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

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.