Assessing the clinical efficacy of new treatments is essential in phase II trials, but traditional endpoints may be inadequate in precision oncology or with cytostatic agent therapy. In this context, the growth modulation index (GMI), defined as the ratio of time to progression (TTP2) under a treatment line to that of the preceding line (TTP1), can be an appealing endpoint. It allows patients to serve as their own controls, reflecting individual treatment dynamics. Since its introduction by Von Hoff in 1998, several statistical methods have been developed to analyse the GMI, relying on the assumption of high correlation between the two paired event times. However, this assumption remains insufficiently validated in the literature. This study aims to estimate the correlation between paired event times using datasets obtained from the literature and simulated, applying advanced statistical methods to evaluate the reliability of GMI's current methods as a trial design endpoint.

We analysed 34 datasets of phase II trials related to GMI, defined precisely or reconstructed from Kaplan-Meier curves using digitalization techniques to recreate individual patient data. To estimate the correlation between paired event times, we applied statistical methodologies that allow us to take into account the dependence such as: Clayton's and Gumbell's copulas models, the shared frailty model stratified on the line of treatment and the linear and the accelerated failure time models. The correlation between paired event times was quantified using Kendall's tau to ensure comparability across methods.

Our analysis revealed relatively low correlations between paired event times across all datasets, with maximum observed Kendall's tau values around 0.4. These findings challenge the assumption of high correlation sustaining the use of GMI as an endpoint to demonstrate clinical treatment efficacy.

The copulas seem to be a reliable way of taking into account paired event times, rather than just the ratio of the two event times. Despite applying multiple statistical approaches, the correlation estimates remained low with our datasets, raising concerns about the reliability of GMI in its current implementation.