MRSL: a causal network pruning algorithm based on GWAS summary data.

Causal discovery is a powerful tool to disclose underlying structures by analyzing purely observational data. Genetic variants can provide useful complementary information for structure learning. Recently, Mendelian randomization (MR) studies have provided abundant marginal causal relationships of traits. Here, we propose a causal network pruning algorithm MRSL (MR-based structure learning algorithm) based on these marginal causal relationships. MRSL combines the graph theory with multivariable MR to learn the conditional causal structure using only genome-wide association analyses (GWAS) summary statistics. Specifically, MRSL utilizes topological sorting to improve the precision of structure learning. It proposes MR-separation instead of d-separation and three candidates of sufficient separating set for MR-separation. The results of simulations revealed that MRSL had up to 2-fold higher F1 score and 100 times faster computing time than other eight competitive methods. Furthermore, we applied MRSL to 26 biomarkers and 44 International Classification of Diseases 10 (ICD10)-defined diseases using GWAS summary data from UK Biobank. The results cover most of the expected causal links that have biological interpretations and several new links supported by clinical case reports or previous observational literatures.

Discovering the effective connectome of the brain with dynamic Bayesian DAG learning.

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method to address the challenges in discovering DEC. The presented dynamic DAG enables us to discover direct feedback loop edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and traditional methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process.

Invited commentary: where do the causal DAGS come from?

How do we construct our causal directed acyclic graphs (DAGs)-for example, for life-course modeling and analysis? In this commentary, I review how the data-driven construction of causal DAGs (causal discovery) has evolved, what promises it holds, and what limitations or caveats must be considered. I find that expert- or theory-driven model-building might benefit from some more checking against the data and that causal discovery could bring new ideas to old theories.

Learning debiased graph representations from the OMOP common data model for synthetic data generation.

BACKGROUND: Generating synthetic patient data is crucial for medical research, but common approaches build up on black-box models which do not allow for expert verification or intervention. We propose a highly available method which enables synthetic data generation from real patient records in a privacy preserving and compliant fashion, is interpretable and allows for expert intervention. METHODS: Our approach ties together two established tools in medical informatics, namely OMOP as a data standard for electronic health records and Synthea as a data synthetization method. For this study, data pipelines were built which extract data from OMOP, convert them into time series format, learn temporal rules by 2 statistical algorithms (Markov chain, TARM) and 3 algorithms of causal discovery (DYNOTEARS, J-PCMCI+, LiNGAM) and map the outputs into Synthea graphs. The graphs are evaluated quantitatively by their individual and relative complexity and qualitatively by medical experts. RESULTS: The algorithms were found to learn qualitatively and quantitatively different graph representations. Whereas the Markov chain results in extremely large graphs, TARM, DYNOTEARS, and J-PCMCI+ were found to reduce the data dimension during learning. The MultiGroupDirect LiNGAM algorithm was found to not be applicable to the problem statement at hand. CONCLUSION: Only TARM and DYNOTEARS are practical algorithms for real-world data in this use case. As causal discovery is a method to debias purely statistical relationships, the gradient-based causal discovery algorithm DYNOTEARS was found to be most suitable.

From correlation to causation using directed topological overlap matrix: Applications in genomics.

Most causal discovery tools assume the local causal Markov condition. However, the theoretical assumptions that underlie the local causal Markov condition are often not met in practice. This is especially marked in genomics, where the unwanted presence of measurement errors, averaging effects, and feedback loops significantly undermine the legitimacy of the local causal Markov condition. Furthermore, these causal discovery algorithms require very large samples, orders above what is often available. In this paper, relaxing the local causal Markov condition and using Reichenbach's common cause principle instead, we present a more flexible approach to causal discovery, the directed topological overlap matrix (DTOM). DTOM is robust w.r.t. the presence of measurement errors, averaging effects, feedback loops, and is significantly more sample efficient. We study the utility of DTOM for discovering causal relations in biological data using three real gene expression data-sets. We first examine if DTOM can help distinguish the Myostatin mutation in the Piedmontese cattle by contrasting the muscle transcriptomes of the Piedmontese and Wagyu crosses: the Myostatin mutation is the cause of the double-muscling the Piedmontese cattle are famous for. We then consider a large-scale gene deletion study in yeast. We show that DTOM allows us to distinguish the deleted gene in a sample knowing only the set of differentially expressed genes in that sample. We then examine the progression of Alzheimer's disease (AD) under the lens of DTOM. The genes implicated as having a causal role in the progression of AD by our DTOM analysis were significantly enriched in cellular components that had been repeatedly implicated in the progression of AD.

