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.

Theory of intermittency applied to classical pathological cases

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations

Proof theory for lattice-ordered groups

Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain. Completeness is also established for an analytic (cut-free) hypersequent calculus using cut elimination and it is proved that the equational theory of the variety is co-NP complete.

Evaluation of public information countermeasures. Analytic study number 7.

National Highway Traffic Safety Administration, Washington, D.C.

Patrol activity - Utah ASAP. Analytic study number three. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Analysis of alcohol rehabilitation activities. Section II - volume 6. Analytic study number 6. Final report.

National Highway Traffic Safety Administration, Office of Driver and Pedestrian Programs, Washington, D.C.

Driver diagnosis and referral activity. Analytic study number five. Final report.

Mode of access: Internet.

Rehabilitation system. Analytic study number six.

National Highway Traffic Safety Administration, Washington, D.C.

Analytic study number six: rehabilitation system; Utah ASAP.

Utah Department of Public Safety, Salt Lake City

ASAP public information and education. Analytic study number seven. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Project impact on ultimate performance measures - Utah ASAP. Analytic study number one. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Analytic study number four: impact on judicial disposition on DUI offenders - Utah ASAP. Final report.

Utah Department of Public Safety, Salt Lake City

A practical grammar of the English language : in which the principles established by Lindley Murray, are inculcated, and the theory of modes clearly illustrated by diagrams, representing the number of tenses in each mode, their signs and the manner in which they are formed /

Williamson,

Calculated atomic photoeffect cross sections by modified Stobbe theory for atomic number from Z=2 through Z=50, add photon energies between 0.5 keV and 40.0 keV.

Mode of access: Internet.