Criteria for Surrogate end Points Based on Causal Distributions

Abstract

When a treatment has a positive average causal effect (ACE) on an intermediate variable or surrogate end point which in turn has a positive ACE on a true end point, the treatment may have a negative ACE on the true end point due to the presence of unobserved confounders, which is called the surrogate paradox. A criterion for surrogate end points based on ACEs has recently been proposed to avoid the surrogate paradox. For a continuous or ordinal discrete end point, the distributional causal effect (DCE) may be a more appropriate measure for a causal effect than the ACE. We discuss criteria for surrogate end points based on DCEs. We show that commonly used models, such as generalized linear models and Cox's proportional hazard models, can make the sign of the DCE of the treatment on the true end point determinable by the sign of the DCE of the treatment on the surrogate even if the models include unobserved confounders. Furthermore, for a general distribution without any assumption of parametric models, we give a sufficient condition for a distributionally consistent surrogate and prove that it is almost necessary. Copyright (c) 2010 Royal Statistical Society.

Principal Stratification -- Uses and Limitations

“…That is to say, a variable S may be a principal surrogate and the treatment may have a positive effect on the surrogate and the surrogate may have a positive effect on the outcome but it may still be the case the effect of the treatment on the outcome is negative! Chen et al (2007) and Ju et al (2010) discuss conditions beyond "principal surrogacy" that ensure that the surrogate paradox is avoided. The application of the principal strati cation framework to the analysis of surrogates is theoretically appealing but, in my view, the jury is still out on how useful principal strati cation ideas will in the end be in this context and a variety of other approaches to surrogate outcomes are also being pursued; see Joffe and Greene (2009) for a review.…”

“…Chen et al (2007) and Ju et al (2010) note that a principal surrogate as de ned by Frangakis and Rubin (2002) does not avert the so called "surrogate paradox." That is to say, a variable S may be a principal surrogate and the treatment may have a positive effect on the surrogate and the surrogate may have a positive effect on the outcome but it may still be the case the effect of the treatment on the outcome is negative!…”

Criteria for Multiple Surrogates

“…It has been noticed that the statistical surrogate criterion, the principal surrogate criterion and the strong surro-gate criterion cannot avoid the surrogate paradox. Although the consistent surrogate criteria proposed by Chen et al (2007), Ju and Geng (2010) and Vanderweele (2013) can avoid the surrogate paradox, they are for a single surrogate and the conditions in their criteria involve unobserved confounders between a surrogate and an endpoint, and thus they are untestable even if the endpoint is observed. In this paper, we proposed the criteria for multiple surrogates which do not involve unobserved confounders, and thus these conditions can be tested if there are validation trials in which the endpoint is observed.…”

“…The conditions can be checked empirically by observed data if the endpoint is observed in a validation study. VanderWeele (2013) extended the results of Chen et al (2007) and Ju and Geng (2010) to the cases where there is a direct effect of the treatment on the endpoint. All of these criteria are only for a single surrogate.…”

“…The surrogate paradox 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. Chen et al (2007) and Ju and Geng (2010) proposed the criteria for consistent surrogates to avoid the surrogate paradox based on the causation knowledge between the surrogate and the endpoint. Wu et al (2011) proposed sufficient conditions to predict the sign of treatment effect on the unmeasured endpoint by the sign of treatment effect on the measured surrogate based on the association knowledge between the surrogate and the endpoint.…”