Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.
Keywords: Bayesian methods; crossover design; delayed-start; longitudinal outcomes; principal stratification; surrogate endpoints.
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