An efficient algorithm to assess multivariate surrogate endpoints in a causal inference framework

Multivariate surrogate endpoints can improve the efficiency of the drug development process, but their evaluation raises many challenges. Recently, the so-called individual causal association (ICA) has been introduced for validation purposes in the causal-inference paradigm. The ICA is a function of a partially identifiable correlation matrix (R) and, hence, it cannot be estimated without making untestable assumptions. This issue has been addressed via a simulation-based analysis. Essentially, the ICA is assessed across a set of values for the non-identifiable entries in R that lead to a valid correlation matrix and this has been implemented using a fast algorithm based on partial correlations (PC). Using theoretical arguments and simulations, it is shown that, in spite of its computational efficiency, the PC algorithm may lead to the spurious effect that adding non-informative surrogates, i.e., surrogates that convey no information on the treatment effect on the true endpoint, seemingly reduces the ICA range. To address this, a modified PC algorithm (MPC) is proposed. Based on simulations, it is shown that the MPC algorithm removes this nuisance effect and increases computational efficiency.