The DIAS: quantifying coupled curve intersections in pharmacology, ecology, demography, and climatology

Abstract The comparison of coupled curves arises in many applied sciences. In vascular physiology, researchers ask how mediator production and vascular relaxation intersect as the concentration of a signalling molecule changes. In ecology, they ask when predator consumption and prey survival are balanced. In demography, they ask when the urban population surpasses the rural population. In all these cases, the point of intersection between two curves is often assessed visually, without formal uncertainty quantification. The Dias’ Intercept Analysis System (DIAS) is a practical framework for estimating the intersection point of two coupled curves and for comparing that point. The DIAS treats the intersection as a bivariate random vector, propagates uncertainty via the Delta Method, and provides a calibrated comparison through a parametric bootstrap procedure. Monte Carlo simulations show that the DIAS estimator is approximately unbiased and that its confidence intervals achieve coverage close to the nominal level. The method is illustrated through applications in pharmacology, ecology, demography, and climatology. In each case, the DIAS provides an estimate of the intersection point with interpretable uncertainty, allowing comparisons that would be difficult to make reliably by visual inspection alone. A free, open-source Shiny application makes it accessible to researchers without programming expertise.