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Selection bias has long been central in methodological discussions across epidemiology and other fields. In epidemiology, the concept of selection bias has been continually evolving over time. In this issue of the Journal, Mathur and Shpitser (Am J Epidemiol. XXXX;XXX(XX):XXXX-XXXX) present simple graphical rules for using a Single World Intervention Graph (SWIG) to assess the presence of selection bias when estimating treatment effects in both the general population and a selected sample. Notably, the authors examine the setting in which the treatment affects selection, an issue not well-addressed in the existing literature on selection bias. To place the work by Mathur and Shpitser in context, we review the evolution of the concept of selection bias in epidemiology, with a primary focus on the developments in the last 20-30 years since the introduction of causal directed acyclic graphs (DAGs) to epidemiologic research.

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The scope of this paper is a multivariate setting involving categorical variables. Following an external manipulation of one variable, the goal is to evaluate the causal effect on an outcome of interest. A typical scenario involves a system of variables representing lifestyle, physical and mental features, symptoms, and risk factors, with the outcome being the presence or absence of a disease. These variables are interconnected in complex ways, allowing the effect of an intervention to propagate through multiple paths. A distinctive feature of our approach is the estimation of causal effects while accounting for uncertainty in both the dependence structure, which we represent through a directed acyclic graph (DAG), and the DAG-model parameters. Specifically, we propose a Markov chain Monte Carlo algorithm that targets the joint posterior over DAGs and parameters, based on an efficient reversible-jump proposal scheme. We validate our method through extensive simulation studies and demonstrate that it outperforms current state-of-the-art procedures in terms of estimation accuracy. Finally, we apply our methodology to analyze a dataset on depression and anxiety in undergraduate students.

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This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption. Then, we propose a novel method, named the Deconfounded Functional Structure Estimation (DeFuSE), consisting of a deconfounding adjustment to remove the confounding effects and a sequential procedure to estimate the causal order of variables. We implement DeFuSE via feedforward neural networks for scalable computation. Moreover, we establish the consistency of DeFuSE under an assumption called the strong causal minimality. In simulations, DeFuSE compares favorably against state-of-the-art competitors that ignore confounding or nonlinearity. Finally, we demonstrate the utility and effectiveness of the proposed approach with an application to gene regulatory network analysis. The Python implementation is available at https://github.com/chunlinli/defuse.

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Here we introduce graphPAF, a comprehensive R package designed for estimation, inference and display of population attributable fractions (PAF) and impact fractions. In addition to allowing inference for standard population attributable fractions and impact fractions, graphPAF facilitates display of attributable fractions over multiple risk factors using fan-plots and nomograms, calculations of attributable fractions for continuous exposures, inference for attributable fractions appropriate for specific risk factor → mediator → outcome pathways (pathway-specific attributable fractions) and Bayesian network-based calculations and inference for joint, sequential and average population attributable fractions in multi-risk factor scenarios. This article can be used as both a guide to the theory of attributable fraction estimation and a tutorial regarding how to use graphPAF in practical examples.

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As IoT metering devices become increasingly prevalent, the smart energy grid encounters challenges associated with the transmission of large volumes of data affecting the latency of control services and the secure delivery of energy. Offloading computational work towards the edge is a viable option; however, effectively coordinating service execution on edge nodes presents significant challenges due to the vast search space making it difficult to identify optimal decisions within a limited timeframe. In this research paper, we utilize the whale optimization algorithm to decide and select the optimal edge nodes for executing services' computational tasks. We employ a directed acyclic graph to model dependencies among computational nodes, data network links, smart grid energy assets, and energy network organization, thereby facilitating more efficient navigation within the decision space to identify the optimal solution. The offloading decision variables are represented as a binary vector, which is evaluated using a fitness function considering round-trip time and the correlation between edge-task computational resources. To effectively explore offloading strategies and prevent convergence to suboptimal solutions, we adapt the feedback mechanisms, an inertia weight coefficient, and a nonlinear convergence factor. The evaluation results are promising, demonstrating that the proposed solution can effectively consider both energy and data network constraints while enduring faster decision-making for optimization, with notable improvements in response time and a low average execution time of approximately 0.03 s per iteration. Additionally, on complex computational infrastructures modeled, our solution shows strong features in terms of diversity, fitness evolution, and execution time.

