Uncertainty-Weighted Parametric Fitting from Summary Statistics: A Monte Carlo Framework for Individual-Level Data Reconstruction

This repository provides open-source software for reconstructing individual-level micro-data from published summary statistics using an uncertainty-weighted parametric fitting approach. The framework is motivated by the problem of recovering plausible sample distributions when only limited statistics (e.g., percentiles and means with confidence intervals) are reported. The package contains two self-contained components: Case study (creatinine, NHANES III 1988–1994):Synthetic urinary creatinine micro-data are generated for 48 demographic subgroups (sex × race × age) by fitting a Generalized Gamma distribution to published percentiles and means. Weighted least squares are used, with weights determined by the inverse of confidence interval widths. Outputs include synthetic samples, fitted parameters, comparative summaries, and 48 figures illustrating observed vs. simulated distributions. Monte Carlo validation (Burr XII):To evaluate methodological robustness, controlled experiments simulate a known Burr XII population, re-fit parameters under different subsets of summary statistics, and quantify reconstruction errors. Outputs include error distributions, Excel summaries, and a comparative boxplot of scenarios. The software is released as Python scripts, accompanied by synthetic datasets, figures, and documentation. All creatinine data provided here are synthetic reconstructions derived from published subgroup summaries; no original NHANES micro-data are distributed. This resource highlights both the practical application to real-world biomonitoring data and the broader methodological contribution, supporting reproducibility and future adaptation to other domains.