Epidemiological evidence is based on multiple data sources including clinical trials, cohort studies, surveys, registries and expert opinions. Merging information from different sources opens up new possibilities for the estimation of causal effects. We show how causal effects can be identified and estimated by combining experiments and observations in real and realistic scenarios. As a new tool, we present do-search, a recently developed algorithmic approach that can determine the identifiability of a causal effect. The approach is based on do-calculus, and it can utilize data with non-trivial missing data and selection bias mechanisms. When the effect is identifiable, do-search outputs an identifying formula on which numerical estimation can be based. When the effect is not identifiable, we can use do-search to recognize additional data sources and assumptions that would make the effect identifiable. Throughout the paper, we consider the effect of salt-adding behavior on blood pressure mediated by the salt intake as an example. The identifiability of this effect is resolved in various scenarios with different assumptions on confounding. There are scenarios where the causal effect is identifiable from a chain of experiments but not from survey data, as well as scenarios where the opposite is true. As an illustration, we use survey data from NHANES 2013--2016 and the results from a meta-analysis of randomized controlled trials and estimate the reduction in average systolic blood pressure under an intervention where the use of table salt is discontinued.
This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of causal effects, and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, definition of identifiability, the choice of priors in both low and high dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. W…
In this paper we develop statistical methods for causal inference in epidemics. Our focus is in estimating the effect of social mobility on deaths in the Covid-19 pandemic. We propose a marginal structural model motivated by a modified version of a basic epidemic model. We estimate the counterfactual time series of deaths under interventions on mobility. We conduct several types of sensitivity analyses. We find that the data support the idea that reduced mobility causes reduced deaths, but the conclusion comes with caveats. There is evidence of sensitivity to model misspecification and unmeasu…
In many scenarios, the observational data needed for causal inferences are spread over two data files. In particular, we consider scenarios where one file includes covariates and the treatment measured on one set of individuals, and a second file includes responses measured on another, partially overlapping set of individuals. In the absence of error free direct identifiers like social security numbers, straightforward merging of separate files is not feasible, so that records must be linked using error-prone variables such as names, birth dates, and demographic characteristics. Typical practi…
Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal statements. One of the most influential framework in quantifying causal effects is the potential outcomes framework. On the other hand, causal graphical models utilizes directed edges to represent causalities and encodes conditional independence relationships among variables in the graphs. A series of research has been done both in reading-off conditional indepen…
The literature for count modeling provides useful tools to conduct causal inference when outcomes take non-negative integer values. Applied to the potential outcomes framework, we link the Bayesian causal inference literature to statistical models for count data. We discuss the general architectural considerations for constructing the predictive posterior of the missing potential outcomes. Special considerations for estimating average treatment effects are discussed, some generalizing certain relationships and some not yet encountered in the causal inference literature.
Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes of the same units under different treatment conditions. Because for each unit at most one of the potential outcomes is observed and the rest are missing, causal inference is inherently a missing data problem. Indeed, there is a close analogy in the terminology and the inferential framework between causal inference and missing data. Despite the intrinsic con…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$, computes a causal query, $Q$, as a function of known population probabilities, $I$, in every model entailed by a set of model assumptions, $M$. Many problems in causal inference can be viewed as the problem of enumerating instances of the relation that satisfy given criteria. This unifies a number of previously studied problems, including causal effect identificat…
This paper is about the general disconnect that we see, both in practice and in literature, between the disciplines of travel demand modeling and causal inference. In this paper, we assert that travel demand modeling should be one of the many fields that focuses on the production of valid causal inferences, and we hypothesize about reasons for the current disconnect between the two bodies of research. Furthermore, we explore the potential benefits of uniting these two disciplines. We consider what travel demand modeling can gain from greater incorporation of techniques and perspectives from th…
A framework for causal inference from two-level factorial designs is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than "average factorial effects" and leads to more flexible inference procedures than those based…
We develop finite-population asymptotic theory for covariate adjustment in randomization-based causal inference for 2K factorial designs. In particular, we confirm that both the unadjusted and covariate-adjusted estimators of the factorial effects are asymptotically normal, and the latter is more precise than the former.
