The Confidence Interval Method for Selecting Valid Instrumental Variables

We propose a new method, the confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs overlapping with each other as the set of valid instruments. Under a plurality rule, we show that the resulting standard IV, or two-stage least squares (2SLS) estimator has oracle properties. This result is the same as for the hard thresholding with voting (HT) method of Guo et al. (Journal of the Royal Statistical Society : Series B, 2018, 80, 793–815). Unlike the HT method, the number of instruments selected as valid by the CI method is guaranteed to be monotonically decreasing for decreasing values of the tuning parameter. For the CI method, we can therefore use a downward testing procedure based on the Sargan (Econometrica, 1958, 26, 393–415) test for overidentifying restrictions and a main advantage of the CI downward testing method is that it selects the model with the largest number of instruments selected as valid that passes the Sargan test

The thermal imprint of continental breakup during the formation of the South China Sea

This research used data provided by the International Ocean Discovery Program (IODP).We thanks the participants to IODP Expedition 367-368 as well as the captains and crew of the Joides Resolution. Seismic sections originate from the IODP Expedition 367/368/368X proceeding volume. Platte River Associates, Inc is thanked for providing an academic licence of BasinMod 2D. We acknowledge IODP France and ECORD for the support. Funding for this research was provided by Total SA R&D (J.N. Ferry). SAB gratefully acknowledges NERC award NE/R002576/1; Measuring Rates of Weathered Petroleum Accumulation, South China Sea.Peer reviewedPublisher PD

An examination of multivariable Mendelian randomization in the single-sample and two-sample summary data settings

AbstractBackgroundMendelian Randomisation (MR) is a powerful tool in epidemiology which can be used to estimate the causal effect of an exposure on an outcome in the presence of unobserved confounding, by utilising genetic variants that are instrumental variables (IVs) for the exposure. This has been extended to Multivariable MR (MVMR) to estimate the effect of two or more exposures on an outcome.Methods/ResultsWe use simulations and theory to clarify the interpretation of estimated effects in a MVMR analysis under a range of underlying scenarios, where a secondary exposure acts variously as a confounder, a mediator, a pleiotropic pathway and a collider. We then describe how instrument strength and validity can be assessed for an MVMR analysis in the single sample setting, and develop tests to assess these assumptions in the popular two-sample summary data setting. We illustrate our methods using data from UK biobank to estimate the effect of education and cognitive ability on body mass index.ConclusionMVMR analysis consistently estimates the effect of an exposure, or exposures, of interest and provides a powerful tool for determining causal effects in a wide range of scenarios with either individual or summary level data.</jats:sec

Spontaneous emission and level shifts in absorbing disordered dielectrics and dense atomic gases: A Green's function approach

Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field. The rate of decay and level shifts are determined by the retarded Green's-function of the interacting electric displacement field, which is calculated from a Dyson equation describing multiple scattering. The positions of the atomic dipoles forming the dielectrics are assumed to be uncorrelated and a continuum approximation is used. The associated unphysical interactions between different atoms at the same location is eliminated by removing the point-interaction term from the free-space Green's-function (local field correction). For the case of an atom in a purely dispersive medium the spontaneous emission rate is altered by the well-known Lorentz local-field factor. In the presence of absorption a result different from previously suggested expressions is found and nearest-neighbour interactions are shown to be important.Comment: 6 pages no figure

Evolution of optimal Hill coefficients in nonlinear public goods games

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function