A reflection on the causal interpretation of individual-level surrogacy.

At the beginning of the 21st century, a new paradigm was introduced for the evaluation of surrogate endpoints based on meta-analysis. In this paradigm, the putative surrogate is assessed at two different levels, the so-called, trial and individual level. Trial level surrogacy is defined as the association between the expected causal treatment effects across different trials populations, whereas the individual level is defined as the association between the surrogate and true endpoints, after adjusting by trial and treatment. It has been argued that the individual level surrogacy does not have a causal interpretation and, consequently, it is a poor metric of surrogacy. In the present work, an alternative definition of individual level surrogacy is introduced based on individual causal treatment effects. In addition, using the maximum entropy principle, a direct link between the individual level surrogacy, as defined in the meta-analytic approach, and the newly proposed definition is established. This new perspective sets the individual level surrogacy in a more coherent framework with respect to the trial level and bridges the two main schools of thought in this domain, namely, the causal inference and meta-analytic schools.

A closed-form estimator for meta-analysis and surrogate markers evaluation.

Estimating complex linear mixed models using an iterative full maximum likelihood estimator can be cumbersome in some cases. With small and unbalanced datasets, convergence problems are common. Also, for large datasets, iterative procedures can be computationally prohibitive. To overcome these computational issues, an unbiased two-stage closed-form estimator for the multivariate linear mixed model is proposed. It is rooted in pseudo-likelihood-based split-sample methodology and useful, for example, when evaluating normally distributed endpoints in a meta-analytic context. However, applications go well beyond this framework. Its statistical and computational performance is assessed via simulation. The method is applied to a study in schizophrenia.