The paper reviews methods that seek to draw causal inference from observational data and demonstrates how they can be applied to empirical problems in engineering research. It presents a framework for causal identification based on the concept of potential outcomes and reviews core contemporary methods that can be used to estimate causal quantities. The paper has two aims: first, to provide a consolidated overview of the statistical literature on causal inference for the data centric engineering community; and second, to illustrate how causal concepts and methods can be applied. The latter aim…
It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We propose a novel framework to nonparametrically identify causal effects with confounders subject to an outcome-independent missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal…
This paper develops a multiply robust (MR) dose-response estimator for causal inference problems involving multivalued treatments. We combine a family of generalised propensity score (GPS) models and a family of outcome regression (OR) models to achieve an average potential outcomes estimator that is consistent if just one of the GPS or OR models in each family is correctly specified. We provide proofs and simulations that demonstrate multiple robustness in the context of multivalued causal inference problems.
Integrating data from multiple heterogeneous sources has become increasingly popular to achieve a large sample size and diverse study population. This paper reviews development in causal inference methods that combines multiple datasets collected by potentially different designs from potentially heterogeneous populations. We summarize recent advances on combining randomized clinical trial with external information from observational studies or historical controls, combining samples when no single sample has all relevant variables with application to two-sample Mendelian randomization, distribu…
Spurious association arises from covariance between propensity for the treatment and individual risk for the outcome. For sensitivity analysis with stochastic counterfactuals we introduce a methodology to characterize uncertainty in causal inference from natural experiments and quasi-experiments. Our sensitivity parameters are standardized measures of variation in propensity and individual risk, and one minus their geometric mean is an intuitive measure of randomness in the data generating process. Within our latent propensity-risk model, we show how to compute from contingency table data a th…
Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high-dimensional settings. Unlike standard fi…
We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional `likelihood times prior' posterior inference; in addition, most methods rely on parametric and distributional assumptions, and presumed correct specification. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision…
Under a general structural equation framework for causal inference, we provide a definition of the causal effect of a variable X on another variable Y, and propose an approach to estimate this causal effect via the use of instrumental variables.
Causal inference from observational data can be viewed as a missing data problem arising from a hypothetical population-scale randomized trial matched to the observational study. This links a target trial protocol with a corresponding generative predictive model for inference, providing a complete framework for transparent communication of causal assumptions and statistical uncertainty on treatment effects, without the need for counterfactuals. The intuitive foundation for the work is that a whole population randomized trial would provide answers to any observable causal question with certaint…
In causal estimation problems, the parameter of interest is often only partially identified, implying that the parameter cannot be recovered exactly, even with infinite data. Here, we study Bayesian inference for partially identified treatment effects in multi-treatment causal inference problems with unobserved confounding. In principle, inferring the partially identified treatment effects is natural under the Bayesian paradigm, but the results can be highly sensitive to parameterization and prior specification, often in surprising ways. It is thus essential to understand which aspects of the …
The research questions that motivate transportation safety studies are causal in nature. Safety researchers typically use observational data to answer such questions, but often without appropriate causal inference methodology. The field of causal inference presents several modeling frameworks for probing empirical data to assess causal relations. This paper focuses on exploring the applicability of two such modeling frameworks---Causal Diagrams and Potential Outcomes---for a specific transportation safety problem. The causal effects of pavement marking retroreflectivity on safety of a road seg…
Intercurrent events (ICEs) and missing values are inevitable in clinical trials of any size and duration, making it difficult to assess the treatment effect for all patients in randomized clinical trials. Defining the appropriate estimand that is relevant to the clinical research question is the first step in analyzing data. The tripartite estimands, which evaluate the treatment differences in the proportion of patients with ICEs due to adverse events, the proportion of patients with ICEs due to lack of efficacy, and the primary efficacy outcome for those who can adhere to study treatment unde…
Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space $\mathbb{R}^p$. However, it is increasingly common that complex datasets are best summarized as data points in non-linear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is non-linear. We develop doubly robust estimators and associated asymptotic theory …
