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The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continous advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models based on neural networks, and its core contributions are as follows: (1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; (2) we outline some typical applications of causal effect estimation to industry; (3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments. [ABSTRACT FROM AUTHOR]

Causal inference is considered a crucial topic in the medical field, as it enables the determination of causal effects for medical treatments through data analysis. However, the vast volume and complexity of medical data present significant challenges for traditional machine learning methods in accurately assessing treatment effects. Issues such as noise in the data, unstructured information, and label sparsity can lead to unstable causal identification and erroneous correlation inference. To address these challenges, we propose a systematic survey of causal inference in the medical field, which encompasses studies utilizing observational data, aimed at organizing and summarizing the key concepts, methods, and applications of causal inference. Moreover, the causal inference applications are presented across various types of medical data, including medical images and Electronic Medical Records (EMR), using specific medical cases as examples. The thorough review not only emphasizes the theoretical and practical significance of causal inference methods but also highlights potential research directions in the medical domain. [ABSTRACT FROM AUTHOR]

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Abstract Background Propensity score analysis is increasingly used to control for confounding factors in observational studies. Unfortunately, unavoidable missing values make estimating propensity scores extremely challenging. We propose a new method for estimating propensity scores in data with missing values. Materials and methods Both simulated and real-world datasets are used in our experiments. The simulated datasets were constructed under 2 scenarios, the presence (T = 1) and the absence (T = 0) of the true effect. The real-world dataset comes from LaLonde’s employment training program. We construct missing data with varying degrees of missing rates under three missing mechanisms: MAR, MCAR, and MNAR. Then we compare MTNN with 2 other traditional methods in different scenarios. The experiments in each scenario were repeated 20,000 times. Our code is publicly available at https://github.com/ljwa2323/MTNN . Results Under the three missing mechanisms of MAR, MCAR and MNAR, the RMSE between the effect and the true effect estimated by our proposed method is the smallest in simulations and in real-world data. Furthermore, the standard deviation of the effect estimated by our method is the smallest. In situations where the missing rate is low, the estimation of our method is more accurate. Conclusions MTNN can perform propensity score estimation and missing value filling at the same time through shared hidden layers and joint learning, which solves the dilemma of traditional methods and is very suitable for estimating true effects in samples with missing values. The method is expected to be broadly generalized and applied to real-world observational studies.

The benefits and harms of lung cancer screening (LCS) for patients in the real-world clinical setting have been argued. Recently, discriminative prediction modeling of lung cancer with stratified risk factors has been developed to investigate the real-world effectiveness of LCS from observational data. However, most of these studies were conducted at the population level that only measured the difference in the average outcome between groups. In this study, we built counterfactual prediction models for lung cancer risk and mortality and examined for individual patients whether LCS as a hypothetical intervention reduces lung cancer risk and subsequent mortality. We investigated traditional and deep learning (DL)-based causal methods that provide individualized treatment effect (ITE) at the patient level and evaluated them with a cohort from the OneFlorida+ Clinical Research Consortium. We further discussed and demonstrated that the ITE estimation model can be used to personalize clinical decision support for a broader population. [ABSTRACT FROM AUTHOR]

Healthcare professionals increasingly rely on observational healthcare data, such as administrative claims and electronic health records, to estimate the causal effects of interventions. However, limited prior studies raise concerns about the real-world performance of the statistical and epidemiological methods that are used. We present the "OHDSI Methods Benchmark" that aims to evaluate the performance of effect estimation methods on real data. The benchmark comprises a gold standard, a set of metrics, and a set of open source software tools. The gold standard is a collection of real negative controls (drug-outcome pairs where no causal effect appears to exist) and synthetic positive controls (drug-outcome pairs that augment negative controls with simulated causal effects). We apply the benchmark using four large healthcare databases to evaluate methods commonly used in practice: the new-user cohort, self-controlled cohort, case-control, case-crossover, and self-controlled case series designs. The results confirm the concerns about these methods, showing that for most methods the operating characteristics deviate considerably from nominal levels. For example, in most contexts, only half of the 95% confidence intervals we calculated contain the corresponding true effect size. We previously developed an "empirical calibration" procedure to restore these characteristics and we also evaluate this procedure. While no one method dominates, self-controlled methods such as the empirically calibrated self-controlled case series perform well across a wide range of scenarios.

