Reliability-oriented CUSUM monitoring of breast cancer features using Burr–X distribution and progressive censoring

Abstract

Accurate monitoring of disease progression is critical in oncology to detect subtle changes in tumor characteristics. In breast cancer (BC) diagnosis and monitoring, morphological features of cell nuclei, such as the mean radius, serve as vital biomarkers. This study propose a monitoring framework by combining an established Cumulative Sum (CUSUM) control chart with Burr-X distributed data under Progressive Type-II censoring. This approach addresses the common clinical challenge of right-censored survival data, where patient follow-up times vary. Comprehensive simulation results demonstrate the chart's effectiveness via lower out-of-control average run lengths (ARLs) under various censoring scenarios. The practical utility of the proposed chart is illustrated using BC diagnostic dataset, focussing on the monitoring of the radius_mean biomarker. Performance is assessed using Average Run Length, Standard Deviation of Run Length, run-length percentiles, Expected Quadratic Loss, Relative Average Run Length, Performance Comparison Index, Relative Mean Index, and confusion-matrix-based classification measures. Comparative analysis reveals that the CUSUM chart outperforms both Exponentially Weighted Moving Average and Shewhart schemes in detecting small to moderate shifts in the radius_mean biomarker. The proposed framework provides a statistically rigorous tool for monitoring continuous biomarkers under progressive censoring.Highlights• A Burr–X distribution-based Cumulative Sum monitoring scheme is developed for Breast Cancer data subject to progressive Type-II censoring.• The method incorporates distribution-specific likelihood adjustments, improving detection sensitivity for heavy-tailed behaviour.• Charting constants are calibrated via Monte Carlo simulation to achieve a stable in-control (IC) Average Run Length (ARL) of approximately 370.• Extensive simulation experiments evaluate IC and out-of-control performance using ARL, Standard Deviation of Run Length, and Run Length quantiles across multiple censoring levels.• A real-data application confirms the robustness of the proposed scheme for identifying both positive and negative mean shifts under censored failure data.• The framework provides a practical and effective tool for reliability monitoring where asymmetric data shapes and censoring are present.

The authors' abstract, as published at the source. Journal of Statistical Computation and Simulation, 2026 · DOI ↗