The Nonlinear Causal Effect Estimation of the Built Environment on Urban Rail Transit Station Flow Under Emergency

Abstract

Urban rail transit (URT) systems are critical for sustainable urban mobility but are increasingly vulnerable to disruptions and emergencies. While extensive research has examined the built environment’s influence on transit demand under normal conditions, the nonlinear causal mechanisms shaping URT passenger flow during emergencies remain understudied. This study proposes an artificial intelligence-based causal machine learning framework integrating causal structure learning and causal effect estimation to investigate how the built environment, network structure, and incident characteristics causally affect URT station-level ridership during emergencies. Using empirical data from Shanghai’s URT network, this study uncovers dual pathways through which built environment attributes affect passenger flow: by directly shaping baseline ridership and indirectly influencing intermodal connectivity (e.g., bus connectivity) that mitigates disruptions. The findings demonstrate significant nonlinear and heterogeneous causal effects; notably, stations with high network centrality experience disproportionately severe ridership losses during disruptions, while robust bus connectivity substantially buffers such impacts. Incident type and timing also notably modulate disruption severity, with peak-hour incidents and severe disruptions (e.g., power failures) amplifying passenger flow declines. These insights highlight critical areas for policy intervention, emphasizing the necessity of targeted management strategies, enhanced intermodal integration, and adaptive emergency response protocols to bolster URT resilience under crisis scenarios.

1. Introduction

Urban rail transit (URT) is widely recognized as a sustainable transportation mode crucial for satisfying human mobility demands in rapidly urbanizing contexts. However, with accelerating urbanization, URT systems are increasingly exposed to diverse emergencies, ranging from natural disasters to transit incidents. For instance, the Shanghai Metro collision in 2011 caused 295 injuries due to delayed emergency responses, and the Moscow Metro derailment in 2014 resulted in 24 fatalities and 160 injuries, highlighting severe consequences from inadequate emergency management [1]. Such incidents underscore the necessity of investigating factors that influence metro passenger flow under emergency conditions.

While extensive studies have investigated the built environment’s influence on transit demand under normal operational conditions [2], there has been relatively little exploration of the causal mechanisms affecting URT passenger flow during emergency scenarios [3]. Conventional studies often rely on linear assumptions or static correlations [4], failing to capture the abrupt, threshold-driven behavioral shifts and spatial reconfigurations characteristic of crisis scenarios. This knowledge gap critically undermines cities’ capacities to develop resilient infrastructure and implement effective emergency response strategies [5]. Moreover, the complexity of URT systems, especially under emergency conditions, highlights the importance of recognizing nonlinear relationships and threshold effects. Leveraging artificial intelligence (AI) becomes essential, as it allows capturing the complex and nonlinear interactions inherent in emergency scenarios [6]. Practically, employing AI-based approaches enhances prediction accuracy and provides critical insights, aiding policymakers and transit planners in designing more robust and adaptive emergency management strategies.

Due to the complex interaction between URT and urban built environment systems, traditional machine learning methods alone are insufficient [7] for accurately quantifying causal effects and understanding influencing mechanisms. Therefore, this study proposes an AI-based causal machine learning model to investigate causal relationships and influence mechanisms among the built environment, URT network structure, and broader urban transportation systems on URT station-level short-term ridership under incident and emergency conditions. Therefore, this study primarily attempts to address three primary questions. Firstly, how to discover the causal relationship among the influencing factors on the URT station-level short-term ridership by following a hypothesis-testing paradigm through Granger causality tests to construct a causal graph model. Among influencing factors, which demonstrate mere correlations, and which exhibit causal relationships with URT station-level ridership? Secondly, the causal effect estimation. Among factors identified as causally related to the URT station-level short-term ridership, how can we accurately measure their causal effects? To address this, we propose a double machine learning-based approach, further measuring heterogeneous causal effects under varying built environment conditions to uncover nonlinear and threshold-driven mechanisms.

Therefore, this study contributes to the existing knowledge in three aspects. First, theoretically, it introduces a framework explicitly capturing nonlinear causality between the built environment and the URT station-level short-term ridership under incident and emergency conditions. Second, the proposed AI-based methodological approach facilitates analyzing the nonlinear and threshold effects of influential factors on URT incidents and emergencies. Third, practically, the findings offer crucial guidance for evidence-based policy formulation, enabling the identification of built environment and rail network conditions that potentially trigger dynamic spatiotemporal passenger flow surges.