Counterfactual formulation of patient-specific root causes of disease.

OBJECTIVE: Root causes of disease intuitively correspond to root vertices of a causal model that increase the likelihood of a diagnosis. This description of a root cause nevertheless lacks the rigorous mathematical formulation needed for the development of computer algorithms designed to automatically detect root causes from data. We seek a definition of patient-specific root causes of disease that models the intuitive procedure routinely utilized by physicians to uncover root causes in the clinic. METHODS: We use structural equation models, interventional counterfactuals and the recently developed mathematical formalization of backtracking counterfactuals to propose a counterfactual formulation of patient-specific root causes of disease matching clinical intuition. RESULTS: We introduce a definition of patient-specific root causes of disease that climbs to the third rung of Pearl's Ladder of Causation and matches clinical intuition given factual patient data and a working causal model. We then show how to assign a root causal contribution score to each variable using Shapley values from explainable artificial intelligence. CONCLUSION: The proposed counterfactual formulation of patient-specific root causes of disease accounts for noisy labels, adapts to disease prevalence and admits fast computation without the need for counterfactual simulation.

Interpretability of Causal Discovery in Tracking Deterioration in a Highly Dynamic Process.

In a dynamic production processes, mechanical degradation poses a significant challenge, impacting product quality and process efficiency. This paper explores a novel approach for monitoring degradation in the context of viscose fiber production, a highly dynamic manufacturing process. Using causal discovery techniques, our method allows domain experts to incorporate background knowledge into the creation of causal graphs. Further, it enhances the interpretability and increases the ability to identify potential problems via changes in causal relations over time. The case study employs a comprehensive analysis of the viscose fiber production process within a prominent textile industry, emphasizing the advantages of causal discovery for monitoring degradation. The results are compared with state-of-the-art methods, which are not considered to be interpretable, specifically LSTM-based autoencoder, UnSupervised Anomaly Detection on Multivariate Time Series (USAD), and Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data (TranAD), showcasing the alignment and validation of our approach. This paper provides valuable information on degradation monitoring strategies, demonstrating the efficacy of causal discovery in dynamic manufacturing environments. The findings contribute to the evolving landscape of process optimization and quality control.

Comparing Causal Bayesian Networks Estimated from Data.

The knowledge of the causal mechanisms underlying one single system may not be sufficient to answer certain questions. One can gain additional insights from comparing and contrasting the causal mechanisms underlying multiple systems and uncovering consistent and distinct causal relationships. For example, discovering common molecular mechanisms among different diseases can lead to drug repurposing. The problem of comparing causal mechanisms among multiple systems is non-trivial, since the causal mechanisms are usually unknown and need to be estimated from data. If we estimate the causal mechanisms from data generated from different systems and directly compare them (the naive method), the result can be sub-optimal. This is especially true if the data generated by the different systems differ substantially with respect to their sample sizes. In this case, the quality of the estimated causal mechanisms for the different systems will differ, which can in turn affect the accuracy of the estimated similarities and differences among the systems via the naive method. To mitigate this problem, we introduced the bootstrap estimation and the equal sample size resampling estimation method for estimating the difference between causal networks. Both of these methods use resampling to assess the confidence of the estimation. We compared these methods with the naive method in a set of systematically simulated experimental conditions with a variety of network structures and sample sizes, and using different performance metrics. We also evaluated these methods on various real-world biomedical datasets covering a wide range of data designs.

Causal Structure Learning with Conditional and Unique Information Groups-Decomposition Inequalities.

