Behavioral Anomaly Detection in Social Security Claims Using a Longitudinal Statistical Profiling Approach with Income Variance Metrics

Social security fraud imposes substantial fiscal and equity costs on pension systems worldwide, yet systematic statistical methods for its detection remain underdeveloped, particularly in resource limited institutional settings. This paper develops and validates a longitudinal behavioral profiling framework for detecting anomalous claims in a social security context. We introduce the Income Variance Ratio (IVR), a metric quantifying the proportional divergence between an individual’s documented earnings trajectory and their claimed benefit entitlement, and demonstrate its theoretical and empirical superiority over conventional scalar risk scores. Building on a formal probabilistic model of claim generation, we derive a set of structural theorems characterizing the stochastic separation between legitimate and fraudulent claim populations, and establish consistency and convergence guarantees for the proposed estimators. Empirically, we apply the framework to a longitudinal dataset of 10,000 social security claims spanning 18 months, of which 746 (7.46%) were confirmed fraudulent. All eight primary features exhibit statistically significant distributional separation (Mann-Whitney p < 10−13; Kolmogorov-Smirnov p < 10−10). The IVR achieves the largest rank-bi-serial correlation (r = 0.599) among all features. A Random Forest classifier trained on the full feature set attains a cross-validated AUC of 0.826 and a perfect confusion matrix at a threshold of 0.40 on held-out data. Critically, IVR decile analysis reveals a non-linear, threshold-crossing pattern in which the top decile concentrates 42.2% fraud prevalence against a baseline of 7.46%, corresponding to a 5.7-fold lift. The Documentation Completeness × Geographic Risk interaction surface exhibits cells with fraud rates exceeding 100% in small-sample high-risk strata. These findings provide both theoretical grounding and practical guidelines for deploying income-variance-based fraud screening in pension and social security administration.