The remainder of this study is organized as follows. Section 2 reviews the existing literature. Section 3 presents the methodology framework. Section 4 introduces the empirical study dataset. Section 5 presents the results and discusses the policy implications for resilient planning. Section 6 concludes the entire study and directs future studies.

2. Literature Review

2.1. The Influencing Mechanism of URT Station-Level Ridership

Numerous studies have investigated that station-level URT ridership is shaped by a wide range of factors, broadly including the surrounding built environment, local socio-economic context, and transit service attributes [8,9,10]. High population and employment densities around stations are among the strongest predictors of greater ridership [11]. For example, a seminal analysis of 268 U.S. light rail stations found that higher residential and job densities within walking distance significantly boost boardings [9]. Land-use diversity and the presence of key destinations (e.g., retail, schools, offices) in the catchment also correlate with increased usage [9]. Mohamad Zulkifli et al. [12] find that the counts of nearby residences, shops, hotels, schools, and workplaces all exhibited positive associations with station entries/exits in Taipei’s metro. These built environment elements collectively enhance the convenience and necessity of using transit, thereby lifting demand.

Socio-economic characteristics of the station area population further modulate ridership levels. Lower income and lower car-ownership communities tend to rely more on transit, boosting station patronage. For example, He et al. [13] have provided the basic knowledge that population and employment densities dominate commuting ridership but with different spatial distributions, while entertainment venues strongly affect weekend ridership in specific urban zones. Wang et al. [14] observed that a higher percentage of nearby residents who are renters (often a proxy for lower car ownership) was associated with greater light-rail boardings in U.S. cities. This underscores the role of car availability and demographics in transit use propensity. Meanwhile, a station’s position within the transit network and the quality of transit services are critical factors. Stations functioning as transfer hubs or line termini typically attract higher ridership due to network connectivity [9]. In the U.S. and Seoul, dummy variables for transfer stations or terminus stations have been found positive and significant in ridership models [15]. Service attributes such as higher train frequency, longer operating hours, and lower fares similarly encourage heavier use, although these are sometimes represented indirectly via ridership patterns in the data. Choi et al. [16] establish a comprehensive modeling framework that quantifies how network expansion impacts existing station ridership through accessibility improvements and land-use changes, demonstrating that accessibility increments positively correlate with ridership growth.

Crucially, the influence of these factors is not uniform across all stations since there is marked heterogeneity across different spatial and temporal contexts. The elasticity of ridership with respect to a given factor can vary by neighborhood type, city, or time period [10,17]. Recent research using geographically weighted regression (GWR) reveals that built environment effects are location-specific, with station-area variables exhibiting stronger impacts in some areas than others [18]. For instance, one study in Madrid showed that an ordinary least squares (OLS) model assuming constant effects understated the complexity of ridership drivers; a GWR model yielded a better fit and uncovered significant spatial variation in how access to jobs, population, and other factors influence different stations [19]. And Cardozo et al. [19] reveal significant spatial heterogeneity in how these factors influence ridership, demonstrating that identical variables can have markedly different impacts across station catchment areas by providing empirical evidence from a developing Asian city context (Kuala Lumpur), addressing a research gap as most existing studies focus on Western or developed Asian cities. Temporal differences add another layer that the determinants of ridership during peak hours or weekdays can differ from those during off-peak or weekends. Yu Li et al. [11] find that some station-level factors (e.g., proximity to workplaces) have a larger impact on weekday commuter ridership, whereas others (e.g., leisure destinations) matter more on weekends. This underscores the importance of context, that a variable’s effect may hinge on land-use context, traveler type, or time of day.

Moreover, studies suggest interactive and causal relationships among factors. Built environment and service quality often interplay: transit-supportive land use may only translate to high ridership if reliable service is provided, and conversely, high service levels amplify the ridership gains from dense, mixed-use development [20]. In normal operating scenarios, built-environment variables exhibit complex, context-dependent associations with metro ridership. Yang et al. [21] employ random forest models on Chengdu smart-card and mobile-signal data to reveal that land-use mix and population density drive morning-peak ridership, whereas employment and road network densities dominate evening-peak demand, highlighting pronounced nonlinearity and temporal heterogeneity. An et al. [22] use POI-based principal component analysis and OLS regression in Shanghai to show that commercial land use and intermodal connectivity positively impact weekday and weekend boardings, while intersection density yields counterintuitive effects, prompting a call for multilevel walkability metrics. Ref. [23] apply gradient boosting trees to Nanjing origin–destination smart-card data and demonstrate discontinuous, nonlinear built-environment impacts that differ by peak period and station role, with origin-side variables more influential in the morning than in the evening. In summary, global evidence confirms a core set of factors, i.e., land use patterns, socio-demographics, and service connectivity, as key drivers of URT station ridership under normal conditions, while highlighting considerable heterogeneity and context-dependent causal interactions in their effects across different cities and times, which illustrates the consideration of the nonlinear effects as well.

