## 2 Materials and Methods
### Validation Apparatus  
The performance of the patient-generator algorithm was evaluated using a structured validation framework designed to test accuracy, generalizability, and robustness. The validation plan tests the generator's ability to reproduce synthetic cohorts that maintain clinical logic and perform reliably under diverse and constrained input conditions. The validation strategy entailed a two-step simulation exercise. First, real-world datasets, NHANES (2021-2023) and the Framingham Heart Study, were analyzed to extract summary statistics including means, standard deviations, parameter bounds, and pairwise correlations (Supplementary Material S1). These derived statistics were then used as input parameters for the patient cohort generator. By creating synthetic datasets based solely on these summary inputs, we could simulate conditions where only aggregate data are available, which is a common situation. Since the objective of the study is to validate the results of the generator, we used publicly available datasets. However, some data were missing in these datasets. We decided to use only the complete cases (i.e., remove the missing records from the analysis) and not to impute the missing data to avoid adding uncertainty to the generated cohort. The final comparison would reflect the combined errors of both the imputation model and the data generator, making it impossible to determine how much of the final discrepancy was due to a weakness in our generator versus a flaw in the imputation. Imputation techniques introduce uncertainty in distinct ways, all of which were unsuitable for this validation context. Single imputation methods like mean or median replacement artificially reduce data variability and underestimate standard errors. While more advanced techniques like Multiple Imputation (MI) properly reflect uncertainty by creating several completed datasets and combining estimates using [PERSON]'s rules, this process presents its own challenges. The pooling of results across imputed datasets widens confidence intervals, which could mask the true performance of the synthetic data algorithm being tested. Because our primary evaluation metrics (R\({}^{2}\), MAE, SSE) are deterministic point estimates, combining them across multiple imputations would obscure interpretation and inflate the computational burden. Critically, all imputation models rely on untestable assumptions about the missing data mechanism. The reliability of any imputation technique depends on whether the data are Missing at Random (MAR) or Missing Not at Random (MNAR). If the true mechanism is MNAR--where the probability of a value being missing depends on the unobserved value itself--a standard imputation model can introduce systematic bias rather than correct for it. Since the true mechanism in the public datasets is unknown, relying on imputation would mean basing our validation on unprovable and potentially incorrect assumptions. Given these factors, we chose to avoid the added layers of complexity and potential bias by using only complete records. We acknowledge that this approach carries a risk of selection bias, potentially limiting the generalizability of our findings if the subsample of complete cases is not representative of the original population and the underlying data are not Missing Completely at Random (MCAR). However, this potential selection bias does not impact the primary objective of this study. Our goal is not to make inferences about the broader population, but to rigorously validate the generator's algorithmic fidelity. The crucial test is whether the synthetic data accurately reproduces the statistical properties of the specific input data, in this case, the complete-case dataset. Therefore, the representativeness of this dataset is outside the scope of our validation. In the second step, the synthetic cohorts generated using these summary statistics were systematically compared against the original datasets.