Data-driven Algorithms for Dimension Reduction in Causal Inference

In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the unconfoundedness assumption, i.e., that all confounding variables are observed. The choice of covariates to control for, which is primarily based on subject matter knowledge, may result in a large covariate vector in the attempt to ensure that unconfoundedness holds. However, including redundant covariates can affect bias and efficiency of nonparametric causal effect estimators, e.g., due to the curse of dimensionality. Data-driven algorithms for the selection of sufficient covariate subsets are investigated. Under the assumption of unconfoundedness the algorithms search for minimal subsets of the covariate vector. Based, e.g., on the framework of sufficient dimension reduction or kernel smoothing, the algorithms perform a backward elimination procedure assessing the significance of each covariate. Their performance is evaluated in simulations and an application using data from the Swedish Childhood Diabetes Register is also presented.Comment: 27 pages, 2 figures, 11 table

The Volume Fraction of a Non-overlapping Germ-grain Model

We discuss the volume fraction of a model of non--overlapping convex grains. It is obtained from thinning a Poisson process where each point has a weight and is the centre of a grain, by removing any grain that is overlapped by one of larger or equal weight. In the limit as the intensity of the Poisson process tends to infinity, the model can be identified with the intact grains in the dead leaves model if the weights are independent of the grain sizes. In this case we can show that the volume fraction is at most $1/2^d$ for $d=1$ or $2$ if the shape is fixed, but the size and the orientation are random. The upper bound is achieved for centrally symmetric sets of the same size and orientation. For general $d$ we can show the upper bound, $1/2^d$, for spherical grains with two--point radius distribution. If dependence between weight and size is allowed, it is possible to achieve a volume fraction arbitrarily close to one

The costs and benefits of uniformly valid causal inference with high-dimensional nuisance parameters

Important advances have recently been achieved in developing procedures yielding uniformly valid inference for a low dimensional causal parameter when high-dimensional nuisance models must be estimated. In this paper, we review the literature on uniformly valid causal inference and discuss the costs and benefits of using uniformly valid inference procedures. Naive estimation strategies based on regularisation, machine learning, or a preliminary model selection stage for the nuisance models have finite sample distributions which are badly approximated by their asymptotic distributions. To solve this serious problem, estimators which converge uniformly in distribution over a class of data generating mechanisms have been proposed in the literature. In order to obtain uniformly valid results in high-dimensional situations, sparsity conditions for the nuisance models need typically to be made, although a double robustness property holds, whereby if one of the nuisance model is more sparse, the other nuisance model is allowed to be less sparse. While uniformly valid inference is a highly desirable property, uniformly valid procedures pay a high price in terms of inflated variability. Our discussion of this dilemma is illustrated by the study of a double-selection outcome regression estimator, which we show is uniformly asymptotically unbiased, but is less variable than uniformly valid estimators in the numerical experiments conducted

Toward a Theory of Effective Supranational Adjudication

Supranational adjudication in Europe is a remarkable and surprising success. Europe\u27s two supranational courts -- the European Court of Justice (ECJ) and the European Court of Human Rights (ECHR) -- issue dozens of judgments each year with which defending national governments habitually comply in essentially the same manner as they would with domestic court rulings. These experiences stand in striking contrast to those of many international tribunals past and present. Can the European experience of supranational adjudication be transplanted beyond Europe? Professors Helfer and Slaughter argue that the effectiveness of the ECJ and the ECHR is linked to their power to hear claims brought by private parties directly against national governments or against other private parties. Such supranational jurisdiction has allowed the European courts to penetrate the surface of the state, to forge direct relationships not only with individual citizens but also with distinct government institutions such as national courts. Over time, this penetration and the deepening relationships between supranational jurists and domestic legal actors have led to the evolution of a community of law, a web of nominally apolitical relations among subnational and supranational legal actors. The simple provision of supranational jurisdiction, however, is not a guarantee of effective adjudication. Drawing on the observations of scholars, practitioners, and judges, Professors Helfer and Slaughter develop a checklist of factors that enhance the effectiveness of supranational adjudication. They distinguish among those factors that are within the control of member states; those that are within the control of the judges themselves; and those that may be beyond the control of either states or judges. Isolating the factors in this way provides both a rough metric for evaluating the effectiveness of other supranational tribunals and a potential set of prescriptions for judges on those tribunals seeking to enhance their institutions\u27 effectiveness. After developing the checklist, Professors Helfer and Slaughter use it to analyze the United Nations Human Rights Committee (UNHRC). Although the UNHRC was established expressly as a committee of experts rather than a court, analysis of its recent practice reveals that it is becoming increasingly court-like. Moreover, within the constraints imposed by severely limited resources, UNHRC members are independently following many of the checklist prescriptions for increased effectiveness. The next step is for the organization to enter into a sustained dialogue with its European counterparts, harmonizing its decisions with theirs in some areas while consciously preserving its own distinctive jurisprudence in others. Structured and regular interaction between these tribunals would add additional voices to an emerging transjudicial conversation, potentially laying the foundation for a global community of law

