Sensitivity analysis is useful in assessing how robust an association is to potential unmeasured or uncontrolled confounding. This article introduces a new measure called the "E-value," which is related to the evidence for causality in observational studies that are potentially subject to confounding. The E-value is defined as the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment-outcome association, conditional on the measured covariates. A large E-value implies that considerable unmeasured confounding would be needed to explain away an effect estimate. A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. The authors propose that in all observational studies intended to produce evidence for causality, the E-value be reported or some other sensitivity analysis be used. They suggest calculating the E-value for both the observed association estimate (after adjustments for measured confounders) and the limit of the confidence interval closest to the null. If this were to become standard practice, the ability of the scientific community to assess evidence from observational studies would improve considerably, and ultimately, science would be strengthened.

Mediation analysis is a useful and widely employed approach to studies in the field of psychology and in the social and biomedical sciences. The contributions of this paper are several-fold. First we seek to bring the developments in mediation analysis for non linear models within the counterfactual framework to the psychology audience in an accessible format and compare the sorts of inferences about mediation that are possible in the presence of exposure-mediator interaction when using a counterfactual versus the standard statistical approach. Second, the work by VanderWeele and Vansteelandt (2009, 2010) is extended here to allow for dichotomous mediators and count outcomes. Third, we provide SAS and SPSS macros to implement all of these mediation analysis techniques automatically and we compare the types of inferences about mediation that are allowed by a variety of software macros.

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This article provides an overview of recent developments in mediation analysis, that is, analyses used to assess the relative magnitude of different pathways and mechanisms by which an exposure may affect an outcome. Traditional approaches to mediation in the biomedical and social sciences are described. Attention is given to the confounding assumptions required for a causal interpretation of direct and indirect effect estimates. Methods from the causal inference literature to conduct mediation in the presence of exposuremediator interactions, binary outcomes, binary mediators, and case-control study designs are presented. Sensitivity analysis techniques for unmeasured confounding and measurement error are introduced. Discussion is given to extensions to time-to-event outcomes and multiple mediators. Further flexible modeling strategies arising from the precise counterfactual definitions of direct and indirect effects are also described. The focus throughout is on methodology that is easily implementable in practice across a broad range of potential applications.

In this tutorial, we provide a broad introduction to the topic of interaction between the effects of exposures. We discuss interaction on both additive and multiplicative scales using risks, and we discuss their relation to statistical models (e.g. linear, log-linear, and logistic models). We discuss and evaluate arguments that have been made for using additive or multiplicative scales to assess interaction. We further discuss approaches to presenting interaction analyses, different mechanistic forms of interaction, when interaction is robust to unmeasured confounding, interaction for continuous outcomes, qualitative or “crossover” interactions, methods for attributing effects to interactions, case-only estimators of interaction, and power and sample size calculations for additive and multiplicative interaction.