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A concentration index, a standardised covariance between a health variable and relative income ranks, is often used to quantify income-related health inequalities. There is a lack of formal approach to study the effect of an exposure, e.g., education, on such measures of inequality. In this paper we contribute by filling this gap and developing the necessary theory and method. Thus, we define a counterfactual concentration index for different levels of an exposure. We give conditions for the identification of this complex estimand, and then deduce its efficient influence function. This allows us to propose estimators, which are regular asymptotic linear under certain conditions. In particular, we show that these estimators are (Formula presented) -consistent and asymptotically normal, as well as locally efficient. The implementation of the estimators is based on the fit of several nuisance functions. The estimators proposed have rate robustness properties allowing for convergence rates slower than (Formula presented) -rate for some of the nuisance function fits. The relevance of the asymptotic results for finite samples is studied with simulation experiments. We also present a case study of the effect of education on income-related health inequalities for a Swedish cohort.

Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. Classical fairness notions, most notably Statistical Parity (SP), demand that predictions be independent of the protected attributes, but are overly restrictive when these attributes influence mediating variables that are considered business necessities. Recent causal formulations relax SP by distinguishing allowed from not-allowed causal paths and by complementing SP with Predictive Parity (PP), requiring the predictor to replicate the legitimate influence of business necessities. Existing path-based definitions are mainly practical when applied to categorical attributes. This paper introduces a new framework for fairness in structural causal models that is tailored to continuous protected attributes. We formalize SP and PP through path-specific partial derivatives, establish conditions under which these criteria coincide with prior causal definitions, and characterize when a fair predictor, one that satisfies SP along not-allowed paths while achieving PP along allowed paths, exists. Building on this theory, we propose a fair tuning algorithm that either constructs such a predictor or, when not possible, allows for a trade-off between SP and PP. We present experiments on simulated and real data to evaluate our proposal, compare it with previously proposed methods, and show that it performs better when PP is considered.

Novel estimators of causal effects for categorical and continuous treatments are proposed by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent and asymptotically normal for causal contrasts of interest, either when the model explaining the treatment assignment is correctly specified, or when the correct set of bases for the outcome models has been chosen and the assignment model is sufficiently rich. For the categorical treatment case, the estimator attains the semiparametric efficiency bound when all models are correctly specified. For the continuous case, the causal parameter of interest is a function of the treatment dose. The latter is not parametrized and the estimators proposed are shown to have bias and variance of the classical nonparametric rate. Asymptotic results are complemented with simulations illustrating the finite sample properties. A data analysis suggests a nonlinear effect of BMI on self-reported health decline among the elderly.

Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data-generating processes when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These methods typically require that all the confounders are observed to ensure identification of the effects. We contribute by showing how valid semiparametric inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We propose uncertainty intervals that allow for unobserved confounding, and show that the resulting inference is valid when the amount of unobserved confounding is not arbitrarily large; the latter is formalized in terms of convergence rates. Simulation experiments illustrate the finite sample properties of the proposed intervals. Finally, a case study on the effect of smoking during pregnancy on birth weight is used to illustrate the use of the methods introduced to perform an informed sensitivity analysis to the presence of unobserved confounding.

This article presents methods to study the causal effect of a binary treatment on a functional outcome with observational data. We define a Functional Average Treatment Effect (FATE) and develop an outcome regression estimator. We show how to obtain valid inference on the FATE using simultaneous confidence bands, which cover the FATE with a given probability over the entire domain. Simulation experiments illustrate how the simultaneous confidence bands take the multiple comparison problem into account. Finally, we use the methods to infer the effect of early adult location on subsequent income development for one Swedish birth cohort.

