Evaluating the Proportion of Treatment Effect Explained by a Continuous Surrogate Marker in Logistic or Probit Regression Models.

Using surrogate endpoints in clinical trials is desirable for drug development because the trials can be shortened and therefore more cost-effective. Validating a surrogate for the clinical endpoint is critical in this context. One of the key steps in statistical validation of a surrogate for a single trial is to estimate the proportion of treatment effect explained (PTE or PE) by a surrogate. Often the measure for PTE is estimated from the difference in coefficients of treatment from two models with or without adjusting for the surrogate for clinical endpoint. Inherent problems with the method are: the two models may not be valid simultaneously; and the estimate can often lie outside the interval [0, 1]. In this article, we provide alternative measures for evaluating the proportion of treatment effect explained by a surrogate in logistic or probit regression models. Our measures can be estimated easily with any statistical programs capable of binary linear regression modeling, and the interpretation of the measures can be illustrated using Ordinal Dominance (OD) curves. The concept can be visually understood by any practical user. Simulation shows our alternative measures yield more accurate estimates which are less biased, less variable, and with narrower confidence intervals. A clinical trial example is provided.