Background: Propensity score analysis is increasingly used to control for confounding factors in observational studies. Unfortunately, unavoidable missing values make estimating propensity scores extremely challenging. We propose a new method for estimating propensity scores in data with missing values. Materials and methods: Both simulated and real-world datasets are used in our experiments. The simulated datasets were constructed under 2 scenarios, the presence (T = 1) and the absence (T = 0) of the true effect. The real-world dataset comes from LaLonde's employment training program. We construct missing data with varying degrees of missing rates under three missing mechanisms: MAR, MCAR, and MNAR. Then we compare MTNN with 2 other traditional methods in different scenarios. The experiments in each scenario were repeated 20,000 times. Our code is publicly available at https://github.com/ljwa2323/MTNN. Results: Under the three missing mechanisms of MAR, MCAR and MNAR, the RMSE between the effect and the true effect estimated by our proposed method is the smallest in simulations and in real-world data. Furthermore, the standard deviation of the effect estimated by our method is the smallest. In situations where the missing rate is low, the estimation of our method is more accurate. Conclusions: MTNN can perform propensity score estimation and missing value filling at the same time through shared hidden layers and joint learning, which solves the dilemma of traditional methods and is very suitable for estimating true effects in samples with missing values. The method is expected to be broadly generalized and applied to real-world observational studies. [ABSTRACT FROM AUTHOR]

Hybrid modeling integrates machine learning with scientific knowledge to enhance interpretability, generalization, and adherence to natural laws. Nevertheless, equifinality and regularization biases pose challenges in hybrid modeling to achieve these purposes. This paper introduces a novel approach to estimating hybrid models via a causal inference framework, specifically employing double machine learning (DML) to estimate causal effects. We showcase its use for the Earth sciences on two problems related to carbon dioxide fluxes. In the Q _10 model, we demonstrate that DML-based hybrid modeling is superior in estimating causal parameters over end-to-end deep neural network approaches, proving efficiency, robustness to bias from regularization methods, and circumventing equifinality. Our approach, applied to carbon flux partitioning, exhibits flexibility in accommodating heterogeneous causal effects. The study emphasizes the necessity of explicitly defining causal graphs and relationships, advocating for this as a general best practice. We encourage the continued exploration of causality in hybrid models for more interpretable and trustworthy results in knowledge-guided machine learning.

This work aims to classify catchments through the lens of causal inference and cluster analysis. In particular, it uses causal effects (CEs) of meteorological variables on river discharge while only relying on easily obtainable observational data. The proposed method combines time series causal discovery with CE estimation to develop features for a subsequent clustering step. Several ways to customize and adapt the features to the problem at hand are discussed. In an application example, the method is evaluated on 358 European river catchments. The found clusters are analyzed using the causal mechanisms that drive them and their environmental attributes. [ABSTRACT FROM AUTHOR]

A cornerstone of clinical medicine is intervening on a continuous exposure, such as titrating the dosage of a pharmaceutical or controlling a laboratory result. In clinical trials, continuous exposures are dichotomized into narrow ranges, excluding large portions of the realistic treatment scenarios. The existing computational methods for estimating the effect of continuous exposure rely on a set of strict assumptions. We introduce new methods that are more robust towards violations of these assumptions. Our methods are based on the key observation that changes of exposure in the clinical setting are often achieved gradually, so effect estimates must be “locally” robust in narrower exposure ranges. We compared our methods with several existing methods on three simulated studies with increasing complexity. We also applied the methods to data from 14 k sepsis patients at M Health Fairview to estimate the effect of antibiotic administration latency on prolonged hospital stay. The proposed methods achieve good performance in all simulation studies. When the assumptions were violated, the proposed methods had estimation errors of one half to one fifth of the state-of-the-art methods. Applying our methods to the sepsis cohort resulted in effect estimates consistent with clinical knowledge. [ABSTRACT FROM AUTHOR]

This work aims to classify catchments through the lens of causal inference and cluster analysis. In particular, it uses causal effects (CEs) of meteorological variables on river discharge while only relying on easily obtainable observational data. The proposed method combines time series causal discovery with CE estimation to develop features for a subsequent clustering step. Several ways to customize and adapt the features to the problem at hand are discussed. In an application example, the method is evaluated on 358 European river catchments. The found clusters are analyzed using the causal mechanisms that drive them and their environmental attributes.

