A Generalizable Distribution Structure Analysis Algorithm with Audit-Ready Framework for Medical Research

Background Conventional statistical methods in medical research often fail to capture real-world complexity due to rigid parametric assumptions, particularly normality, which frequently do not hold for clinical and epidemiological data. Heterogeneous distributions, heavy-tailed patterns, and multimodal structures are common in healthcare data, yet conventional methods often fail to capture these structural characteristics, leading to information loss and potentially misleading conclusions. Furthermore, regulatory audits and reproducibility requirements demand transparent, traceable analytical frameworks.

This study presents a comprehensive Distribution Structure Analysis (DSA) algorithm with an integrated audit-ready framework designed specifically for medical research. The algorithm systematically identifies distributional structures, ensures statistical rigor through explicit estimand specification and goodness-of-fit testing, and maintains complete audit trails for regulatory compliance.

The DSA algorithm integrates five key components: (1) explicit estimand specification aligned with research design, (2) automated distribution type identification (normal, log-normal, exponential, Weibull, power-law, and mixture models), (3) comprehensive goodness-of-fit assessment using multiple criteria (AIC/BIC, visual diagnostics, and statistical tests), (4) causal inference support through Directed Acyclic Graphs (DAG), and (5) automated audit logging with a three-tier quality control system (red/yellow/green). The algorithm was validated using both simulated datasets with known distributions and real-world medical data from clinical trials and epidemiological studies.

Validation studies demonstrated that the DSA algorithm correctly identified distribution types with 95% accuracy across 1,000 simulated datasets. In clinical trial data analysis, the algorithm detected heavy-tailed distributions in adverse event frequencies that were missed by conventional normality-based methods, leading to more accurate safety assessments. The audit logging system successfully recorded all analytical decisions, enabling complete reproducibility. The three-tier quality control system flagged 12% of analyses for re-examination, preventing potential methodological errors. Application to epidemiological data revealed multimodal patterns in disease incidence that informed targeted public health interventions.

The DSA algorithm with integrated audit-ready framework provides a rigorous, transparent, and reproducible approach to distribution structure analysis in medical research. By explicitly addressing estimands, ensuring goodness-of-fit, and maintaining complete audit trails, the framework meets both statistical rigor and regulatory compliance requirements. The algorithm is applicable across diverse medical research domains, including clinical trials, epidemiology, health economics, and pharmacovigilance. Open-source implementation and comprehensive documentation facilitate adoption and validation by the research community. Competing Interest Statement The author (Michio Okazaki) is the founder and owner of S.I Lab Inc., a company that may have commercial interests related to the DSA algorithm described in this manuscript. The DSA algorithm core methodology is the subject of a patent application that has been filed (application pending). The DAG integration component described in this manuscript is planned for future patent filing. The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a conflict of interest beyond the ownership and patent interests disclosed above. No external funding was received for this research. The algorithm will be made available as open-source software under the MIT License to ensure broad accessibility to the research community. Funding Statement This study did not receive any external funding. The research was conducted independently by the author at S.I Lab Inc. without financial support from third-party organizations, grants, or commercial entities. No payments or services were received from any third party for any aspect of the submitted work, including study design, data analysis, manuscript preparation, or statistical analysis. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: This manuscript describes a methodological study and does not involve human participants or identifiable patient data. The applied studies used de-identified secondary data from existing databases. Therefore, institutional review board (IRB) approval was not required. For the clinical trial data, the original trial received IRB approval and all participants provided informed consent. For the epidemiological and health economics data, the data providers obtained appropriate ethics approvals and data use agreements. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data used in this study are simulated datasets generated for validation purposes and are available in the GitHub repository at https://github.com/Okazaki-Lab/DSA-algorithm. The repository includes: (1 ) R and Python implementation code for the DSA algorithm core modules, (2) simulated datasets used in the validation study, (3) example datasets demonstrating the algorithm's application, and (4) comprehensive documentation and user guides. No real patient data or personally identifiable information were used in this study.