression (LASSO) with refitted unpenalized models. In conventional survey-weighted logistic regressions, CKD showed a strong associational relationship with high CV risk (odds ratio = 5.66; 95\% CI: 2.71--11.82; $p < 0.001$), and effect sizes remained stable after LASSO-based variable selection. To assess causal relevance under confounding and potential endogeneity, we implemented two endogeneity-aware estimators: two-stage residual inclusion (2SRI) and Double/Debiased Machine Learning (DML). The DML estimator, defined as the primary causal estimand, reports the average treatment effect of CKD on the probability of high CV risk. After adjustment for age and major cardiometabolic comorbidities, the DML estimate was attenuated and statistically non-significant (average treatment effect = $-0.094$; 95\% CI: $[-0.409,\,0.220]$). The 2SRI approach yielded highly unstable odds-ratio estimates with wide confidence intervals, consistent with limited effective sample size and weak identification power. Simulation experiments under ENS-like complex sampling confirmed that naive predictive associations substantially overestimate the structural contribution of CKD under confounding, whereas orthogonalized estimators recover attenuated causal effects when identification holds. Overall, the results demonstrate a fundamental divergence between predictive relevance and causal importance in finite-population settings, underscoring the need for design-aware and endogeneity-robust methods in mathematical statistics and applied risk modeling.