The main aim of mediation analysis is to study the direct and indirect effects of an exposure on an outcome. To date, the literature on mediation analysis with multiple mediators has mainly focused on continuous and dichotomous outcomes. However, the development of methods for multiple mediation analysis of survival outcomes is still limited. Here we extend to survival outcomes a method for multiple mediation analysis based on the computation of appropriate weights. The approach considered has the advantages of not requiring specific models for mediators, allowing nonindependent mediators of any nature, and not relying on the assumption of rare outcomes. Simulation studies show good performance of the proposed estimator in terms of bias and coverage probability. The method is further applied to an example from a published study on prostate cancer mortality aimed at understanding the extent to which the effect of DNA methyltransferase 3b (DNMT3b) genotype on mortality was explained by DNA methylation and tumor aggressiveness. This approach can be used to quantify the marginal time-dependent direct and indirect effects carried by multiple indirect pathways, and software code is provided to facilitate its application.

A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When d = 2 this equation reduces to the well known connection between mutual information and entropy of the copula function associated to the original random variables. Hence, the problem of estimating the mutual information of the original random vector is reduced to the estimation of the entropy of a random vector obtained through a multidimensional transformation. The estimator we propose is a two–step method: first estimate the transformation and obtain the transformed sample, then estimate its entropy. The properties of the new estimator are discussed through simulation examples and its performances are compared to those of the best estimators in the literature. The precision of the estimator converges to values of the same order of magnitude of the best estimator tested. However, the new estimator is unbiased even for larger dimensions and smaller sample sizes, while the other tested estimators show a bias in these cases.

Background: Many studies have shown that socioeconomic position (SEP) is associated with the incidence of malignant tumors at different sites. This study aims to estimate the association between educational level (as proxy for SEP) and cancer incidence and to understand whether the observed associations might be partially explained by lifestyle behaviors. Methods: The analyses were performed on data from the European Prospective Investigation into Cancer and Nutrition (EPIC) study, globally and by sex. We used Cox proportional hazards models together with mediation analysis to disentangle the total effect (TE) of educational level [measured through the Relative Index of Inequality (RII)] on cancer incidence into pure direct (PDE) and total indirect (TIE) effect, unexplained and explained by mediators, respectively. PDE and TIE were then combined to compute the proportions mediated (PM). Results: After an average of 14 years of follow-up, 52,422 malignant tumors were ascertained. Low educated participants showed higher risk of developing stomach, lung, kidney (in women), and bladder (in men) cancers, and, conversely, lower risk of melanoma and breast cancer (in post-menopausal women), when compared with more educated participants. Mediation analyses showed that portions of the TE of RII on cancer could be explained by site-specific related lifestyle behaviors for stomach, lung, and breast (in women). Conclusions: Cancer incidence in Europe is determined at least in part by a socioeconomically stratified distribution of risk factors. Impact: These observational findings support policies to reduce cancer occurrence by altering mediators, such as lifestyle behaviors, particularly focusing on underprivileged strata of the population.

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t₁ and of a diffusion process conditioned to cross the boundary for the first time at t₁. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.