Volume 6, Issue 2

In this paper we present a continuous extension for longitudinal analysis settings of the recently proposed Covariate Balancing Propensity Score (CBPS) methodology. While extensions of the CBPS methodology to both marginal structural models and general treatment regimes have been proposed, these extensions have been kept separately. We propose to bring them together using the generalized method of moments to estimate inverse probability weights such that after weighting the association between time-varying covariates and the treatment is minimized. A simulation analysis confirms the correlation-breaking performance of the proposed technique. As an empirical application we look at the impact the gradual roll-out of Seguro Popular, a universal health insurance program, has had on the resources available for the provision of healthcare services in Mexico.

An important goal in causal inference is to achieve balance in the covariates among the treatment groups. In this article, we introduce the concept of distributional balance preserving which requires the distribution of the covariates to be the same in different treatment groups. We also introduce a new balance measure called kernel distance, which is the empirical estimate of the probability metric defined in the reproducing kernel Hilbert spaces. Compared to the traditional balance metrics, the kernel distance measures the difference in the two multivariate distributions instead of the difference in the finite moments of the distributions. Simulation results show that the kernel distance is the best indicator of bias in the estimated casual effect compared to several commonly used balance measures. We then incorporate kernel distance into genetic matching, the state-of-the-art matching procedure and apply the proposed approach to analyze the Early Dieting in Girls study. The study indicates that mothers’ overall weight concern increases the likelihood of daughters’ early dieting behavior, but the causal effect is not significant.

In randomized trials in which two treatment arms are compared with a binary outcome, the causal effect can be identified by assuming that the two treatment arms are exchangeable. In trials with an ordinal outcome, which is categorized as more than two, the causal effect can be identified by assuming that the potential outcomes are independent and that the two treatment arms are exchangeable. In this article, we propose a Bayesian approach to causal inference that does not rely on these two assumptions. To achieve this purpose, we use a randomization-based approach and response type. Then, the likelihood function is derived by physical randomization in which subjects who belong to a response type are randomly assigned to the treatment or control, with no modeling assumption on the outcome. Our approach can derive not only the posterior distribution of the causal effect but also that of the number of subjects in each response type. The proposed approach is illustrated with two examples from randomized clinical trials.

Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania.

An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system’s underlying causal structure. To this end, Invariant Causal Prediction (ICP) [1] has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence. In this work, we present and evaluate an array of methods for nonlinear and nonparametric versions of ICP for learning the causal parents of given target variables. We find that an approach which first fits a nonlinear model with data pooled over all environments and then tests for differences between the residual distributions across environments is quite robust across a large variety of simulation settings. We call this procedure “invariant residual distribution test”. In general, we observe that the performance of all approaches is critically dependent on the true (unknown) causal structure and it becomes challenging to achieve high power if the parental set includes more than two variables. As a real-world example, we consider fertility rate modeling which is central to world population projections. We explore predicting the effect of hypothetical interventions using the accepted models from nonlinear ICP. The results reaffirm the previously observed central causal role of child mortality rates.

We extend the inference procedure for the synthetic control method in two ways. First, we propose parametric weights for the p-value that includes the equal weights benchmark of Abadie et al. [1]. By changing the value of this parameter, we can analyze the sensitivity of the test’s result to deviations from the equal weights benchmark. Second, we modify the RMSPE statistic to test any sharp null hypothesis , including, as a specific case, the null hypothesis of no effect whatsoever analyzed by Abadie et al. [1]. Based on this last extension, we invert the test statistic to estimate confidence sets that quickly show the point-estimates’ precision, and the test’s significance and robustness. We also extend these two tools to other test statistics and to problems with multiple outcome variables or multiple treated units. Furthermore, in a Monte Carlo experiment, we find that the RMSPE statistic has good properties with respect to size, power and robustness. Finally, we illustrate the usefulness of our proposed tools by reanalyzing the economic impact of ETA’s terrorism in the Basque Country, studied first by Abadie and Gardeazabal [2] and Abadie et al. [3].

Non-manipulable factors, such as gender or race have posed conceptual and practical challenges to causal analysts. On the one hand these factors do have consequences, and on the other hand, they do not fit into the experimentalist conception of causation. This paper addresses this challenge in the context of public debates over the health cost of obesity, and offers a new perspective, based on the theory of Structural Causal Models (SCM).