We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the confounder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.

Nitrogen (N) and carbon-nitrogen (C:N) ratio are key foliar traits with great ecological importance, but their patterns across biomes have only recently been explored. We conducted a systematic census of foliar C, N and C:N ratio for 213 species, from 41 families over 199 research sites across the grassland biomes of China following the same protocol, to explore how different environmental conditions and species composition affect leaf N and C:N stoichiometry. Leaf C:N stoichiometry is stable in three distinct climatic regions in Inner Mongolia, the Tibetan Plateau, and Xinjiang Autonomous Region, despite considerable variations among co-existing species and among different vegetation types. Our results also show that life form and genus identity explain more than 70% of total variations of foliar N and C:N ratio, while mean growing season temperature and growing season precipitation explained only less than 3%. This suggests that, at the biome scale, temperature affects leaf N mainly through a change in plant species composition rather than via temperature itself. When our data were pooled with a global dataset, the previously observed positive correlation between leaf N and mean annual temperature (MAT) at very low MATs, disappeared. Thus, our data do not support the previously proposed biogeochemical hypothesis that low temperature limitations on mineralization of organic matter and N availability in soils lead to low leaf N in cold environments.

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A surrogate end point is often used to evaluate the effects of treatments or exposures on the true end point in medical researches. Various criteria for the statistical surrogate, principal surrogate and strong surrogate have been proposed. We first illustrate that, with a surrogate end point that is defined by these criteria, it is possible that a treatment has a positive effect on the surrogate, which in turn has a positive effect on the true end point, but the treatment has a negative effect on the true end point. We define such a phenomenon as a surrogate paradox. The surrogate paradox also means that the sign of the treatment effect on the true end point is unpredictable by the effect signs of both the treatment on the surrogate and the surrogate on the true end point. Then we propose two notions for a consistent surrogate and a strictly consistent surrogate to avoid the surrogate paradox. With the causal network that was presented by Lauritzen, we discuss the conditions for a strong surrogate to be a consistent surrogate and a strictly consistent surrogate. Copyright 2007 Royal Statistical Society.

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We conducted a series of triaxial creep experiments on shale specimens coming from Tournemire, France, using the stress‐stepping method up to failure, at a confining pressure of 80 MPa, on two orientations (parallel and perpendicular to bedding), and at temperatures of 26 and 75 °C. In these week‐long experiments, stress, strains, and P wave ultrasonic velocities were recorded (quasi‐) continuously. The strength at creep failure of Tournemire shale was ~70% higher than the peak strength measured during constant strain rate (~10−7/s) experiments, and failure was reached at larger strains. An overall transition from P wave velocity increase at moderate differential stress to P wave velocity decrease closer to brittle failure was also observed. At a smaller timescale, P wave velocities initially decreased and then increased gradually during each step of creep deformation. The magnitude of these variations showed important (i) stress, (ii) orientation, and (iii) temperature dependences: larger increase was observed for P wave propagating along the main compressive stress orientation, larger decrease for P wave propagating perpendicular to it, and a changing behavior enhanced at a higher temperature. Scanning electron microscopy performed postmortem revealed evidence of time‐dependent pressure solution, localized compaction, crack growth, and sealing/healing. Our data reveal that shale deformation is highly stress sensitive only in a narrow stress domain where stress corrosion cracking‐induced brittle dilatant creep deformation is dominant. At stresses below, pressure solution compaction creep dominates the deformation and shales compact, consolidate, and heal. This has important implications for the mechanics of shallow fault zones and accretionary prisms.

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.