The causal structure of a system imposes constraints on the joint probability distribution of variables that can be generated by the system. Archetypal constraints consist of conditional independencies between variables. However, particularly in the presence of hidden variables, many causal structures are compatible with the same set of independencies inferred from the marginal distributions of observed variables. Additional constraints allow further testing for the compatibility of data with specific causal structures. An existing family of causally informative inequalities compares the information about a set of target variables contained in a collection of variables, with a sum of the information contained in different groups defined as subsets of that collection. While procedures to identify the form of these groups-decomposition inequalities have been previously derived, we substantially enlarge the applicability of the framework. We derive groups-decomposition inequalities subject to weaker independence conditions, with weaker requirements in the configuration of the groups, and additionally allowing for conditioning sets. Furthermore, we show how constraints with higher inferential power may be derived with collections that include hidden variables, and then converted into testable constraints using data processing inequalities. For this purpose, we apply the standard data processing inequality of conditional mutual information and derive an analogous property for a measure of conditional unique information recently introduced to separate redundant, synergistic, and unique contributions to the information that a set of variables has about a target.

Constructing Causal Life-Course Models: Comparative Study of Data-Driven and Theory-Driven Approaches.

Life-course epidemiology relies on specifying complex (causal) models that describe how variables interplay over time. Traditionally, such models have been constructed by perusing existing theory and previous studies. By comparing data-driven and theory-driven models, we investigated whether data-driven causal discovery algorithms can help in this process. We focused on a longitudinal data set on a cohort of Danish men (the Metropolit Study, 1953-2017). The theory-driven models were constructed by 2 subject-field experts. The data-driven models were constructed by use of the temporal Peter-Clark (TPC) algorithm. The TPC algorithm utilizes the temporal information embedded in life-course data. We found that the data-driven models recovered some, but not all, causal relationships included in the theory-driven expert models. The data-driven method was especially good at identifying direct causal relationships that the experts had high confidence in. Moreover, in a post hoc assessment, we found that most of the direct causal relationships proposed by the data-driven model but not included in the theory-driven model were plausible. Thus, the data-driven model may propose additional meaningful causal hypotheses that are new or have been overlooked by the experts. In conclusion, data-driven methods can aid causal model construction in life-course epidemiology, and combining both data-driven and theory-driven methods can lead to even stronger models.

Causal pathways to social and occupational functioning in the first episode of schizophrenia: uncovering unmet treatment needs.

BACKGROUND: We aimed to identify unmet treatment needs for improving social and occupational functioning in early schizophrenia using a data-driven causal discovery analysis. METHODS: Demographic, clinical, and psychosocial measures were obtained for 276 participants from the Recovery After an Initial Schizophrenia Episode Early Treatment Program (RAISE-ETP) trial at baseline and 6-months, along with measures of social and occupational functioning from the Quality of Life Scale. The Greedy Fast Causal Inference algorithm was used to learn a partial ancestral graph modeling causal relationships across baseline variables and 6-month functioning. Effect sizes were estimated using a structural equation model. Results were validated in an independent dataset (N = 187). RESULTS: In the data-generated model, greater baseline socio-affective capacity was a cause of greater baseline motivation [Effect size (ES) = 0.77], and motivation was a cause of greater baseline social and occupational functioning (ES = 1.5 and 0.96, respectively), which in turn were causes of their own 6-month outcomes. Six-month motivation was also identified as a cause of occupational functioning (ES = 0.92). Cognitive impairment and duration of untreated psychosis were not direct causes of functioning at either timepoint. The graph for the validation dataset was less determinate, but otherwise supported the findings. CONCLUSIONS: In our data-generated model, baseline socio-affective capacity and motivation are the most direct causes of occupational and social functioning 6 months after entering treatment in early schizophrenia. These findings indicate that socio-affective abilities and motivation are specific high-impact treatment needs that must be addressed in order to promote optimal social and occupational recovery.

Functional Bayesian networks for discovering causality from multivariate functional data.

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model.

Causal discovery analysis: A promising tool in advancing precision medicine for eating disorders.

