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...

Is the right amount of effort exerted in multiperson tournaments where contestants have two different levels of initial endowments (termed "favorites" and "underdogs")? We develop theoretical predictions for the level of effort and the effect of varying the prize structure. We test these...

The self-consistent mode-coupling approximation of Colaiori and Moore [Phys. Rev. Lett. 86 (2001) 3946] is generalized to the analysis of the Sun–Guo–Grant equation to investigate its dynamic scaling properties in the strong-coupling regime. The corresponding values of the dynamic exponents...