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Estimating dependence relationships between variables is a crucial issue in many applied domains and in particular psychology. When several variables are entertained, these can be organized into a network which encodes their set of conditional dependence relations. Typically however, the underlying network structure is completely unknown or can be partially drawn only; accordingly it should be learned from the available data, a process known as structure learning. In addition, data arising from social and psychological studies are often of different types, as they can include categorical, discrete and continuous measurements. In this paper, we develop a novel Bayesian methodology for structure learning of directed networks which applies to mixed data, i.e., possibly containing continuous, discrete, ordinal and binary variables simultaneously. Whenever available, our method can easily incorporate known dependence structures among variables represented by paths or edge directions that can be postulated in advance based on the specific problem under consideration. We evaluate the proposed method through extensive simulation studies, with appreciable performances in comparison with current state-of-the-art alternative methods. Finally, we apply our methodology to well-being data from a social survey promoted by the United Nations, and mental health data collected from a cohort of medical students. R code implementing the proposed methodology is available at https://github.com/FedeCastelletti/bayes_networks_mixed_data .

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Purpose: To explore a potential interaction between the effect of specific maternal smoking patterns and the presence of antenatal depression, as independent exposures, in causing postpartum depression (PPD). Methods: This case-control study of participants with singleton term births (N = 51220) was based on data from the 2017-2018 Pregnancy Risk Assessment Monitoring System. Multivariable log-binomial regression models examined the main effects of smoking patterns and self-reported symptoms of antenatal depression on the risk of PPD on the adjusted risk ratio (aRR) scale and tested a two-way interaction adjusting for covariates selected in a directed acyclic graph (DAG). The interaction effects were measured on the additive scale using relative excess risk due to interaction (RERI), the attributable proportion of interaction (AP), and the synergy index (SI). Causal effects were defined in a counterfactual framework. The E-value quantified the potential impact of unobserved/unknown covariates, conditional on observed covariates. Results: Among 6841 women in the sample who self-reported PPD, 35.7% also reported symptoms of antenatal depression. Out of 3921 (7.7%) women who reported smoking during pregnancy, 32.6% smoked at high intensity (≥10 cigarettes/day) in all three trimesters and 36.6% had symptoms of antenatal depression. The main effect of PPD was the strongest for women who smoked at high intensity throughout pregnancy (aRR 1.65; 95% CI: 1.63, 1.68). A synergistic interaction was detected, and the effect of all maternal smoking patterns was augmented, particularly in late pregnancy for Increasers and Reducers. Conclusion: Strong associations and interaction effects between maternal smoking patterns and co-occurring antenatal depression support smoking prevention and cessation interventions during pregnancy to lower the likelihood of PPD.

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Purpose: The objective of this study is to describe patterns in barriers to breast cancer screening uptake with the end goal of improving screening adherence and decreasing the burden of mortality due to breast cancer. This study looks at social determinants of health and their association to screening and mortality. It also investigates the extent that models trained on county data are generalizable to individuals. Methods: County level screening uptake and age adjusted mortality due to breast cancer are combined with the Centers for Disease Controls Social Vulnerability Index (SVI) to train a model predicting screening uptake rates. Patterns learned are then applied to de-identified electronic medical records from individual patients to make predictions on mammogram screening follow through. Results: Accurate predictions can be made about a county's breast cancer screening uptake with the SVI. However, the association between increased screening, and decreased age adjusted mortality, doesn't hold in areas with a high proportion of minority residents. It is also shown that patterns learned from county SVI data have little discriminative power at the patient level. Conclusion: This study demonstrates that social determinants in the SVI can explain much of the variance in county breast cancer screening rates. However, these same patterns fail to discriminate which patients will have timely follow through of a mammogram screening test. This study also concludes that the core association between increased screening and decreased age adjusted mortality does not hold in high proportion minority areas. Objective: The objective of this study is to describe patterns in social determinants of health and their association with female breast cancer screening uptake, age adjusted breast cancer mortality rate and the extent that models trained on county data are generalizable to individuals.

