Mediation analysis in causal inference has traditionally focused on binary treatment regimes and deterministic interventions, as well as a decomposition of the average treatment effect in terms of direct and indirect effects. In this paper we present an analogous decomposition of the population intervention effect, defined through stochastic interventions. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct and indirect effects for the population intervention effect requires weaker assumptions than its average treatment effect counterpart. In particular, identification of direct effects is guaranteed in experiments that randomize the treatment and the mediator. We discuss various estimators of the direct and indirect effects, including substitution, re-weighted, and efficient estimators based on flexible regression techniques. Our efficient estimator is asymptotically linear under a condition requiring $n^{\frac{1}{4}}$-consistency of certain regression functions. We perform a simulation study in which we assess the finite-sample properties of our proposed estimators. We present the results of an illustrative study where we assess the effect of participation in a sports team on BMI among children, using mediators such as exercise habits, daily consumption of snacks, and overweight status.

The advent and subsequent widespread availability of preventive vaccines has altered the course of public health in the twentieth century. In spite of the overall success, vaccines are still lacking for many high-burden diseases, including HIV. An important step in the process of developing effective vaccines is identifying immune responses that are indicative of protective efficacy. In this work, we use a causal inference framework to propose a new approach to studying immune responses in the context of vaccines. We focus on causal quantities defined by stochastic interventions, which may be more relevant than alternative approaches for describing the effects of immune responses on risk of infection or disease. We propose methodology for efficiently estimating these quantities using data generated by preventive vaccine trials with two-phase sampling of immune responses. We propose and evaluate two strategies for estimating these quantities: an inverse probability weighting-based method and an augmented method. The latter method is shown to be nonparametric efficient and multiply robust to misspecification of nuisance estimators. We also provide methods for constructing confidence intervals and hypothesis tests, and provide an open source software implementation of the proposed methodology. We illustrate the methods using data from a recent preventive HIV vaccine trial.

We focus on variable importance analysis in high-dimensional biological data sets with modest sample sizes, using semiparametric statistical models. We present a method that is robust in small samples, but does not rely on arbitrary parametric assumptions, in the context of studies of gene expression and environmental exposures. Such analyses are faced not only with issues of multiple testing, but also the problem of teasing out the associations of biological expression measures with exposure, among numerous confounds such as age, race, and smoking. Specifically, we propose the use of targeted minimum loss-based estimation, coupled with generalizations of moderated empirical Bayes statistics, to obtain estimates of variable importance measures. The result is a data-adaptive approach that can estimate individual associations in high-dimensional data, even in the presence of relatively small samples.