A Comparison of the Performance of Six Surrogacy Models, Including Weighted Linear Regression, Meta-regression, and Bivariate Meta-Analysis.

Objectives: Several trial-level surrogate methods have been proposed in the literature. However, often only one method is presented in practice. By plotting trial-level associations between surrogate and final outcomes with prediction intervals and by presenting results from cross-validation procedures, this research demonstrates the value of comparing a range of model predictions.

Methods: Two oncology data sets were used as examples. One contained 34 trials and had an overall moderate surrogate association; the other contained 14 trials and had an overall strong association. The models fitted included weighted linear regression, meta-regression, and Bayesian bivariate random-effects meta-analysis (BRMA).

Results: Predictions from the models showed a high degree of variation when there was a moderate association (surrogate threshold effect [STE] of 0.413-0.906) and less variation when there was a strong association (STE of 0.696-0.887). For both data sets, BRMA provided the most robust results, although informative priors for the heterogeneity distribution were needed for the smaller data set. Weighted linear regression models provided reasonable predictions in cases of moderate association. However, in the case of strong association, Bayesian BRMA demonstrated greater uncertainty in predictions.

Conclusion: Weighted linear regression provides a useful reference because prediction intervals represent 95% of variance in the data. However, the weights used in such a model must include information on follow-up time. In cases with small data sets, as well as in cases where there appeared to be a strong association, Bayesian BRMA provided predictions that were more robust than those provided by weighted linear regression.