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In the context of missing data, the identifiability or "recoverability" of the average causal effect (ACE) depends not only on the usual causal assumptions but also on missingness assumptions that can be depicted by adding variable-specific missingness indicators to causal diagrams, creating missingness directed acyclic graphs (m-DAGs). Previous research described canonical m-DAGs, representing typical multivariable missingness mechanisms in epidemiological studies, and examined mathematically the recoverability of the ACE in each case. However, this work assumed no effect modification and did not investigate methods for estimation across such scenarios. Here, we extend this research by determining the recoverability of the ACE in settings with effect modification and conducting a simulation study to evaluate the performance of widely used missing data methods when estimating the ACE using correctly specified g-computation. Methods assessed were complete case analysis (CCA) and various implementations of multiple imputation (MI) with varying degrees of compatibility with the outcome model used in g-computation. Simulations were based on an example from the Victorian Adolescent Health Cohort Study (VAHCS), where interest was in estimating the ACE of adolescent cannabis use on mental health in young adulthood. We found that the ACE is recoverable when no incomplete variable (exposure, outcome, or confounder) causes its own missingness, and nonrecoverable otherwise, in simplified versions of 10 canonical m-DAGs that excluded unmeasured common causes of missingness indicators. Despite this nonrecoverability, simulations showed that MI approaches that are compatible with the outcome model in g-computation may enable approximately unbiased estimation across all canonical m-DAGs considered, except when the outcome causes its own missingness or causes the missingness of a variable that causes its own missingness. In the latter settings, researchers may need to consider sensitivity analysis methods incorporating external information (e.g., delta-adjustment methods). The VAHCS case study illustrates the practical implications of these findings.

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AIM: It is essential for health researchers to have a systematic understanding of third-party variables that influence both the exposure and outcome under investigation, as shown by a directed acyclic graph (DAG). The traditional construction of DAGs through literature review and expert knowledge often needs to be more systematic and consistent, leading to potential biases. We try to introduce an automatic approach to building network linking variables of interest. METHODS: Large-scale text mining from medical literature was utilized to construct a conceptual network based on the Semantic MEDLINE Database (SemMedDB). SemMedDB is a PubMed-scale repository of the "concept-relation-concept" triple format. Relations between concepts are categorized as Excitatory, Inhibitory, or General. RESULTS: To facilitate the use of large-scale triple sets in SemMedDB, we have developed a computable biomedical knowledge (CBK) system (https://cbk.bjmu.edu.cn/), a website that enables direct retrieval of related publications and their corresponding triples without the necessity of writing SQL statements. Three case studies were elaborated to demonstrate the applications of the CBK system. CONCLUSIONS: The CBK system is openly available and user-friendly for rapidly capturing a set of influencing factors for a phenotype and building candidate DAGs between exposure-outcome variables. It could be a valuable tool to reduce the exploration time in considering relationships between variables, and constructing a DAG. A reliable and standardized DAG could significantly improve the design and interpretation of observational health research.

