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.

Spinal Muscular Atrophy: position and functional importance of the branch site preceding SMN exon 7

In spinal muscular atrophy, the SMN1 gene is deleted or destroyed by mutation, while the neigbouring, nearly identical SMN2 gene acts as a partial functional substitute. However, due to a single nucleotide exchange, the seventh exon of SMN2 is mostly excluded from the mature mRNA, and the resulting shorter protein is non-functional. Here, we map the previously uncharacterised intron 6 branch point by RT-PCR. Moreover we show that exon 7 inclusion can be either abolished or improved by mutations in this branch site region.

Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Dissecting abdominal aortic aneurysm in Ang II-infused mice: suprarenal branch ruptures and apparent luminal dilatation.

AIMS In this work, we provide novel insight into the morphology of dissecting abdominal aortic aneurysms in angiotensin II-infused mice. We demonstrate why they exhibit a large variation in shape and, unlike their human counterparts, are located suprarenally rather than infrarenally. METHODS AND RESULTS We combined synchrotron-based, ultra-high resolution ex vivo imaging (phase contrast X-Ray tomographic microscopy) with in vivo imaging (high-frequency ultrasound and contrast-enhanced micro-CT) and image-guided histology. In all mice, we observed a tear in the tunica media of the abdominal aorta near the ostium of the celiac artery. Independently we found that, unlike the gradual luminal expansion typical for human aneurysms, the outer diameter increase of angiotensin II-induced dissecting aneurysms in mice was related to one or several intramural haematomas. These were caused by ruptures of the tunica media near the ostium of small suprarenal side branches, which had never been detected by the established small animal imaging techniques. The tear near the celiac artery led to apparent luminal dilatation, while the intramural haematoma led to a dissection of the tunica adventitia on the left suprarenal side of the aorta. The number of ruptured branches was higher in those aneurysms that extended into the thoracic aorta, which explained the observed variability in aneurysm shape. CONCLUSION Our results are the first to describe apparent luminal dilatation, suprarenal branch ruptures, and intramural haematoma formation in dissecting abdominal aortic aneurysms in mice. Moreover, we validate and demonstrate the vast potential of phase contrast X-ray tomographic microscopy in cardiovascular small animal applications.

Comparing the effectiveness of equivalence partitioning, branch testing and code reading by stepwise abstraction applied by subjects

Some verification and validation techniques have been evaluated both theoretically and empirically. Most empirical studies have been conducted without subjects, passing over any effect testers have when they apply the techniques. We have run an experiment with students to evaluate the effectiveness of three verification and validation techniques (equivalence partitioning, branch testing and code reading by stepwise abstraction). We have studied how well able the techniques are to reveal defects in three programs. We have replicated the experiment eight times at different sites. Our results show that equivalence partitioning and branch testing are equally effective and better than code reading by stepwise abstraction. The effectiveness of code reading by stepwise abstraction varies significantly from program to program. Finally, we have identified project contextual variables that should be considered when applying any verification and validation technique or to choose one particular technique.

Sequences upstream of the branch site are required to form helix II between U2 and U6 snRNA in a trans-splicing reaction

Three different base paired stems form between U2 and U6 snRNA over the course of the mRNA splicing reaction (helices I, II and III). One possible function of U2/U6 helix II is to facilitate subsequent U2/U6 helix I and III interactions, which participate directly in catalysis. Using an in vitro trans-splicing assay, we investigated the function of sequences located just upstream from the branch site (BS). We find that these upstream sequences are essential for stable binding of U2 to the branch region, and for U2/U6 helix II formation, but not for initial U2/BS pairing. We also show that non-functional upstream sequences cause U2 snRNA stem–loop IIa to be exposed to dimethylsulfate modification, perhaps reflecting a U2 snRNA conformational change and/or loss of SF3b proteins. Our data suggest that initial binding of U2 snRNP to the BS region must be stabilized by an interaction with upstream sequences before U2/U6 helix II can form or U2 stem–loop IIa can participate in spliceosome assembly.

Tectono-sedimentary evolution of the ’Numidian Formation’ and Lateral Facies (southern branch of the western Tethys): constraints for central-western Mediterranean geodynamics

The origin of the Numidian Formation (latest Oligocene to middle Miocene), characterized by ultra-mature quartzose arenites with abundant well-rounded frosted quartz grains, remains controversial. This formation, sedimented in the external domain of the Maghrebian Flysch Basin, displays three characteristic stratigraphic members with marked longitudinal (proximal–distal) and transverse (along-chain) variations with palaeogeographical importance. The origin of the Numidian supply is related to the outward tectogenetic propagation when a forebulge evolved in the African foreland, leading to the erosion of African cratonic areas rich in quartzose arenites (Nubian Sandstone-like). The ages of the Numidian Formation checked by Betic, Maghrebian and Southern Apennine data suggest a timing for the accretionary orogenic wedge, earlier in the Betic-Rifian Arc (after middle Burdigalian), later in the Algerian-Tunisian Tell (after late Burdigalian) and afterwards in Sicily and the Southern Apennines (after Langhian). A geodynamic evolutionary model for the central-western Mediterranean is proposed.

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