OBJECTIVE: Precision medicine (i.e., individually tailored treatments) represents an optimal goal for treating complex psychiatric disorders, including eating disorders. Within the eating disorders field, most treatment development efforts have been limited in their ability to identify individual-level models of eating disorder psychopathology and to develop and apply an individually tailored treatment for a given individual's personalized model of psychopathology. In addition, research is still needed to identify causal relationships within a given individual's model of eating disorder psychopathology. Addressing this limitation of the current state of precision medicine-related research in the field will allow us to progress toward advancing research and practice for eating disorders treatment. METHOD: We present a novel set of analytic tools, causal discovery analysis (CDA) methods, which can facilitate increasingly fine-grained, person-specific models of causal relations among cognitive, behavioral, and affective symptoms. RESULTS: CDA can advance the identification of an individual's causal model that maintains that individuals' eating disorder psychopathology. DISCUSSION: In the current article, we (1) introduce CDA methods as a set of promising analytic tools for developing precision medicine methods for eating disorders including the potential strengths and weaknesses of CDA, (2) provide recommendations for future studies utilizing this approach, and (3) outline the potential clinical implications of using CDA to generate personalized models of eating disorder psychopathology. PUBLIC SIGNIFICANCE STATEMENT: CDA provides a novel statistical approach for identifying causal relationships among variables of interest for a given individual. Person-specific causal models may offer a promising approach to individualized treatment planning and inform future personalized treatment development efforts for eating disorders.

Causal inference in genetic trio studies.

We introduce a method to draw causal inferences-inferences immune to all possible confounding-from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed digital twin test compares an observed offspring to carefully constructed synthetic offspring from the same parents to determine statistical significance, and it can leverage any black-box multivariate model and additional nontrio genetic data to increase power. Crucially, our inferences are based only on a well-established mathematical model of recombination and make no assumptions about the relationship between the genotypes and phenotypes. We compare our method to the widely used transmission disequilibrium test and demonstrate enhanced power and localization.

Browning of vegetation in efficient carbon sink regions of India during the past two decades is driven by climate change and anthropogenic intrusions.

Accurate estimation of carbon cycle is a challenging task owing to the complexity and heterogeneity of ecosystems. Carbon Use Efficiency (CUE) is a metric to define the ability of vegetation to sequester carbon from the atmosphere. It is key to understand the carbon sink and source pathways of ecosystems. Here, we quantify CUE using remote sensing measurements to examine its variability, drivers and underlying mechanisms in India for the period 2000-2019, by applying the principal component analyses (PCA), multiple linear regression (MLR) and causal discovery. Our analysis shows that the forests in the hilly regions (HR) and northeast (NE), and croplands in the western areas of South India (SI) exhibit high (>0.6) CUE. The northwest (NW), Indo-Gangetic plain (IGP) and some areas in Central India (CI) show low (<0.3) CUE. In general, the water availability as soil moisture (SM) and precipitation (P) promote higher CUE, but higher temperature (T) and air organic carbon content (AOCC) reduce CUE. It is found that SM has the strongest relative influence (33%) on CUE, followed by P. Also, SM has a direct causal link with all drivers and CUE; reiterating its importance in driving vegetation carbon dynamics (VCD) for the cropland dominated India. The long-term analysis reveals that the low CUE regions in NW (moisture induced greening) and IGP (irrigation induced agricultural boom) have an increasing trend in productivity (greening). However, the high CUE regions in NE (deforestation and extreme events) and SI (warming induced moisture stress) exhibit a decreasing trend in productivity (browning), which is a great concern. Our study, therefore, provides new insights on the rate of carbon allocation and the need of proper planning for maintaining balance in the terrestrial carbon cycle. This is particularly important in the context of drafting policy decisions for the mitigation of climate change, food security and sustainability.

Detecting heterogeneity in the causal direction of dependence: A model-based recursive partitioning approach.

Methods of causal discovery and direction of dependence to evaluate causal properties of variable relations have experienced rapid development. The majority of causal discovery methods, however, relies on the assumption of causal effect homogeneity, that is, the identified causal structure is expected to hold for the entire population. Because causal mechanisms can vary across subpopulations, we propose combining methods of model-based recursive partitioning and non-Gaussian causal discovery to identify such subpopulations. The resulting algorithm can discover subpopulations with potentially varying magnitude and causal direction of effects under mild parameter inequality assumptions. Feasibility conditions are described and results from synthetic data experiments are presented suggesting that large effects and large sample sizes are beneficial for detecting causally competing subgroups with acceptable statistical performance. In a real-world data example, the extraction of meaningful subgroups that differ in the causal mechanism underlying the development of numerical cognition is illustrated. Potential extensions and recommendations for best practice applications are discussed.

