Identifiability of Subgroup Causal Effects in Randomized Experiments with Nonignorable Missing Covariates

Although randomized experiments are widely regarded as the gold standard for estimating causal effects, missing data of the pretreatment covariates makes it challenging to estimate the subgroup causal effects. When the missing data mechanism of the covariates is nonignorable, the parameters of interest are generally not pointly identifiable, and we can only get bounds for the parameters of interest, which may be too wide for practical use. In some real cases, we have prior knowledge that some restrictions may be plausible. We show the identifiability of the causal effects and joint distributions for four interpretable missing data mechanisms, and evaluate the performance of the statistical inference via simulation studies. One application of our methods to a real data set from a randomized clinical trial shows that one of the nonignorable missing data mechanisms fits better than the ignorable missing data mechanism, and the results conform to the study's original expert opinions. We also illustrate the potential applications of our methods to observational studies using a data set from a job-training program.Comment: Statistics in Medicine (2014

Identifiability of Normal and Normal Mixture Models With Nonignorable Missing Data

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form, the model is not identifiable without specifying a parametric outcome distribution. Although it is fundamental for valid statistical inference, identifiability under nonignorable missing mechanisms is not established for many commonly-used models. In this paper, we first demonstrate identifiability of the normal distribution under monotone missing mechanisms. We then extend it to the normal mixture and $t$ mixture models with non-monotone missing mechanisms. We discover that models under the Logistic missing mechanism are less identifiable than those under the Probit missing mechanism. We give necessary and sufficient conditions for identifiability of models under the Logistic missing mechanism, which sometimes can be checked in real data analysis. We illustrate our methods using a series of simulations, and apply them to a real-life dataset

Qualitative Evaluation of Associations by the Transitivity of the Association Signs

We say that the signs of association measures among three variables {X, Y, Z} are transitive if a positive association measure between the variable X and the intermediate variable Y and further a positive association measure between Y and the endpoint variable Z imply a positive association measure between X and Z. We introduce four association measures with different stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us to draw conclusions about the signs of the association measures between X and Z based only on two separate studies about {X, Y} and {Y, Z}.Comment: Statistica Sinica 201

Principal causal effect identification and surrogate endpoint evaluation by multiple trials

Principal stratification is a causal framework to analyze randomized experiments with a post-treatment variable between the treatment and endpoint variables. Because the principal strata defined by the potential outcomes of the post-treatment variable are not observable, we generally cannot identify the causal effects within principal strata. Motivated by a real data set of phase III adjuvant colon clinical trials, we propose approaches to identifying and estimating the principal causal effects via multiple trials. For the identifiability, we remove the commonly-used exclusion restriction assumption by stipulating that the principal causal effects are homogeneous across these trials. To remove another commonly-used monotonicity assumption, we give a necessary condition for the local identifiability, which requires at least three trials. Applying our approaches to the data from adjuvant colon clinical trials, we find that the commonly-used monotonicity assumption is untenable, and disease-free survival with three-year follow-up is a valid surrogate endpoint for overall survival with five-year follow-up, which satisfies both the causal necessity and the causal sufficiency. We also propose a sensitivity analysis approach based on Bayesian hierarchical models to investigate the impact of the deviation from the homogeneity assumption

Synthesis and thermodynamic characterization of free and surface water of colloidal unimolecular polymer (CUP) particles utilizing DSC and TGA

“Colloidal Unimolecular Polymer (CUP) is spheroidal nanoscale polymer particle (3-9 nm) with charged hydrophilic gruops on the surface and a hydrophobic core. The formation of CUPs involves a simple free radical polymerization and a water reduction process. CUPs are thermodynamically stable in water, molecular weight, particle size and charge density can be designed and controlled. CUPs have a layer of surface associated water, due to the small particle size, the surface water/CUP volume ratio is ultra-high. Therefore, CUP is a very promising candidate to investigate the thermodynamic of surface water characteristics. In addition, CUP solution is free of surfactant and has zero volatile content, which exhibit great potential in coatings applications. DSC evaluation was performed to determine the characteristics of surface water. Surface water thickness varies from 0.427 to 0.766 nm, and it is charge density dependent. The surface water has a larger density than free water and increased with the increase in surface charge density. The specific heat of surface water was found to be 3.04~3.07 J/g·K at 253.15 K and 3.07~3.09 J/g·K at 293.15 K, which was larger than ice but smaller than free water. The average area occupied by carboxylate and ester groups on the CUP surface were determined to be 0.287 nm2 and 0.374 nm2. The evaporation rate of CUP solutions was investigated by TGA, results showed that CUP was capable to increase the evaporation rate of free water due to the deformation of air-water interface, caused by electrostatic repulsion. Surface water presented a much slower evaporation rate compared with free water, and did not evaporate until there is no free water. Thus, CUP was able to be used as an additive to give freeze thaw stability, wet edge retention and open time for coatings”--Abstract, page i

Mobile Formation Coordination and Tracking Control for Multiple Non-holonomic Vehicles

This paper addresses forward motion control for trajectory tracking and mobile formation coordination for a group of non-holonomic vehicles on SE(2). Firstly, by constructing an intermediate attitude variable which involves vehicles' position information and desired attitude, the translational and rotational control inputs are designed in two stages to solve the trajectory tracking problem. Secondly, the coordination relationships of relative positions and headings are explored thoroughly for a group of non-holonomic vehicles to maintain a mobile formation with rigid body motion constraints. We prove that, except for the cases of parallel formation and translational straight line formation, a mobile formation with strict rigid-body motion can be achieved if and only if the ratios of linear speed to angular speed for each individual vehicle are constants. Motion properties for mobile formation with weak rigid-body motion are also demonstrated. Thereafter, based on the proposed trajectory tracking approach, a distributed mobile formation control law is designed under a directed tree graph. The performance of the proposed controllers is validated by both numerical simulations and experiments

Probing gravitational non-minimal coupling with dark energy surveys

We investigate observational constraints on a specific one-parameter extension to the minimal quintessence model, where the quintessence field acquires a quadratic coupling to the scalar curvature through a coupling constant $\xi$. The value of $\xi$ is highly suppressed in typical tracker models if the late-time cosmic acceleration is driven at some field values near the Planck scale. We test $\xi$ in a second class of models in which the field value today becomes a free model parameter. We use the combined data from type-Ia supernovae, cosmic microwave background, baryon acoustic oscillations and matter power spectrum, to weak lensing measurements and find a best-fit value $\xi > 0.289$ where $\xi = 0$ is excluded outside the 95 per cent confidence region. The effective gravitational constant $G_{\rm eff}$ subject to the hint of a non-zero $\xi$ is constrained to $-0.003 < 1- G_{\rm eff}/G < 0.033$ at the same confidence level on cosmological scales, and can be narrowed down to $1- G_{\rm eff}/G < 2.2 \times 10^{-5}$ when combining with Solar System tests.Comment: Context extended, figures and references added, title changed to match with accepted version for publicatio