Evaluation Methods for T-association of a Surrogate Endpoint

A surrogate endpoint is a biomarker that is reasonably likely to predict clinical benefit and is used as a substitute for a direct measure of clinical benefit under the Food and Drug Administration (FDA) Accelerated Approval pathway. According to FDA guidelines, a valid surrogate endpoint must meet two associations: I-association (the association between the surrogate and true endpoints, such as disease response and overall survival) and T-association (the association between treatment effects on both endpoints, such as odds ratio and hazard ratio). I-association is commonly evaluated, but T-association is often overlooked due to the lack of appropriate statistical methods. Failure to satisfy T-association precludes a biomarker from supporting accelerated approval. To address this gap, we propose a new method to rigorously assess T-association in accordance with FDA guidelines. This method assumes that treatment effects on the surrogate and true endpoints follow a bivariate normal distribution, accounting for both within-study and between-study variances. The key evaluation metric is the correlation coefficient, which quantifies the relationship between treatment effects on both endpoints. Model parameters, including this correlation, are estimated using maximum likelihood, restricted maximum likelihood, and a Bayesian approach. We demonstrate the method using both simulated and real-world data. The method will serve as the statistical foundation that aligns with FDA guidelines and supports future accelerated approvals. The R package to implement the proposed method is available at https://github.com/jybelindahung/T-association .