Knowledge Discovery: Methods from data mining and machine learning.

The interdisciplinary field of knowledge discovery and data mining emerged from a necessity of big data requiring new analytical methods beyond the traditional statistical approaches to discover new knowledge from the data mine. This emergent approach is a dialectic research process that is both deductive and inductive. The data mining approach automatically or semi-automatically considers a larger number of joint, interactive, and independent predictors to address causal heterogeneity and improve prediction. Instead of challenging the conventional model-building approach, it plays an important complementary role in improving model goodness of fit, revealing valid and significant hidden patterns in data, identifying nonlinear and non-additive effects, providing insights into data developments, methods, and theory, and enriching scientific discovery. Machine learning builds models and algorithms by learning and improving from data when the explicit model structure is unclear and algorithms with good performance are difficult to attain. The most recent development is to incorporate this new paradigm of predictive modeling with the classical approach of parameter estimation regressions to produce improved models that combine explanation and prediction.

Kernel-Based Independence Tests for Causal Structure Learning on Functional Data.

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert-Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert-Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.

Aristotle: stratified causal discovery for omics data.

BACKGROUND: There has been a simultaneous increase in demand and accessibility across genomics, transcriptomics, proteomics and metabolomics data, known as omics data. This has encouraged widespread application of omics data in life sciences, from personalized medicine to the discovery of underlying pathophysiology of diseases. Causal analysis of omics data may provide important insight into the underlying biological mechanisms. Existing causal analysis methods yield promising results when identifying potential general causes of an observed outcome based on omics data. However, they may fail to discover the causes specific to a particular stratum of individuals and missing from others. METHODS: To fill this gap, we introduce the problem of stratified causal discovery and propose a method, Aristotle, for solving it. Aristotle addresses the two challenges intrinsic to omics data: high dimensionality and hidden stratification. It employs existing biological knowledge and a state-of-the-art patient stratification method to tackle the above challenges and applies a quasi-experimental design method to each stratum to find stratum-specific potential causes. RESULTS: Evaluation based on synthetic data shows better performance for Aristotle in discovering true causes under different conditions compared to existing causal discovery methods. Experiments on a real dataset on Anthracycline Cardiotoxicity indicate that Aristotle's predictions are consistent with the existing literature. Moreover, Aristotle makes additional predictions that suggest further investigations.

Asymmetric directed functional connectivity within the frontoparietal motor network during motor imagery and execution.

Both imagery and execution of motor control consist of interactions within a neuronal network, including frontal motor-related and posterior parietal regions. To reveal neural representation in the frontoparietal motor network, two approaches have been proposed thus far: one is decoding of actions/modes related to motor control from the spatial pattern of brain activity; and the other is estimating directed functional connectivity (a directed association between two brain regions within motor areas). However, directed connectivity among multiple regions of the frontoparietal motor network during motor imagery (MI) or motor execution (ME) has not been investigated. Here, we attempted to characterize the directed functional connectivity representing the MI and ME conditions. We developed a delayed sequential movement and imagery task to evoke brain activity associated with ME and MI, which can be recorded by functional magnetic resonance imaging. We applied a causal discovery approach, a linear non-Gaussian acyclic causal model, to identify directed functional connectivity among the frontoparietal motor-related brain regions for each condition. We demonstrated higher directed functional connectivity from the contralateral dorsal premotor cortex (dPMC) to the primary motor cortex (M1) in ME than in MI. We further identified significant direct effects of the dPMC and ventral premotor cortex (vPMC) to the parietal regions. In particular, connectivity from the dPMC to the superior parietal lobule (SPL) in the same hemisphere showed significant positive effects across all conditions, while interlateral connectivities from the vPMC to the SPL showed significantly negative effects across all conditions. Finally, we found positive effects from A1 to M1, that is, the audio-motor pathway, in the same hemisphere. These results indicate that the sources of motor command originating in the d/vPMC influenced the M1 and parietal regions for achieving ME and MI. Additionally, sequential sounds may functionally facilitate temporal motor processes.