Criteria for Multiple Surrogates

Abstract

An observed surrogate endpoint is often used to predict treatment effect on an unobserved true endpoint when the true endpoint is difficult or expensive to be measured. Although there have been several criteria for surrogate endpoints, they cannot avoid the surrogate paradox, which means that a treatment has a positive effect on a surrogate and the surrogate has a positive effect on an endpoint, but the treatment has a negative effect on the endpoint. To avoid the surrogate paradox, some investigators provided criteria for a single surrogate which blocks the path from the treatment to the endpoint. This requires that there is only a single path from treatment to endpoint and the surrogate can block the single path. However, in many applications, a treatment may affect an endpoint through several paths. In this paper, we propose some criteria for multiple surrogates. We make use of stochastic orders of random vectors to give criteria for multiple surrogates to avoid the surrogate paradox and to predict the sign of treatment effect on the unobserved true endpoint. Further under the conditional independence of the treatment and the true endpoint given the multiple surrogates, we propose some sufficient conditions for the sign equivalence of treatment effects on the surrogates and on the true endpoint. Furthermore, Statistica Sinica: Newly accepted Paper (accepted version subject to English editing)Criteria for multiple surrogates we illustrate how these criteria can be applied to several commonly-used models.

Statistical approaches for causal inference

“…令人惊讶 的是, 主替代指标和强替代指标有非常严格的要求条件, 但是它们仍然不能避免替代指标悖论; 替代 指标悖论从根基上完全动摇了替代指标和标记物的价值 [109] . 在文献 [ [107,109,111,112] [113] 给出了下面的结果: 如果下面 3 个条件成立: [11] .…”