A Novel Approach for Analyzing Non‐Proportional Hazards With Long‐Term Survivors: The Defective Yang–Prentice Model

ABSTRACT In survival analysis, addressing non‐proportional hazards and the presence of long‐term survivors poses substantial methodological challenges, as traditional models often fail to capture these features adequately. To overcome these limitations, a novel long‐term survival model is proposed that integrates the Yang and Prentice framework with a defective Gompertz distribution. The proposed model provides a robust approach for analyzing time‐to‐event data with non‐proportional hazards and a cure fraction. Comprehensive simulation studies and an application to colorectal cancer data illustrate its flexibility in capturing time‐varying hazard ratios and long‐term survivors, making it a useful alternative to existing methods.