Propensity Score Matching (PSM) is a useful method to reduce the impact of Treatment-Selection Bias in the estimation of causal effects in observational studies. After matching, the PSM significantly reduces the sample under investigation, which may lead to other possible biases (due to overfitting, excess of covariation or a reduced number of observations). In this sense, we wanted to analyze the behavior of this PSM compared with other widely used methods to deal with non-comparable groups, such as the Multivariate Regression Model (MRM). Monte Carlo Simulations are made to construct groups with different effects in order to compare the behavior of PSM and MRM estimating these effects. In addition, the Treatment Selection Bias reduction for the PSM is calculated. With the PSM a reduction in the Treatment Selection Bias is achieved (0.983 [0.982, 0.984]), with a reduction in the Relative Real Treatment Effect Estimation Error (0.216 [0.2, 0.232]), but despite this bias reduction and estimation error reduction, the MRM reduces this estimation error significantly more than the PSM (0.539 [0.522, 0.556], p < 0.001). In addition, the PSM leads to a 30% reduction in the sample. This loss of information derived from the matching process may lead to another not known bias and thus to the inaccuracy of the effect estimation compared with the MRM. [ABSTRACT FROM AUTHOR]

Trajectory forecasting is crucial for the advancement of autonomous vehicles. While much progress has been made, extant approaches often fall short in accounting for intricate social interactions and the unpredictability of human behavior. This paper introduces a novel multi-modal trajectory forecasting model named Multi-scale Interaction and Multi-pseudo-target Supervision (MIMS). Central to our approach is a multiscale hypergraph that discerns latent interactions across all scales, evaluating both their strength and type. Further enhancing our model's capabilities is a causal-effect-estimation-based pseudo-target generation method. This facilitates multi-modality modeling in motion forecasting by offering explicit supervision with multiple latent targets. We validate MIMS using the Argoverse Motion Forecasting dataset. The results reveal that MIMS outperforms current state-of-the-art models across various traffic conditions. Specifically, our multiscale hypergraph exhibits a superior capacity for capturing complex spatiotemporal dependencies compared to pairwise methods. Moreover, our multi-pseudo-target supervision eliminates the pattern convergence of multi-modal forecasting. [ABSTRACT FROM AUTHOR]

Out-of-distribution (OOD) generalization aims to generalize a model trained on source domains to unseen target domains. Recently, causality-based generalization methods have focused on learning invariant causal relationships around the label variable, as causal mechanisms are robust across different domains. However, these methods would yield an inaccurate causal variable set due to the lack of heterogeneous domain data or a prior causal structure, which severely weakens their generalization capacity. To address this problem, we propose a Causally Invariant Features Discovery (CIFD) framework, which combines causal structure discovery and causal effect estimation for selecting a high-quality causal variable set and realizing better OOD generalization. Specifically, CIFD first identifies all potential causal variables by learning a double-layer-based local causal structure around the label variable. Secondly, CIFD uses a double-layer causal effect estimator for estimating the causality of potential causal variables and obtaining true causal variables. The comprehensive experiments on both regression and classification tasks clearly demonstrate the superiority of our framework over the state-of-art methods. • We propose a CIFD framework to find accurate causal variables for OOD generalization. • Potential causal variables are identified by a double-layer local causal structure. • True causal variables are learnt by a double-layer total causal effect estimator. • Comprehensive experiments demonstrate the superiority of CIFD over the SOTA methods. [ABSTRACT FROM AUTHOR]

Time series data are a collection of chronological observations which are generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting and clustering have been proposed to analyze this type of data. Time series data have been also used to study the effect of interventions overtime. Moreover, in many fields of science, learning the causal structure of dynamic systems and time series data is considered an interesting task which plays an important role in scientific discoveries. Estimating the effect of an intervention and identifying the causal relations from the data can be performed via causal inference. Existing surveys on time series discuss traditional tasks such as classification and forecasting or explain the details of the approaches proposed to solve a specific task. In this paper, we focus on two causal inference tasks, i.e., treatment effect estimation and causal discovery for time series data and provide a comprehensive review of the approaches in each task. Furthermore, we curate a list of commonly used evaluation metrics and datasets for each task and provide an in-depth insight. These metrics and datasets can serve as benchmark for research in the field. [ABSTRACT FROM AUTHOR]

