Most methods for evaluating surrogate endpoints measure validity in terms of net effects (i.e., treatment effects adjusted for the biomarker measured after randomization). Frangakis and Rubin (2002, Biometrics) criticized these approaches because net effects may reflect selection bias, and suggested an alternative definition of a surrogate endpoint (a "principal" surrogate) based on causal effects. For evaluating principal surrogates we introduce a causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. The CEP surface is not identifiable in general due to missing potential outcomes. However, by incorporating baseline covariates that predict the biomarker, the CEP surface is identified under relatively weak assumptions in the important special case that the biomarker has no variability in one treatment arm. For this setting we develop an estimated likelihood method for estimating the CEP surface. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection.



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