The individual-level surrogate threshold effect in a causal-inference setting with normally distributed endpoints

In the meta-analytic surrogate evaluation framework, the trial-level coefficient of determination $$ quantifies the strength of the association between the expected causal treatment effects on the surrogate (S) and the true (T) endpoints. Burzykowski and Buyse supplemented this metric of surrogacy with the surrogate threshold effect (STE), which is defined as the minimum value of the causal treatment effect on S for which the predicted causal treatment effect on T exceeds zero. The STE supplements $$ with a more direct clinically interpretable metric of surrogacy. Alonso et al. proposed to evaluate surrogacy based on the strength of the association between the individual (rather than expected) causal treatment effects on S and T. In the current paper, the individual-level surrogate threshold effect (ISTE) is introduced in the setting where S and T are normally distributed variables. ISTE is defined as the minimum value of the individual causal treatment effect on S for which the lower limit of the prediction interval around the individual causal treatment effect on T exceeds zero. The newly proposed methodology is applied in a case study, and it is illustrated that ISTE has an appealing clinical interpretation. The R package surrogate implements the methodology and a web appendix (supporting information) that details how the analyses can be conducted in practice is provided.