BackgroundIn two-sample Mendelian randomization (MR) studies, sex instrumental heterogeneity is an important problem needed to address carefully, which however is often overlooked and may lead to misleading causal inference.MethodsWe first employed cross-trait linkage disequilibrium score regression (LDSC), Pearson’s correlation analysis, and the Cochran’s Q test to examine sex genetic similarity and heterogeneity in instrumental variables (IVs) of exposures. Simulation was further performed to explore the influence of sex instrumental heterogeneity on causal effect estimation in sex-specific two-sample MR analyses. Furthermore, we chose breast/prostate cancer as outcome and four anthropometric traits as exposures as an illustrative example to illustrate the importance of taking sex heterogeneity of instruments into account in MR studies.ResultsThe simulation definitively demonstrated that sex-combined IVs can lead to biased causal effect estimates in sex-specific two-sample MR studies. In our real applications, both LDSC and Pearson’s correlation analyses showed high genetic correlation between sex-combined and sex-specific IVs of the four anthropometric traits, while nearly all the correlation coefficients were larger than zero but less than one. The Cochran’s Q test also displayed sex heterogeneity for some instruments. When applying sex-specific instruments, significant discrepancies in the magnitude of estimated causal effects were detected for body mass index (BMI) on breast cancer (P = 1.63E-6), for hip circumference (HIP) on breast cancer (P = 1.25E-20), and for waist circumference (WC) on prostate cancer (P = 0.007) compared with those generated with sex-combined instruments.ConclusionOur study reveals that the sex instrumental heterogeneity has non-ignorable impact on sex-specific two-sample MR studies and the causal effects of anthropometric traits on breast/prostate cancer would be biased if sex-combined IVs are incorrectly employed.

Background: In two-sample Mendelian randomization (MR) studies, sex instrumental heterogeneity is an important problem needed to address carefully, which however is often overlooked and may lead to misleading causal inference. Methods: We first employed cross-trait linkage disequilibrium score regression (LDSC), Pearson's correlation analysis, and the Cochran's Q test to examine sex genetic similarity and heterogeneity in instrumental variables (IVs) of exposures. Simulation was further performed to explore the influence of sex instrumental heterogeneity on causal effect estimation in sex-specific two-sample MR analyses. Furthermore, we chose breast/prostate cancer as outcome and four anthropometric traits as exposures as an illustrative example to illustrate the importance of taking sex heterogeneity of instruments into account in MR studies. Results: The simulation definitively demonstrated that sex-combined IVs can lead to biased causal effect estimates in sex-specific two-sample MR studies. In our real applications, both LDSC and Pearson's correlation analyses showed high genetic correlation between sex-combined and sex-specific IVs of the four anthropometric traits, while nearly all the correlation coefficients were larger than zero but less than one. The Cochran's Q test also displayed sex heterogeneity for some instruments. When applying sex-specific instruments, significant discrepancies in the magnitude of estimated causal effects were detected for body mass index (BMI) on breast cancer (P = 1.63E-6), for hip circumference (HIP) on breast cancer (P = 1.25E-20), and for waist circumference (WC) on prostate cancer (P = 0.007) compared with those generated with sex-combined instruments. Conclusion: Our study reveals that the sex instrumental heterogeneity has non-ignorable impact on sex-specific two-sample MR studies and the causal effects of anthropometric traits on breast/prostate cancer would be biased if sex-combined IVs are incorrectly employed. [ABSTRACT FROM AUTHOR]

Propensity Score Matching (PSM) is a useful method to reduce the impact of Treatment-Selection Bias in the estimation of causal effects in observational studies. After matching, the PSM significantly reduces the sample under investigation, which may lead to other possible biases (due to overfitting, excess of covariation or a reduced number of observations). In this sense, we wanted to analyze the behavior of this PSM compared with other widely used methods to deal with non-comparable groups, such as the Multivariate Regression Model (MRM). Monte Carlo Simulations are made to construct groups with different effects in order to compare the behavior of PSM and MRM estimating these effects. In addition, the Treatment Selection Bias reduction for the PSM is calculated. With the PSM a reduction in the Treatment Selection Bias is achieved (0.983 [0.982, 0.984]), with a reduction in the Relative Real Treatment Effect Estimation Error (0.216 [0.2, 0.232]), but despite this bias reduction and estimation error reduction, the MRM reduces this estimation error significantly more than the PSM (0.539 [0.522, 0.556], p < 0.001). In addition, the PSM leads to a 30% reduction in the sample. This loss of information derived from the matching process may lead to another not known bias and thus to the inaccuracy of the effect estimation compared with the MRM.