A Longitudinal Study of Peripheral and Central Auditory Function in Alzheimer’s Disease and in Mild Cognitive Impairment

Background/Aim: Central auditory processing disorder (CAPD) might precede the onset of Alzheimer’s disease (AD). A method of evaluating CAPD is the dichotic digits test (DDT). The aim was to address this in a longitudinal setting. Methods: A total of 136 individuals were assessed with peripheral and central hearing tests at baseline and at 5-year follow-up. Results: Subjects with AD showed a significant decline in DDT scores of the right ear from baseline to follow-up. The other groups retained high DDT scores. Peripheral auditory function declined as expected according to age. Conclusions: Our study indicates that DDT performance reflects an ongoing process resulting in dementia

Identification of novel genetic risk factors of dilated cardiomyopathy: from canine to human

BackgroundDilated cardiomyopathy (DCM) is a life-threatening heart disease and a common cause of heart failure due to systolic dysfunction and subsequent left or biventricular dilatation. A significant number of cases have a genetic etiology; however, as a complex disease, the exact genetic risk factors are largely unknown, and many patients remain without a molecular diagnosis.MethodsWe performed GWAS followed by whole-genome, transcriptome, and immunohistochemical analyses in a spontaneously occurring canine model of DCM. Canine gene discovery was followed up in three human DCM cohorts.ResultsOur results revealed two independent additive loci associated with the typical DCM phenotype comprising left ventricular systolic dysfunction and dilatation. We highlight two novel candidate genes, RNF207 and PRKAA2, known for their involvement in cardiac action potentials, energy homeostasis, and morphology. We further illustrate the distinct genetic etiologies underlying the typical DCM phenotype and ventricular premature contractions. Finally, we followed up on the canine discoveries in human DCM patients and discovered candidate variants in our two novel genes.ConclusionsCollectively, our study yields insight into the molecular pathophysiology of DCM and provides a large animal model for preclinical studies

The associations of anthropometric, behavioural and sociodemographic factors with circulating concentrations of IGF-I, IGF-II, IGFBP-1, IGFBP-2, and IGFBP-3 in a pooled analysis of 16,024 men from 22 studies

Insulin‐like growth factors (IGFs) and insulin‐like growth factor binding proteins (IGFBPs) have been implicated in the aetiology of several cancers. To better understand whether anthropometric, behavioural and sociodemographic factors may play a role in cancer risk via IGF signalling, we examined the cross‐sectional associations of these exposures with circulating concentrations of IGFs (IGF‐I and IGF‐II) and IGFBPs (IGFBP‐1, IGFBP‐2 and IGFBP‐3). The Endogenous Hormones, Nutritional Biomarkers and Prostate Cancer Collaborative Group dataset includes individual participant data from 16,024 male controls (i.e. without prostate cancer) aged 22–89 years from 22 prospective studies. Geometric means of protein concentrations were estimated using analysis of variance, adjusted for relevant covariates. Older age was associated with higher concentrations of IGFBP‐1 and IGFBP‐2 and lower concentrations of IGF‐I, IGF‐II and IGFBP‐3. Higher body mass index was associated with lower concentrations of IGFBP‐1 and IGFBP‐2. Taller height was associated with higher concentrations of IGF‐I and IGFBP‐3 and lower concentrations of IGFBP‐1. Smokers had higher concentrations of IGFBP‐1 and IGFBP‐2 and lower concentrations of IGFBP‐3 than nonsmokers. Higher alcohol consumption was associated with higher concentrations of IGF‐II and lower concentrations of IGF‐I and IGFBP‐2. African Americans had lower concentrations of IGF‐II, IGFBP‐1, IGFBP‐2 and IGFBP‐3 and Hispanics had lower IGF‐I, IGF‐II and IGFBP‐3 than non‐Hispanic whites. These findings indicate that a range of anthropometric, behavioural and sociodemographic factors are associated with circulating concentrations of IGFs and IGFBPs in men, which will lead to a greater understanding of the mechanisms through which these factors influence cancer risk