Convolutional neural networks (CNN) have been successful in machine learning applications including image classification. When it comes to images, their success relies on their ability to consider the space invariant local features in the data. Here, we consider the use of CNN to fit nuisance models in semiparametric estimation of a one dimensional causal parameter: the average causal effect of a binary treatment. In this setting, nuisance models are functions of pre-treatment covariates that need to be controlled for. In an application where we want to estimate the effect of early retirement on a health outcome, we propose to use CNN to control for time-structured covariates. Thus, CNN is used when fitting nuisance models explaining the treatment assignment and the outcome. These fits are then combined into an augmented inverse probability weighting estimator yielding efficient and uniformly valid inference. Theoretically, we contribute by providing rates of convergence for CNN equipped with the rectified linear unit activation function and compare it to an existing result for feedforward neural networks. We also show when those rates guarantee uniformly valid inference for the proposed estimator. A Monte Carlo study is provided where the performance of the proposed estimator is evaluated and compared with other strategies. Finally, we give results on a study of the effect of early retirement on later hospitalization using a database covering the whole Swedish population.

Background: The COVID-19 control policies might negatively impact older adults’ participation in volunteer work, instrumental support provision, and the likelihood of receiving instrumental support. Studies that quantify changes in these activities and the related factors are limited. The current study aimed to examine the level of volunteering, instrumental support provision and receipt before and during the first phase of the COVID-19 pandemic in Europe and to determine whether older adults’ volunteering, instrumental support provision and receipt were associated with individual exposure to COVID-19 and the stringency of country’s COVID-19 control policy during the first phase of the COVID-19 pandemic.

Methods: A cross-sectional survey using data from the Survey of Health, Ageing and Retirement in Europe (SHARE) Corona Survey 1 was designed to focus on community-dwelling Europeans aged ≥50 years. History of participation in volunteering work and instrumental support provision or receipt was assessed from the previous SHARE Wave data. The country’s COVID-19 control policy stringency index (S-Index) was from the Oxford COVID-19 Government Response Tracker database. A total of 45,669 respondents from 26 European countries were included in the volunteering analysis. Seventeen European countries were included in the analyses of instrumental support provision (N = 36,518) and receipt (N = 36,526). The multilevel logistic regression model was fitted separately to analyse each activity.

Results: The level of volunteering and instrumental support provision was lower during the pandemic, but instrumental support receipt was higher. The country S-Index was positively associated with support provision (OR:1.13;95%CI:1.02–1.26) and negatively associated with support receipt (OR:0.69;95%CI:0.54–0.88). Exposure to COVID-19 was positively associated with support receipt (OR:1.64;95%CI:1.38–1.95). COVID-19 exposure on close ones positively associated with volunteering (OR:1.47;95%CI:1.32–1.65), support provision (OR:1.28;95%CI:1.19–1.39), and support receipt (OR:1.25;95%CI:1.15–1.35).

Conclusions: The COVID-19 pandemic impacted older Europeans’ volunteering, instrumental support provision, and instrumental support receipt from outside their household. When someone close to them was exposed to COVID-19, older Europeans were likely to receive instrumental support and to volunteer and provide instrumental support. A stricter country’s COVID-19 control policy might motivate older adults to provide instrumental support, but it prevents them from receiving instrumental support from outside their households. 

Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework:  the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We provide the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We demonstrate that neither of the identification models provides uniformly the most efficient estimation and give conditions under which some bounds are lower than others. We show when semiparametric estimating equation estimators based on influence functions  attain the bounds, and study the robustness of the estimators to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Our results show that this choice implies a trade-off between efficiency and robustness to misspecification of the nuisance models. 

Causality is relatively unexplored in robotics even if it is highly relevant, in several respects. In this paper, we study how a robot’s causal understanding can be improved by allowing the robot to ask humans causal questions. We propose a general algorithm for selecting direct causal effects to ask about, given a partial causal representation (using partially directed acyclic graphs, PDAGs) obtained from observational data. We propose three versions of the algorithm inspired by different causal discovery techniques, such as constraint-based, score-based, and interventions. We evaluate the versions in a simulation study and our results show that asking causal questions improves the causal representation over all simulated scenarios. Further, the results show that asking causal questions based on PDAGs discovered from data provides a significant improvement compared to asking questions at random, and the version inspired by score-based techniques performs particularly well over all simulated experiments.

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.