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Objective: The present study examines the network structure and, using Bayesian network analysis, estimates the directional pathways among symptoms of posttraumatic stress disorder (PTSD), major depressive disorder (MDD), and levels of alcohol and cannabis use. Method: A sample of 1471 adults in the United States, who reported at least one potentially traumatic event, completed the PTSD Checklist (PCL-5), Patient Health Questionnaire (PHQ-9), and the Alcohol/Cannabis Use Disorders Identification Test (AUDIT/CUDIT). A regularized partial correlation network provided estimates of symptoms clusters and connections. Directional pathways within the network were then estimated using a directed acyclic graph (DAG). Results: Symptoms clustered in theoretically consistent ways. Risky behavior demonstrated the highest strength centrality and bridge strength. Neither alcohol nor cannabis use appeared central in the network, and DAG results suggested that MDD and PTSD symptoms are more likely to lead to substance use than the other way around. Conclusions: Results suggest that cannabis use is largely connected to alcohol use. Consistent with prior research, risky behavior appeared to be the primary bridge between substance use and PTSD. The direction of associations between substance use and psychological symptoms requires further attention.

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Bayesian networks (BNs) are suitable models for studying complex interdependencies between multiple health outcomes, simultaneously. However, these models fail the assumption of independent observation in the case of hierarchical data. Therefore, this study proposes a two and three-level random intercept multilevel Bayesian network (MBN) models to study the conditional dependencies between multiple outcomes. The structure of MBN was learned using the connected three parent set block Gibbs sampler, where each local network was included based on Bayesian information criteria (BIC) score of multilevel regression. These models were examined using simulated data assuming features of both multilevel models and BNs. The estimated area under the receiver operating characteristics for both models were above 0.8, indicating good fit. The MBN was then applied to real child morbidity data from the 2016 Ethiopian Demographic Health Survey (EDHS). The result shows a complex causal dependencies between malnutrition indicators and child morbidities such as anemia, acute respiratory infection (ARI) and diarrhea. According to this result, families and health professionals should give special attention to children who suffer from malnutrition and also have one of these illnesses, as the co-occurrence of both can worsen the health of a child.

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As the potential of directed acyclic graph (DAG)-based distributed ledgers in IoT systems unfolds, a need arises to understand their intricate dynamics in real-world scenarios. It is well known that discrete event simulations can provide high-fidelity evaluations of protocols. However, there is a lack of public discrete event simulators capable of assessing DAG-based distributed ledgers. In this paper, a discrete-event-based distributed ledger simulator is introduced, with which we investigate a custom Python-based implementation of IOTA's Tangle DAG protocol. The study reveals the dynamics of Tangle (particularly Poisson processes in transaction dynamics), the efficiency and intricacies of the random walk in Tangle, and the quantitative assessment of node convergence. Furthermore, the research underscores the significance of weight updates without depth limitations and provides insights into the role, challenges, and implications of the coordinator/validator in DAG architectures. The results are striking, and although the findings are reported only for Tangle, they demonstrate the need for adaptable and versatile discrete event simulators for DAG architectures and tip selection methodologies in general.

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Tumor budding as a prognostic marker in colorectal cancer has not previously been investigated in a cohort of screened stage II colon cancer patients. We assessed the prognostic significance of tumor budding in a thoroughly characterized stage II colon cancer population comprising surgically resected patients in the Region of Southern Denmark from 2014 to 2016. Tumors were re-staged according to the 8th edition of UICC TNM Classification, undergoing detailed histopathological evaluation and tumor budding assessment following guidelines from the International Tumor Budding Consensus Conference. Prognostic evaluation utilized Kaplan-Meier curves, log-rank tests, and Cox proportional hazard models for time to recurrence (TTR), recurrence-free survival (RFS), and overall survival (OS). Out of 497 patients, 20% were diagnosed through the national colorectal cancer screening program. High-grade tumor budding (Bd3) was found in 19% of tumors and was associated with glandular subtype, perineural invasion, mismatch repair proficient tumors, and tumor recurrence (p < 0.001, p < 0.001, p = 0.045, and p = 0.007 respectively). In multivariable Cox regression, high-grade budding was a significant prognostic factor for TTR compared to low-grade (Bd3 HR 2.617; p = 0.007). An association between tumor budding groups and RFS was observed, and the difference was significant in univariable analysis for high-grade compared to low-grade tumor budding (Bd3 HR 1.461; p = 0.041). No significant differences were observed between tumor budding groups and OS. High-grade tumor budding is a predictor of recurrence in a screened population of patients with stage II colon cancer and should be considered a high-risk factor in a shared decision-making process when stratifying patients to adjuvant chemotherapy.

