Semiparametric Theory for Causal Mediation Analysis: efficiency bounds, multiple robustness, and sensitivity analysis

Whilst estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of the exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies, that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.

An introduction to low-level analysis methods of DNA microarray data

This article gives an overview over the methods used in the low--level analysis of gene expression data generated using DNA microarrays. This type of experiment allows to determine relative levels of nucleic acid abundance in a set of tissues or cell populations for thousands of transcripts or loci simultaneously. Careful statistical design and analysis are essential to improve the efficiency and reliability of microarray experiments throughout the data acquisition and analysis process. This includes the design of probes, the experimental design, the image analysis of microarray scanned images, the normalization of fluorescence intensities, the assessment of the quality of microarray data and incorporation of quality information in subsequent analyses, the combination of information across arrays and across sets of experiments, the discovery and recognition of patterns in expression at the single gene and multiple gene levels, and the assessment of significance of these findings, considering the fact that there is a lot of noise and thus random features in the data. For all of these components, access to a flexible and efficient statistical computing environment is an essential aspect.