Causal Graph Theory Research Articles

A hybrid constrained continuous optimization approach for optimal causal discovery from biological data.

Understanding causal effects is a fundamental goal of science and underpins our ability to make accurate predictions in unseen settings and conditions. While direct experimentation is the gold standard for measuring and validating causal effects, the field of causal graph theory offers a tantalizing alternative: extracting causal insights from observational data. Theoretical analysis has shown that this is indeed possible, given a large dataset and if certain conditions are met. However, biological datasets, frequently, do not meet such requirements but evaluation of causal discovery algorithms is typically performed on synthetic datasets, which they meet all requirements. Thus, real-life datasets are needed, in which the causal truth is reasonably known. In this work we first construct such a large-scale real-life dataset and then we perform on it a comprehensive benchmarking of various causal discovery methods. We find that the PC algorithm is particularly accurate at estimating causal structure, including the causal direction which is critical for biological applicability. However, PC does only produces cause-effect directionality, but not estimates of causal effects. We propose PC-NOTEARS (PCnt), a hybrid solution, which includes the PC output as an additional constraint inside the NOTEARS optimization. This approach combines PC algorithm's strengths in graph structure prediction with the NOTEARS continuous optimization to estimate causal effects accurately. PCnt achieved best aggregate performance across all structural and effect size metrics. https://github.com/zhu-yh1/PC-NOTEARS.

Graphical Causal Models for Survey Inference

Directed acyclic graphs (DAGs) are now a popular tool to inform causal inferences. We discuss how DAGs can also be used to encode theoretical assumptions about nonprobability samples and survey nonresponse and to determine whether population quantities including conditional distributions and regressions can be identified. We describe sources of bias and assumptions for eliminating it in various selection scenarios. We then introduce and analyze graphical representations of multiple selection stages in the data collection process, and highlight the strong assumptions implicit in using only design weights. Furthermore, we show that the common practice of selecting adjustment variables based on correlations with sample selection and outcome variables of interest is ill-justified and that nonresponse weighting when the interest is in causal inference may come at severe costs. Finally, we identify further areas for survey methodology research that can benefit from advances in causal graph theory.

A Data-driven Causality Modeling Framework: An Empirical Study of Modeling the Effect of Indoor Air Quality Perception on Students' Cognitive Performance

In the information age, a paradigm revolution in applied data mining methods has emerged in response to the data explosion in management science research, but this artificial intelligence-based automated data-driven modeling process creates a new "big relationship" problem, where a large number of correlations obfuscate the identification of true causal relationships. In this paper, we use a causality modeling framework that combines correlation modeling and causality pruning processes. First, symbolic regression is used to model white-box correlations of human intelligence, and then spurious correlations that do not conform to causal graph theory are pruned so that ultimately causal relationships and explicit candidate models describing these relationships can be found automatically. In an empirical research problem, the framework is compared with a traditional hypothesis construction-validation process, and the results are consistent between the two. The proposed framework implements a data-driven "correlation + causation" automatic modeling capability, which will greatly improve modeling efficiency and reliability.

Coherent causal control: a new distinction within causation

The recent literature on causation has seen the introduction of several distinctions within causation, which are thought to be important for understanding the widespread scientific practice of focusing causal explanations on a subset of the factors that are causally relevant for a phenomenon. Concepts used to draw such distinctions include, among others, stability, specificity, proportionality, or actual-difference making. In this contribution, I propose a new distinction that picks out an explanatorily salient class of causes in biological systems. Some select causes in complex biological systems, I argue, have the property of enabling coherent causal control of these systems. Examples of such control variables include hormones and other signaling molecules, e.g., TOR (target of rapamycin), morphogens or the products of homeotic selector genes in embryonic pattern formation. I propose an analysis of this notion based on concepts borrowed from causal graph theory.

The selfish environment meets the selfish gene: Coevolution and inheritance of RNA and DNA pools: A model for organismal life incorporating coevolution, horizontal transfer, and inheritance of internal and external RNA and DNA pools.: A model for organismal life incorporating coevolution, horizontal transfer, and inheritance of internal and external RNA and DNA pools.

