Correlations between sedimentary rock and fossil records may involve a combination of rock-record sampling bias and common response to external forcing. Quantifying their relative importance from incomplete and uncertain proxy data is not trivial given the potential complexity of interactions among the underlying processes. This paper shows how a non-parametric method can be used to detect causal interactions directly from incomplete and irregular time series, by quantifying directional information transfer between variables. A numerical experiment illustrates how estimates of the relative strength, scale, and directionality of coupling can correctly distinguish a common-cause variable from a spurious relationship, even in cases where correlations are misleading. With a joint analysis of Phanerozoic rock and fossil records pending, the method is applied to oxygen, carbon, and sulphur stable isotope records from marine carbonates, identifying complex interactions between climatic changes and the cycling of carbon and sulphur over the Phanerozoic.