## Appendix E Comparisons Between Real-World Datasets and Synthetic Cohorts  
Tables A1-A3 present detailed comparisons of summary statistics between real-world datasets and synthetic cohorts for all five generation scenarios across three patient populations: general (NHANES), cardiac (Framingham Heart Study), and low-dimensional (NHANES subset). Table A4 provides correlation fit metrics comparing estimates of two clinical expert and their average in synthetic data generation. These comparisons validate the fundamental statistical fidelity of the patient cohort generator, demonstrating its accuracy in reproducing central tendencies and variability across diverse clinical variables. The inclusion of \(p\)-values confirms the statistical equivalence between real and synthetic datasets, demonstrating that the tool reliably maintains individual variable distributions. Presenting these foundational validation tables is essential, as they establish the baseline accuracy required for further advanced validations, including the preservation of inter-variable correlations. The comparisons revealed near-perfect agreement in means and standard deviations across all variables and scenarios. For every variable assessed, the generated synthetic values remained statistically indistinguishable from the real-world reference data, with \(p\)-values consistently exceeding 0.90. In many instances, notably within the Framingham cohort (Table A2), \(p\)-values reached 1.000 across all variables and scenarios. This suggests the generator's exceptional capacity to match target input distributions with high fidelity, even in large and complex cohorts. This trend held true across all simulation scenarios, including Scenario E, which lacked any correlation inputs. While this scenario performed poorly in terms of preserving inter-variable relationships, it nonetheless produced synthetic datasets with central tendency and dispersion metrics closely matching those of the real cohort. This highlights a key limitation of summary statistics alone as a validation metric. Many existing synthetic data generators are capable of replicating marginal distributions (e.g., mean and standard deviation) by design. As such, achieving agreement in summary statistics is necessary, but insufficient, to claim realism in synthetic data. Consequently, our model's primary validation focused on preserving correlation structures and clinical plausibility. Interestingly, while the Framingham cohort showed virtually no variation in \(p\)-values across scenarios, the NHANES normal population cohort exhibited slightly lower--though still non-significant--\(p\)-values. This variation may be attributable to the distributional assumptions used. The NHANES simulations predominantly relied on log-normal distributions, whereas Framingham scenarios employed a mix of normal and gamma distributions. Conversely, the low-dimensional NHANES cohort achieved perfect \(p\)-values across scenarios despite also using log-normal distributions. This suggests that smaller parameter sets can yield highly accurate and reliable synthetic results, even under skewed distributions. Moreover, the NHANES general population cohort included deterministic logical constraints--making it unique among test groups. Despite this added complexity, the synthetic data remained statistically consistent with the real dataset, affirming the robustness of the generator's constraint-resolution logic. Finally, binary and categorical variables, particularly those in the Framingham dataset, were replicated with absolute precision across all simulations. As reflected in Table A2, binary prevalence rates and categorical distributions matched exactly with their real-world counterparts. This underscores the algorithm's efficacy in handling non-continuous parameters using its percentile-thresholding method and validates its deterministic approach to preserving prevalence and logical constraints in categorical data.