Throughout evolution, there has been interaction and exchange between RNA pools in the environment, and DNA and RNA pools of eukaryotic organisms. Metagenomic and metatranscriptomic sequencing of invertebrate hosts and their microbiota has revealed a rich evolutionary history of RNA virus shuttling between species. Horizontal transfer adapted the RNA pool for successful future interactions which lead to zoonotic transmission and detrimental RNA viral pandemics like SARS-CoV2. In eukaryotes, noncoding RNA (ncRNA) is an established mechanism derived from prokaryotes to defend against viral attack through innate immunity and regulation of host-derived mRNA. Transgenerational inheritance of ncRNA is evidence for feedforward adaptive immunity and epigenetically encoded environmental change across generations, which may explain the ''missing heritability'' of common disease. Causal graph theory and the Price Equation can model epigenetic inheritance involving dynamic internal and external RNA pools. Experimental designs should include metatranscriptomic analyses to understand how ncRNA responds to rapidly changing environmental conditions, within and between organisms, and across generations.

The Epidemiologic Toolbox: Identifying, Honing, and Using the Right Tools for the Job.

There has been much debate about the relative emphasis of the field of epidemiology on causal inference. We believe this debate does short shrift to the breadth of the field. Epidemiologists answer myriad questions that are not causal and hypothesize about and investigate causal relationships without estimating causal effects. Descriptive studies face significant and often overlooked inferential and interpretational challenges; we briefly articulate some of them and argue that a more detailed treatment of biases that affect single-sample estimation problems would benefit all types of epidemiologic studies. Lumping all questions about causality creates ambiguity about the utility of different conceptual models and causal frameworks; 2 distinct types of causal questions include 1) hypothesis generation and theorization about causal structures and 2) hypothesis-driven causal effect estimation. The potential outcomes framework and causal graph theory help efficiently and reliably guide epidemiologic studies designed to estimate a causal effect to best leverage prior data, avoid cognitive fallacies, minimize biases, and understand heterogeneity in treatment effects. Appropriate matching of theoretical frameworks to research questions can increase the rigor of epidemiologic research and increase the utility of such research to improve public health.

Computation in Causal Graphs

The goal of this paper is to introduce some of the important concepts in causal graph theory and examine them from combinatorial and computational perspectives. Of fundamental importance in applications of causal models that use graphs are dependence-separators or, simply, $d$-separators. A vertex set $Z$ is a $d$-separator for a pair of disjoint vertex sets $(X,Y)$ if $X$ and $Y$ are independent conditioned on $Z$. For the case of a single-setpair it is known that $d$-separators can be found efficiently by elegant network flow techniques. In this paper, we consider $d$-separators for a collection $\{(X_1,Y_1),(X_2,Y_2),\dots,(X_k,Y_k)\}$ of setpairs. We focus on two classes of combinatorial objects in this multiple-setpair framework: $d$-separators and $d$-super-separators. We say that $Z$ is a $d$-separator for multiple setpairs if, for each $i$, $X_i$ and $Y_i$ are independent conditioned on $Z$; we say that $Z$ is a $d$-super-separator if, for each $i$, there exists $Z_i\subseteq Z$, such that $X_i$ and $Y_i$ are independent conditioned on $Z_i$. For the latter object, we give an $O(\log^2k)$-approximation algorithm for the problem of finding a minimum cost $d$-super-separator. The focus on approximation algorithms is necessary as we show this problem is NP-complete. For the former object, we show it is hard to determine whether a $d$-separator exists, even when there are just five setpairs. This problem remains hard even if each setpair consists of singleton vertices, provided the number of setpairs is large. On the positive side, we show that if there are a fixed number of singleton setpairs then a $d$-separator for multiple setpairs can be found in polynomial time, if one exists.

On the Limits of Causal Modeling: Spatially-Structurally Complex Biological Phenomena

This article examines the adequacy of causal graph theory as a tool for modeling biological phenomena. I argue that the causal graph approach reaches its limits when it comes to modeling biological phenomena that involve complex spatial and chemical-structural relations. Using a case study from molecular biology, I show why causal graph models fail to adequately represent and explain biological phenomena of this kind. The inadequacy of these models is due to their failure to include relevant spatial-structural information in a way that does not render the models nonexplanatory, unmanageable, or inconsistent with basic assumptions of causal graph theory.

