Evaluation of binary intermediate endpoints for their departure from perfect surrogacy
Filiaci, Virginia L.
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Methods of evaluating and validating potential surrogate variables have received considerable attention in the statistical and medical literature. While there is an implicit recognition of a connection with path analysis, it has not been exploited fully or utilized correctly. Methods are proposed to evaluate the adequacy of surrogate variables utilizing path analytic concepts and theory. Statistical criteria are developed for assessing the adequacy of a dichotomous surrogate endpoint that involves estimation of the direct effect of treatment on a true endpoint and the indirect effect through the surrogate when a calculus of effects holds. Two criteria are suggested for perfect surrogacy: (1) The total effect of treatment must be comprised solely of its indirect effect through the surrogate; and (2) The outcome must be perfectly predicted by the surrogate and treatment. Two statistics are proposed to assess adequacy. The first, C 1 , is the ratio of the indirect effect of treatment on outcome mediated through the surrogate to the total effect of treatment on outcome. The second, C 2 , is an R 2 -like coefficient that measures the variation of the true endpoint explained by the surrogate when adjusting for treatment. Values of C 1 and C 2 near 1.0 reflect near perfect surrogacy. These methods are extended to time to failure endpoints and applied to assess the adequacy of response to treatment as a surrogate for the survival time of women with endometrial cancer. Monte Carlo simulation studies are used to compare this method with other methods that estimate the proportion of treatment effect explained (PTE) or apply path analytic methods. Confidence intervals are used to assess the precision of the two proposed measures.