The Impact of Model Misspecification on the Individual Causal Association in Surrogate Endpoint Evaluation

Surrogate endpoints are often used in place of expensive, delayed, or rare clinical endpoints in clinical trials. However, regulatory authorities require thorough evaluation to accept these surrogate endpoints as reliable substitutes. One evaluation approach is the information-theoretic causal inference framework, which quantifies surrogacy using the individual causal association (ICA). Like most causal inference methods, this approach relies on models that are only partially identifiable. For continuous outcomes, a normal model is often used. In this study, we explored the effects of model misspecification across various scenarios. We first considered true data-generating mechanisms based on multivariate $t$ and log-normal distributions. We then used D-vine copulas with Gaussian, Clayton, Gumbel, and Frank families to vary the unidentifiable copulas involving counterfactual pairs while preserving the observable bivariate margins, and considered intuitive restrictions on nonidentified correlations, including positivity and conditional independence. In all settings, the identifiability issue was addressed through sensitivity analysis. Finally, we illustrate the proposed sensitivity analyses using clinical-trial data from schizophrenia studies, evaluating the ICA under several modeling assumptions. The results show that, in most scenarios considered, the impact of model misspecification is small; however, certain departures from the assumed model can materially affect the surrogacy assessment.