The results from Genome-Wide Association Studies (GWAS) on thousands of phenotypes provide an unprecedented opportunity to infer the causal effect of one phenotype (exposure) on another (outcome). Mendelian randomization (MR), an instrumental variable (IV) method, has been introduced for causal inference using GWAS data. Due to the polygenic architecture of complex traits/diseases and the ubiquity of pleiotropy, however, MR has many unique challenges compared to conventional IV methods. We propose a Bayesian weighted Mendelian randomization (BWMR) for causal inference to address these challeng…
Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become an important task, especially in high dimensional settings. In this paper, we propose a framework for estimating Individualized Treatment Effects in high-dimensional non-experimental data. We provide both theoretical and empirical justifications, the latter by comparing our framework with current best-performing methods. Our proposed framework rivals the stat…
This paper presents a topological learning-theoretic perspective on causal inference by introducing a series of topologies defined on general spaces of structural causal models (SCMs). As an illustration of the framework we prove a topological causal hierarchy theorem, showing that substantive assumption-free causal inference is possible only in a meager set of SCMs. Thanks to a known correspondence between open sets in the weak topology and statistically verifiable hypotheses, our results show that inductive assumptions sufficient to license valid causal inferences are statistically unverifia…
Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome's dependence structure need to be considered. We focus on the case of binary outcomes framing our discussion in the potential outcome approach to causal inference. We define causal effects of treatment on joint outcomes introducing the notion of product outcomes. We also discuss a decomposition of the causal effect on product outcomes into intrinsic and extrinsic causal effects, which respectively provide information on treatment effect on the i…
Improving public policy is one of the key roles of governments, and they can do this in an evidence-based way using administrative data. Causal inference for observational data improves on current practice of using descriptive or predictive analyses to inform policy decisions. Causal inference allows analysts to estimate the impact a policy change would have on the population if the encoded assumptions about the data generation process are valid. In this paper, we discuss the importance of causal analysis methods when analysing data to inform policy decisions. We take the education sector as a…
Under the potential outcomes framework, we introduce matched-pair factorial designs, and propose the matched-pair estimator of the factorial effects. We also calculate the randomization-based covariance matrix of the matched-pair estimator, and provide the "Neymanian" estimator of the covariance matrix.
Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms. Time-series representations like discrete Fourier and wavelet transforms have been widely applied in order to obtain insights on the temporal structure of complex dynamical systems. Questions of cause and effect can be formalized in the causal inference framework. We propose an elementary and systematic approach to combine time-series representations with causal i…
For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. We also introduce methods for likelihood and Bayesian inference based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment-based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach which allows for the characterization o…
Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenot…
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This paper considers a flexible semi-parametric potential outcome model that allows for possibly invalid instruments. We propose new identifiability conditions to identify the causal parameters when the majority of the instrumental variables are valid. We devise a novel inference procedure for a new average structural function and the conditional average treatmen…
Many causal models of interest in epidemiology involve longitudinal exposures, confounders and mediators. However, repeated measurements are not always available or used in practice, leading analysts to overlook the time-varying nature of exposures and work under over-simplified causal models. Our objective is to assess whether - and how - causal effects identified under such misspecified causal models relates to true causal effects of interest. We derive sufficient conditions ensuring that the quantities estimated in practice under over-simplified causal models can be expressed as weighted av…
This brief note documents the data generating processes used in the 2017 Data Analysis Challenge associated with the Atlantic Causal Inference Conference (ACIC). The focus of the challenge was estimation and inference for conditional average treatment effects (CATEs) in the presence of targeted selection, which leads to strong confounding. The associated data files and further plots can be found on the first author's web page.
We give a selective review of some recent developments in causal inference, intended for researchers who are not familiar with graphical models and causality, and with a focus on methods that are applicable to large data sets. We mainly address the problem of estimating causal effects from observational data. For example, one can think of estimating the effect of single or multiple gene knockouts from wild-type gene expression data, that is, from gene expression measurements that were obtained without doing any gene knockout experiments. We assume that the observational data are generated from…
We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive datasets with a variety of causal effects, in a performant, general, and robust way. The focus on software improves research agility, and enables causal inference to be easily integrated into large engineering systems. In particular, we use computational causal inference to deepen the relationship between causal inference, online experimentation, and algorithmic …