2.2. URT Passenger Flow Under Incident and Emergency Conditions

The incident and emergency conditions in URT network led to complex behavioral and network responses. Early investigations into transit disruptions relied heavily on simulation-based approaches to estimate impacts under hypothetical failure scenarios, and in the past few years, the increasing availability of empirical data on disruptions has enabled data-driven analysis of ridership under real incident conditions [24]. Several studies have leveraged smart card data to perform counterfactual analyses comparing ridership during disruption periods to what would be expected normally. Liu et al. [25] used AFC data in Beijing to estimate the drop in entries and exits at affected stations during disruptions relative to typical days. By constructing a baseline of normal ridership patterns, they quantified the immediate demand loss due to an incident. Sun and Guan [26] took this further by combining passenger flows with network topology to estimate not only station-level demand loss but also how the major disruption propagates through a metro network.

More routine disruptions (like equipment failures or minor floods) can likewise have network-wide repercussions. A study by Silva et al. [27] focused on predicting not only where disruptions would occur but also the resulting passenger delays and network effects, using Dutch transit data. Research employing origin–destination (OD) matrix prediction has also emerged: by forecasting short-term OD flows under partial outages, operators can proactively manage crowding and arrange bridging services [28]. For example, one deep learning model can predict how the usual OD matrix of a metro system will redistribute if a station is closed, providing a basis for real-time intervention [29,30].

Traditional analyses often assumed disruptions occur randomly, but recent work recognizes that some stations are more prone to failures (due to aging infrastructure, etc.), and ridership changes could be confounded by external factors (weather, special events) [31]. To tackle this, Zhang et al. [32] proposed a causal evaluation framework for metro disruptions using a synthetic control approach. In their method, each disrupted station-day is paired with a “synthetic” control built from similar days without disruptions, enabling an estimate of the counterfactual ridership had the disruption not occurred. Other studies using causal inference include propensity score matching to compare disrupted vs. non-disrupted scenarios while controlling for station characteristics [33] and even instrumental variable approaches (e.g., using infrastructure aging as an instrument for disruption likelihood) to estimate long-term ridership attrition after repeated incidents [34]. Simulation remains valuable for exploring extreme scenarios [35], but these newer data-driven and causal methods have provided unprecedented insight by leveraging actual disruption observations [27].

2.3. Research Gap

From the above review, it is evident that station-level ridership under normal conditions has been extensively studied, yielding well-established relationships with the built environment and service features. In contrast, the causal mechanisms during emergencies and disruptions remain less understood. While recent works have started to quantify these impacts, there is a notable gap in examining how the built environment and network structure together influence ridership resilience or vulnerability during incidents. Another limitation in past studies is in model interpretability and causal insight. Traditional regression models offered clear interpretation but did not handle disruptions, whereas many modern predictive models (machine learning, simulation outputs) provide detailed forecasts yet function as black boxes with respect to causation [36]. Thus, there is a strong need for approaches that can discern true causal relationships in the context of disruptions.

Addressing this gap is important for both theory and practice. By applying a causal AI framework, the current study aims to integrate data-driven modeling with causal inference techniques to reveal not just correlations but the underlying cause–effect mechanisms in URT ridership, in both normal and disrupted scenarios. Such an approach can improve interpretability without sacrificing the complexity needed to capture networked, spatiotemporal phenomena. This study will fill the identified gap by illuminating the coupled role of network structure and station context in shaping disruption outcomes.

3. Methodology

3.1. Research Framework

Nonlinear causal mechanisms describe situations in which the magnitude or direction of a treatment effect varies in a non-proportional manner across the range of covariates or treatment intensities. For example, incremental increases in transfer penalties may initially have modest impact on ridership but accelerate rapidly beyond a certain penalty level. Threshold effects refer to specific points at which small changes in a covariate produce abrupt shifts in the treatment effect.