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Graphomotor and time-based variables from the digital Clock Drawing Test (dCDT) characterize cognitive functions. However, no prior publications have quantified the strength of the associations between digital clock variables as they are produced. We hypothesized that analysis of the production of clock features and their interrelationships, as suggested, will differ between the command and copy test conditions. Older adults aged 65+ completed a digital clock drawing to command and copy conditions. Using a Bayesian hill-climbing algorithm and bootstrapping (10,000 samples), we derived directed acyclic graphs (DAGs) to examine network structure for command and copy dCDT variables. Although the command condition showed moderate associations between variables (µ|ßz|= 0.34) relative to the copy condition (µ|ßz| = 0.25), the copy condition network had more connections (18/18 versus 15/18 command). Network connectivity across command and copy was most influenced by five of the 18 variables. The direction of dependencies followed the order of instructions better in the command condition network. Digitally acquired clock variables relate to one another but differ in network structure when derived from command or copy conditions. Continued analyses of clock drawing production should improve understanding of quintessential normal features to aid in early neurodegenerative disease detection.

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Estimating phenotype networks is a growing field in computational biology. It deepens the understanding of disease etiology and is useful in many applications. In this study, we present a method that constructs a phenotype network by assuming a Gaussian linear structure model embedding a directed acyclic graph (DAG). We utilize genetic variants as instrumental variables and show how our method only requires access to summary statistics from a genome-wide association study (GWAS) and a reference panel of genotype data. Besides estimation, a distinct feature of the method is its summary statistics-based likelihood ratio test on directed edges. We applied our method to estimate a causal network of 29 cardiovascular-related proteins and linked the estimated network to Alzheimer's disease (AD). A simulation study was conducted to demonstrate the effectiveness of this method. An R package sumdag implementing the proposed method, all relevant code, and a Shiny application are available.

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Background: Links between diet and food security are well established, but less is known about how food and nutrition security affect a household's ability to decide what to consume. Objectives: This study's purpose was to quantify and compare causal pathways from 1) food and nutrition security to perceived dietary choice and 2) food and nutrition security to perceived healthfulness of food choice while testing for mediation by perceived limited availability of foods and utilization barriers to healthful meals. Methods: Causal mediation analysis was conducted using an observational data set. Exposures included food insecurity and nutrition insecurity; mediators included perceived limited availability and utilization barriers; outcomes included perceived dietary choice and healthfulness choice; covariates included income and education. Results: Dietary choice (range 0-4) was 0.9 to 1.1 points lower for participants with food/nutrition insecurity compared with participants with food/nutrition security (direct effects). Neither mediation nor moderation by perceived limited availability were present. Seventeen percent and 11 %, respectively, of the effects of food and nutrition security on dietary choice could be contributed to utilization barriers (mediation). Moderation by utilization barriers was present only for nutrition security (differences in dietary choice only present when barriers were low). Healthfulness choice (range 0-4) was 0.6 to 0.7 points lower for participants with food/nutrition insecurity compared with participants with food/nutrition security (direct effects). Mediation by perceived limited availability and utilization barriers was not present. Moderation was present only for nutrition security (differences in healthfulness choice only present when perceived limited availability was low; differences in healthfulness choice only present when barriers were low). Conclusions: Food and nutrition security affect food choices, with utilization barriers acting as an intermediary step. When environmental and household utilization barriers to healthful food purchasing and preparation are high, the ability to decide what to consume does not differ between households with nutrition security and those with nutrition insecurity.