Estimation of time to progression and post progression survival using joint modeling of summary level OS and PFS data with an ordinary differential equation model

Summary measures such as progression-free survival (PFS) and overall survival (OS) are commonly reported in literature for oncology trials, while time to progression (TTP) and post progression survival (PPS) are not usually reported. A time-variant transition hazard model was developed using an ordinary differential equation (ODE) model to estimate TTP and PPS from summary level PFS and OS. The model was applied to published data from immune checkpoint inhibitor trials for non-small cell lung cancer (NSCLC) in a meta-analysis framework. This model-based method was able to robustly estimate TTP and PPS from summary level OS and PFS data, provided a quantitative approach for understanding the patterns of disease progression across different treatments through the time-variant disease progression rate function, and provided a summary of how different treatments affect TTP and PPS. The proposed method can be generalized to characterize and quantify multiple time-to-event endpoints jointly in oncology trials and improve our understanding of disease prognostics for different treatments.