This study proposes a causal machine learning framework to investigate the nonlinear causal mechanisms and threshold effects behind station-level URT ridership changes during emergency incidents and service disruptions. The proposed framework integrates causal structure learning and causal effect estimation in a two-module setup. The overall structure is designed to identify which factors (e.g., network topology measures, built environment characteristics, external disruption factors) have a causal influence on ridership drops at stations and to quantify the magnitude of these influences.

The outcome variable in this study is the station-level URT ridership change during the incident and emergency conditions (e.g., decrease in passenger entries/exits compared to normal conditions). Treatment variables denote the specific disruptions or interventions whose causal impact on station-level ridership is under investigation, such as service suspension events or incident durations. Confounders refer to background factors that influence both the treatment and the outcome but are not themselves the focus of the analysis, such as station-area characteristics or prevailing weather conditions. By accounting for these confounding influences, the analysis isolates the direct effect of each treatment variable on ridership change. Let $Y$ denote this outcome variable. This study considers a set of potential determinant variables that may causally affect $Y$. Specifically, the explanatory variables include three categories.

• First, URT network structure indicators (e.g., a station’s connectivity, centrality, transfer degree, or availability of alternative lines);
• Second, station-level built environment features around the station (e.g., land-use mix, job accessibility, presence of nearby transit options);
• Third, external factors (e.g., characteristics of the disruption incident, service suspension duration, weather, or policy interventions).

In the first module, we learn a causal directed acyclic graph (DAG) $G=(N,E)$ from data using a structure learning algorithm, where $N$ represents the set of variables (including the outcome variable $Y$, treatment variables $T$, and confounders $X$), and E denotes the directed causal edges. The DAG encodes hypothesized causal relationships among all variables in $N$. An edge $A\to B$ in $E$ indicates that variable $A$ has a direct causal influence on $B$. The second module then performs causal effect estimation using each casual edge in the identified DAG. We estimate both the average treatment effect (ATE) and the conditional average treatment effect (CATE) for specific conditions. This module employs a double machine learning approach to obtain robust estimates of these causal effects. The causal effect estimation framework is demonstrated in Figure 1.

3.2. Causal Discovery and Structure Learning

The accurate discovery of causal relationships from observational data faces substantial challenges due to potential overfitting and spurious relationships, especially in purely data-driven approaches. Therefore, this study proposes a hybrid causal discovery framework that combines the NOTEARS algorithm [1], a purely data-driven causal discovery method, with domain knowledge to ensure robust and interpretable causal relationships. It should be noted that the incident dataset comprises cross-sectional observations of discrete disruption events, each without follow-up measurements at subsequent time points. As a result, there is no panel or time-series structure in which lagged variables could be used to test temporal precedence. Granger causality tests require sequential data across uniform time intervals to validate predictive causal ordering. In the absence of such longitudinal incidence records, Granger methods are not applicable for temporal validation in this study.

3.2.1. Integration with Domain Knowledge

Purely data-driven causal discovery algorithms often risk identifying spurious relationships or overly dense causal graphs, limiting interpretability and practical utility. To mitigate this issue, we integrate domain knowledge from urban transportation theory and network analysis to pre-specify structural constraints, reducing implausible causal relationships.

Specifically, we construct a prior constraint matrix (PCM) to limit the causal search space of the NOTEARS algorithm. PCM is defined as Equation (1):

$${\mathrm{PCM}}_{ij}=\left\{\begin{array}{c}0,\mathrm{if}\mathrm{causal}\mathrm{link}\mathrm{from}\mathrm{i}\mathrm{to}\mathrm{j}\mathrm{is}\mathrm{impossible}\\ 1,\mathrm{if}\mathrm{causal}\mathrm{link}\mathrm{from}\mathrm{i}\mathrm{to}\mathrm{j}\mathrm{is}\mathrm{possible}\end{array}\right.$$

(1)

For example, consider the link between incident type and incident duration. Domain expertise indicates that the nature of an event such as signal failure determines how long the service disruption will last, whereas the actual length of the disruption cannot casually change the incident type. By encoding this one-way constraint in the prior matrix, only the path from incident type to duration is explored, and any reverse connection is prohibited. Thus, links from outcome variables to certain treatments are set as zero in PCM, constraining the causal discovery algorithm to explore only plausible directional relationships.