Using causal models to integrate proximate and ultimate causation

Ernst Mayr’s classical work on the nature of causation in biology has had a huge influence on biologists as well as philosophers. Although his distinction between proximate and ultimate causation recently came under criticism from those who emphasize the role of development in evolutionary processes, the formal relationship between these two notions remains elusive. Using causal graph theory, this paper offers a unified framework to systematically translate a given “proximate” causal structure into an “ultimate” evolutionary response, and illustrates evolutionary implications of various kinds of causal mechanisms including epigenetic inheritance, maternal effects, and niche construction. These results not only reveal the essential interplay between proximate and ultimate causation in the study of evolution, but also provide a formal method to evaluate or discover non-standard or yet unknown evolutionary phenomena.

Medical home characteristics and asthma control: a prospective, observational cohort study protocol.

Background:This paper describes the methods for an observational comparative effectiveness research study designed to test the association between practice-level medical home characteristics and asthma control in children and adults receiving care in safety-net primary care practices.Methods:This is a prospective, longitudinal cohort study, utilizing survey methodologies and secondary analysis of existing structured clinical, administrative, and claims data. The Scalable Architecture for Federated Translational Inquiries Network (SAFTINet) is a safety net-oriented, primary care practice-based research network, with federated databases containing electronic health record (EHR) and Medicaid claims data. Data from approximately 20,000 patients from 50 practices in four healthcare organizations will be included. Practice-level medical home characteristics will be correlated with patient-level asthma outcomes, controlling for potential confounding variables, using a clustered design. Linear and non-linear mixed models will be used for analysis. Study inception was July 1, 2012. A causal graph theory approach was used to guide covariate selection to control for bias and confounding.Discussion:Strengths of this design include a priori specification of hypotheses and methods, a large sample of patients with asthma cared for in safety-net practices, the study of real-world variations in the implementation of the medical home concept, and the innovative use of a combination of claims data, patient-reported data, clinical data from EHRs, and practice-level surveys. We address limitations in causal inference using theory, design and analysis.

Solving the Flagpole Problem

In this paper I demonstrate that the causal structure of flagpole-like systems can be determined by application of causal graph theory. Additional information about the ordering of events in time or about how parameters of the systems of interest can be manipulated is not needed.

Iron Status Predicts Malaria Risk in Malawian Preschool Children

IntroductionIron deficiency is highly prevalent in pre-school children in developing countries and an important health problem in sub-Saharan Africa. A debate exists on the possible protective effect of iron deficiency against malaria and other infections; yet consensus is lacking due to limited data. Recent studies have focused on the risks of iron supplementation but the effect of an individual's iron status on malaria risk remains unclear. Studies of iron status in areas with a high burden of infections often are exposed to bias. The aim of this study was to assess the predictive value of baseline iron status for malaria risk explicitly taking potential biases into account.Methods and materialsWe prospectively assessed the relationship between baseline iron deficiency (serum ferritin <30 µg/L) and malaria risk in a cohort of 727 Malawian preschool children during a year of follow-up. Data were analyzed using marginal structural Cox regression models and confounders were selected using causal graph theory. Sensitivity of results to bias resulting from misclassification of iron status by concurrent inflammation and to bias from unmeasured confounding were assessed using modern causal inference methods.Results and ConclusionsThe overall incidence of malaria parasitemia and clinical malaria was 1.9 (95% CI 1.8–2.0) and 0.7 (95% CI 0.6–0.8) events per person-year, respectively. Children with iron deficiency at baseline had a lower incidence of malaria parasitemia and clinical malaria during a year of follow-up; adjusted hazard ratio's 0.55 (95%-CI:0.41–0.74) and 0.49 (95%-CI:0.33–0.73), respectively. Our results suggest that iron deficiency protects against malaria parasitemia and clinical malaria in young children. Therefore the clinical importance of treating iron deficiency in a pre-school child should be weighed carefully against potential harms. In malaria endemic areas treatment of iron deficiency in children requires sustained prevention of malaria.