Cold‐pool‐driven convective initiation is investigated in high‐resolution, convection‐permitting simulations with a focus on the diurnal cycle and organization of convection and the sensitivity to grid size. Simulations of four different days over Germany were performed using the ICON‐LEM model with grid sizes from 156 to 625 m. In these simulations, we identify cold pools, cold‐pool boundaries and initiated convection. Convection is triggered much more efficiently in the vicinity of cold pools than in other regions and can provide as much as 50% of total convective initiation, in particular in the late afternoon. By comparing different model resolutions, we find that cold pools are more frequent, smaller and less intense in lower‐resolution simulations. Furthermore, their gust fronts are weaker and less likely to trigger new convection. To identify how model resolution affects this triggering probability, we use a linear causal graph analysis. In doing so, we postulate a graph structure with potential causal pathways and then apply multi‐linear regression accordingly. We find a dominant, systematic effect: reducing grid sizes directly reduces upward mass flux at the gust front, which causes weaker triggering probabilities. These findings are expected to be even more relevant for km‐scale, numerical weather prediction models. We thus expect that a better representation of cold‐pool‐driven convective initiation will improve forecasts of convective precipitation. [ABSTRACT FROM AUTHOR]

The benefits and harms of lung cancer screening (LCS) for patients in the real-world clinical setting have been argued. Recently, discriminative prediction modeling of lung cancer with stratified risk factors has been developed to investigate the real-world effectiveness of LCS from observational data. However, most of these studies were conducted at the population level that only measured the difference in the average outcome between groups. In this study, we built counterfactual prediction models for lung cancer risk and mortality and examined for individual patients whether LCS as a hypothetical intervention reduces lung cancer risk and subsequent mortality. We investigated traditional and deep learning (DL)-based causal methods that provide individualized treatment effect (ITE) at the patient level and evaluated them with a cohort from the OneFlorida+ Clinical Research Consortium. We further discussed and demonstrated that the ITE estimation model can be used to personalize clinical decision support for a broader population.

Terza (2016b, Health Services Research 51: 1109-1113) gives the correct generic expression for the asymptotic standard errors of statistics formed as sample means of nonlinear data transformations. In this article, I assess the performance of the Stata margins command as a relatively simple alternative for calculating such standard errors. I note that margins is not available for all packaged nonlinear regression commands in Stata and cannot be implemented in conjunction with user-defined-and-coded nonlinear estimation protocols that do not make a predict command available. When margins is available, however, I establish (using a real-data example) that it produces standard errors that are asymptotically equivalent to those obtained from the formulations in Terza (2016b) and the appendix available with this article. This result favors using margins (with its relative coding simplicity) when available. In all other cases, use Mata to code the standard-error formulations in Terza (2016b). I discuss examples, and I give corresponding Stata do-files in appendices. [ABSTRACT FROM AUTHOR]

This paper shows how Monte Carlo simulation can be used for sample size, power or precision calculations when planning medical research studies. Standard study designs can lead to the use of analysis methods for which power formulae do not exist. This may be because complex modelling techniques with optimal statistical properties are used but power formulae have not yet been derived or because analysis models are employed that divert from the population model due to lack of availability of more appropriate analysis tools. Our presentation concentrates on the conceptual steps involved in carrying out power or precision calculations by simulation. We demonstrate these steps in three examples concerned with (i) drop out in longitudinal studies, (ii) measurement error in observational studies and (iii) causal effect estimation in randomised controlled trials with non-compliance. We conclude that the Monte Carlo simulation approach is an important general tool in the methodological arsenal for assessing power and precision. [ABSTRACT FROM AUTHOR]