Differences in surrogate threshold effect estimates between original and simplified correlation-based validation approaches

Abstract

Surrogate endpoint validation has been well established by the meta-analytical correlation-based approach as outlined in the seminal work of Buyse et al. (Biostatistics, 2000). Surrogacy can be assumed if strong associations on individual and study levels can be demonstrated. Alternatively, if an effect on a true endpoint is to be predicted from a surrogate endpoint in a new study, the surrogate threshold effect (STE, Burzykowski and Buyse, Pharmaceutical Statistics, 2006) can be used. In practice, as individual patient data (IPD) are hard to obtain, some authors use only aggregate data and perform simplified regression analyses. We are interested in to what extent such simplified analyses are biased compared with the ones from a full model with IPD. To this end, we conduct a simulation study with IPD and compute STEs from full and simplified analyses for varying data situations in terms of number of studies, correlations, variances and so on. In the scenarios considered, we show that, for normally distributed patient data, STEs derived from ordinary (weighted) linear regression generally underestimate STEs derived from the original model, whereas meta-regression often results in overestimation. Therefore, if individual data cannot be obtained, STEs from meta-regression may be used as conservative alternatives, but ordinary (weighted) linear regression should not be used for surrogate endpoint validation.

Keywords: meta-analysis; surrogate endpoint validation; surrogate threshold effect.