Mediation analysis aims at disentangling the effects of a treatment on an outcome through alternative causal mechanisms and has become a popular practice in biomedical and social science applications. The causal framework based on counterfactuals is currently the standard approach to mediation, with important methodological advances introduced in the literature in the last decade, especially for simple mediation, that is with one mediator at the time. Among a variety of alternative approaches, Imai et al. showed theoretical results and developed an R package to deal with simple mediation as well as with multiple mediation involving multiple mediators conditionally independent given the treatment and baseline covariates. This approach does not allow to consider the often encountered situation in which an unobserved common cause induces a spurious correlation between the mediators. In this context, which we refer to as mediation with uncausally related mediators, we show that, under appropriate hypothesis, the natural direct and joint indirect effects are non-parametrically identifiable. Moreover, we adopt the quasi-Bayesian algorithm developed by Imai et al. and propose a procedure based on the simulation of counterfactual distributions to estimate not only the direct and joint indirect effects but also the indirect effects through individual mediators. We study the properties of the proposed estimators through simulations. As an illustration, we apply our method on a real data set from a large cohort to assess the effect of hormone replacement treatment on breast cancer risk through three mediators, namely dense mammographic area, nondense area and body mass index.

Background Menopausal hormone therapy (MHT) is a risk factor for breast cancer (BC). Evidence suggests that its effect on BC risk could be partly mediated by mammographic density. The aim of this study was to investigate the relationship between MHT, mammographic density and BC risk using data from a prospective study. Methods We used data from a case-control study nested within the French cohort E3N including 453 cases and 453 matched controls. Measures of mammographic density, history of MHT use during follow-up and information on potential confounders were available for all women. The association between MHT and mammographic density was evaluated by linear regression models. We applied mediation modelling techniques to estimate, under the hypothesis of a causal model, the proportion of the effect of MHT on BC risk mediated by percent mammographic density (PMD) for BC overall and by hormone receptor status. Results Among MHT users, 4.2% used exclusively oestrogen alone compared with 68.3% who used exclusively oestrogens plus progestogens. Mammographic density was higher in current users (for a 60-year-old woman, mean PMD 33%; 95% CI 31 to 35%) than in past (29%; 27 to 31%) and never users (24%; 22 to 26%). No statistically significant association was observed between duration of MHT and mammographic density. In past MHT users, mammographic density was negatively associated with time since last use; values similar to those of never users were observed in women who had stopped MHT at least 8 years earlier. The odds ratio of BC for current versus never MHT users, adjusted for age, year of birth, menopausal status at baseline and BMI, was 1.67 (95% CI, 1.04 to 2.68). The proportion of effect mediated by PMD was 34% for any BC and became 48% when the correlation between BMI and PMD was accounted for. These effects were limited to hormone receptor-positive BC. Conclusions Our results suggest that, under a causal model, nearly half of the effect of MHT on hormone receptor-positive BC risk is mediated by mammographic density, which appears to be modified by MHT for up to 8 years after MHT termination.

Purpose Anorexia nervosa (AN) is a life-threatening condition in which temperament, anxiety, depression, and core AN body-related psychopathology (drive for thinness, DT, and body dissatisfaction, BD) are intertwined. This relationship has not been to date disentangled; therefore, we performed a multiple mediation analysis aiming to quantify the effect of each component. Methods An innovative multiple mediation statistical method has been applied to data from 184 inpatients with AN completing: Temperament Evaluation of Memphis, Pisa, Paris, and San Diego Autoquestionnaire, Eating Disorders Inventory-2, State-Trait Anxiety Inventory, and Beck Depression Inventory. Results All affective temperaments but the hyperthymic one were involved in the relationship with DT and BD. Only the anxious temperament had a significant unmediated direct effect on DT after the strictest correction for multiple comparisons, while the depressive temperament had a significant direct effect on DT at a less strict significance level. State anxiety was the strongest mediator of the link between affective temperament and core AN body-related psychopathology. Depression showed intermediate results while trait anxiety was not a significant mediator at all. Conclusion Affective temperaments had a relevant impact on body-related core components of AN; however, a clear direct effect could be identified only for the anxious and depressive temperaments. Also, state anxiety was the strongest mediator thus entailing interesting implications in clinical practice. Level of evidence V, cross-sectional study.

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BACKGROUND: Menopausal hormone therapy (MHT) is a risk factor for breast cancer (BC). Evidence suggests that its effect on BC risk could be partly mediated by mammographic density. The aim of this study is to investigate the relationship between MHT, mammographic density and BC risk using data from a prospective study.METHODS: The data analyzed refer to a case-control study nested into the French cohort E3N and include 453 cases and 453 matched controls. A quantitative measure of mammographic density, a detailed history of MHT use during follow-up and information on potential confounders were available for all women. The association of mammographic density with MHT duration and time since last use was evaluated by linear regression models. Mediation modelling techniques were applied to estimate under the hypothesis of a causal model the proportion of the effect of MHT on BC risk mediated by percent mammographic density for BC overall and by ER/PR status.RESULTS: Mammographic density was higher in current (mean percent mammographic density 33%; 95% CI: 31–35%) than in former (29%; 95% CI 27% to 31) and never users (24%; 95% CI, 22–26%). Mammographic density increased with the duration of MHT within one year of therapy and reached a steady state thereafter. After discontinuation of the therapy, mammographic density decreased with time since last use and reached values similar to those of never users after 8 years. The OR of BC for current versus never MHT users, adjusted for age, year of birth, menopausal status at baseline and BMI, was 1.67 (95% CI, 1.04 to 2.68). The proportion of effect mediated by percent mammographic density was 34% on the log scale for any BC and became 48% when the correlation between BMI and percent mammographic density was accounted for. These results are limited to hormone receptor positive BCs.CONCLUSIONS: Our results suggest that under a causal model the effect of MHT on BC risk was partially mediated by MD that appeared to be modified by MHT for up to 8 years after MHT termination.