We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To account for uncertainty in both structure and parameters, we introduce a flexible family of prior distributions over staged trees. These include product partition models to encourage parsimony, a novel distance-based prior to promote interpretable dependence patterns, and an extension that incorporates continuous covariates into the learning process. Posterior inference is achieved via a tailored Markov Chain Monte Carlo algorithm with split-and-merge moves, yielding posterior samples of staged trees from which average treatment effects and uncertainty measures are derived. Posterior summaries and uncertainty measures are obtained via techniques from the Bayesian nonparametrics literature. Two case studies on electronic fetal monitoring and cesarean delivery and on anthracycline therapy and cardiac dysfunction in breast cancer illustrate the methods.
Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the equivalence class of a given staged tree. Here, two staged trees are said to be statistically equivalent when they represent the same set of distributions. Probabilistic graphical models such as staged trees are increasingly being used for causal analyses. Staged trees which are within the same equivalence class can encode very different causal hypotheses but data al…
IE University（IE大学）；Universitat de València（瓦伦西亚大学）
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents non-symmetric conditional independences via vertex coloring. However, since they are based on a tree representation of the sample space, the underlying graph becomes cluttered and difficult to visualize as the number of variables increases. Here we introduce the first structural learning algorithms for the class of simple staged trees, entertaining a compact coa…
Universitat de València（瓦伦西亚大学）；Università degli Studi di Genova（热那亚大学）；IE University（IE大学）
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they can be seen as a special case of the much more general class of models called staged trees, which can represent any type of non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of the staged tree, which can be used to read conditional independences in an i…
IE University（IE大学）；Universitat de València（瓦伦西亚大学）
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between categorical variables. We provide a first graphical representation of the equivalence class of a staged tree, by looking only at a specific subset of its underlying independences. We further define a new pre-metric, inspired by the widely used structural intervention distance, to quantify the closeness between two staged trees in terms of their correspondin…
Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to account for uncertainty induced by error correction when fitting an exposure-response function (ERF). To remedy these def…
We present a new framework for learning Granger causality networks for multivariate categorical time series, based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective, non-identifiability, and presence of many local optima. To circumvent these problems, we recast inference in the MTD as a convex problem. The new formulation facilitates the application of MTD to high-dimensional multivariate time series. As a baseline, we also formulate a multi-output logistic autoregressive model (mLTD), which while a straightforward extension of autoregre…
Unmeasured confounding is a threat to causal inference in observational studies. In recent years, use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a longstanding tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao et al. (2018) have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to nonparametrically identify the average treatment effect (…
Causal discovery for quantitative data has been extensively studied but less is known for categorical data. We propose a novel causal model for categorical data based on a new classification model, termed classification with optimal label permutation (COLP). By design, COLP is a parsimonious classifier, which gives rise to a provably identifiable causal model. A simple learning algorithm via comparing likelihood functions of causal and anti-causal models suffices to learn the causal direction. Through experiments with synthetic and real data, we demonstrate the favorable performance of the pro…
Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large parameter space and the difficulty in searching for a sparse structure. In this article, we develop a maximum penalized likelihood method to tackle this problem. Instead of the commonly used multinomial distribution, we model the conditional distribution of a node given its parents by multi-logit regression, in which an edge is parameterized by a set of coefficient …
Causal discovery for purely observational, categorical data is a long-standing challenging problem. Unlike continuous data, the vast majority of existing methods for categorical data focus on inferring the Markov equivalence class only, which leaves the direction of some causal relationships undetermined. This paper proposes an identifiable ordinal causal discovery method that exploits the ordinal information contained in many real-world applications to uniquely identify the causal structure. The proposed method is applicable beyond ordinal data via data discretization. Through real-world and …
The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, estimation of causal effects requires additional assumptions and techniques, the implementations of which have varied across disciplines. This paper reviews current methods, and it identifies and contrasts the treatment effects that each one …
Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic interaction which acknowledges asymmetries of the kind "factor A interferes with factor B, but not viceversa". A class of tests for mechanistic interaction is proposed, which works on discrete or continuous causal variables, in any combination. Conditions under which these tests can be applied under a generic regime of data collection, be it interventional …
Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix. Likely each of these two matrices simultaneously embraces heterogeneous data types: continuous, discrete and categorical. Here a matrix is used as a practical platform to ideally keep hidden dependency among/between subjects and features intact on its lattice. Response and covariate dependency is individually computed and expressed through mutliscale blocks via …
Causal decomposition analysis provides a way to identify mediators that contribute to health disparities between marginalized and non-marginalized groups. In particular, the degree to which a disparity would be reduced or remain after intervening on a mediator is of interest. Yet, estimating disparity reduction and remaining might be challenging for many researchers, possibly because there is a lack of understanding of how each estimation method differs from other methods. In addition, there is no appropriate estimation method available for a certain setting (i.e., a regression-based approach …
Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. In this paper we present an analogous decomposition of the \textit{population intervention effect}, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct an…
Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if ?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is in general not identifiable from the observed factual distribution. Nevertheless, in this work, we show that under the as…
This research was motivated by studying anti-drug antibody (ADA) formation and its potential impact on long-term benefit of a biologic treatment in a randomized controlled trial, in which ADA status was not only unobserved in the control arm but also in a subset of patients from the experimental treatment arm. Recent literature considers the principal stratum estimand strategy to estimate treatment effect in groups of patients defined by an intercurrent status, i.e. in groups defined by a post-randomization variable only observed in one arm and potentially associated with the outcome. However,…
Continuous treatments have posed a significant challenge for causal inference, both in the formulation and identification of scientifically meaningful effects and in their robust estimation. Traditionally, focus has been placed on techniques applicable to binary or categorical treatments with few levels, allowing for the application of propensity score-based methodology with relative ease. Efforts to accommodate continuous treatments introduced the generalized propensity score, yet estimators of this nuisance parameter commonly utilize parametric regression strategies that sharply limit the ro…
Causal mediation analysis has historically been limited in two important ways: (i) a focus has traditionally been placed on binary treatments and static interventions, and (ii) direct and indirect effect decompositions have been pursued that are only identifiable in the absence of intermediate confounders affected by treatment. We present a theoretical study of an (in)direct effect decomposition of the population intervention effect, defined by stochastic interventions jointly applied to the treatment and mediators. In contrast to existing proposals, our causal effects can be evaluated regardl…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching methods do not pass basic sanity checks: they fail when irrelevant variables are introduced, and tend to be either computationally slow or produce low-quality matches. The method proposed in this work aims to match units on a weighted Hamming distance, taking into account the relative importance of the covariates; the algorithm aims to match units on as many …
We propose a new approach for estimating causal effects when the exposure is measured with error and confounding adjustment is performed via a generalized propensity score (GPS). Using validation data, we propose a regression calibration (RC)-based adjustment for a continuous error-prone exposure combined with GPS to adjust for confounding (RC-GPS). The outcome analysis is conducted after transforming the corrected continuous exposure into a categorical exposure. We consider confounding adjustment in the context of GPS subclassification, inverse probability treatment weighting (IPTW) and match…
Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments
Didi Chuxing（滴滴出行）；School of Statistics, East China Normal University（华东师范大学统计学院）；School of Mathematics and Statistics, Beijing Jiaotong University（北京交通大学数学与统计学院）；School of Statistics and Data Science, Shanghai University of Finance and Economics（上海财经大学统计与数据科学学院）；Institute of Data Science and Statistics, Shanghai University of Finance and Economics（上海财经大学数据科学与统计研究院）
Uncertainty in the estimation of the causal effect in observational studies is often due to unmeasured confounding, i.e., the presence of unobserved covariates linking treatments and outcomes. Instrumental Variables (IV) are commonly used to reduce the effects of unmeasured confounding. Existing methods for IV estimation either require strong parametric assumptions, use arbitrary distance metrics, or do not scale well to large datasets. We propose a matching framework for IV in the presence of observed categorical confounders that addresses these weaknesses. Our method first matches units exac…