3.2.2. Domain-Constrained NOTEARS Optimization

Using PCM, we modify the NOTEARS algorithm’s optimization problem to Equation (2):

$$\begin{array}{l}\underset{B\in {ℝ}^{d\times d}}{\min }{\displaystyle \frac{1}{2n}}{‖X-X{B}^T‖}_F^2+\lambda {‖B‖}_1\\ s.t.\left\{\begin{array}{c}h\left(B\right)=Tr\left(e^{B\circ B}\right)-d=0\\ B_{ij}=0{\mathrm{if}\mathrm{PCM}}_{ij}=0\end{array}\right.\end{array}$$

(2)

where $B\in {ℝ}^{d\times d}$ denotes the weighted adjacency matrix of DAG, where nonzero entries represent causal relationships; $X\in {ℝ}^{d\times d}$ is the observed data matrix; ${‖B‖}_1$ is the sum of absolute values in $B$, promoting sparsity; $\lambda$ is the regularization parameter to control sparsity; and $h(B)$ is the constraint function ensuring the resulting graph is a DAG.

Then, the constrained optimization can be solved via an augmented Lagrangian method, as in Equation (3):

$$\mathcal{L}\left(B,\alpha \right)={\displaystyle \frac{1}{2n}}{‖X-X{B}^T‖}_F^2+\lambda {‖B‖}_1+\alpha h\left(B\right)+{\displaystyle \frac{\rho }{2}}{\left[h\left(B\right)\right]}^2$$

(3)

where $\alpha$ is the Lagrange multiplier and $\rho$ is the penalty coefficient. Based on the gradient descent on Equation (3), we can learn an optimized causal DAG. The pseudocode of the NOTEARS algorithm is presented in Appendix A Algorithm A1.

3.3. Double Machine Learning for Causal Effect Estimation

3.3.1. Causal Effect Estimation

The double machine learning procedure is now presented as a three-step framework designed for intuitive understanding. Gradient boosting decision trees fit flexible predictive models for both the outcome and the treatment to capture potential nonlinearities. Model predictions are subtracted from observed values to yield residuals that isolate variation not explained by confounders. A simple regression of residualized outcome on residualized treatment produces an unbiased estimate of the causal effect. K-fold cross-fitting is applied throughout to prevent overfitting, ensuring that estimated effects reflect genuine causal relationships rather than artifacts of the sample.

Specifically, based on the learned structure DAG, the model could be defined as

$$\left\{\begin{array}{c}Y=F\left(V\right)\cdot X+g\left(V,W\right)+\epsilon \\ X=h\left(V,W\right)+\upsilon \end{array}\right.$$

(4)

where $F(V)$ denotes the function representing heterogeneous treatment effect (i.e., the conditional average treatment effect), needing to be estimated in a three-step double machine learning (DML) method. $g(V,W)$ and $h(V,W)$ denote the influencing functions of external factors with the exclusion of $X$; $\epsilon$ and $\upsilon$ denote stochastic error terms.

We employ the DML algorithm to estimate $F(V)$ accounting for the high-dimensional $(V,W)$ flexibly. The estimating process can be summarized in three main steps:

• Firstly, learn the influencing functions $g(V,W)$ and $h(V,W)$ using a machine learning algorithm, such as the gradient boosting decision tree [37].
• Secondly, residualize $Y$ and $X$ to remove variation due to $(V,W)$.
• Thirdly, regress the residualized outcome on residualized treatment to estimate the causal effect. We also utilize cross-fitting to avoid overfitting in the estimation.

The prediction models of the outcome and treatment variables are first trained to capture all variations explained by confounders. Observed values are then adjusted by subtracting these model predictions, yielding residuals that are stripped of confounding influences. Because the residualized treatment is rendered orthogonal to any function of the confounders, and the residualized outcome likewise contains only variations unrelated to those confounders, the subsequent regression of residualized outcome on residualized treatment isolates the direct causal association. This procedure effectively simulates a randomized experiment by ensuring that, conditional on the revisualization, the treatment assignment is independent of unobserved factors, thereby strengthening the validity of the estimated causal effect.

Specifically, using the observational data, we firstly estimate $\widehat{g}(V,W)$ and $\widehat{h}(V,W)$, which are models for the outcome and treatment regression functions, respectively. $\widehat{g}(V,W)\approx \mathbb{E}[Y\left|V,W\right.]$ predicts ridership change given the adjustment and covariate variables (but not using $X$), and $\widehat{h}(V,W)\approx \mathbb{E}[X\left|V,W\right.]$ predicts the treatment level given the confounders. We use Xgboost in this estimation process to capture possibly nonlinear relationships.

Next, we partial out the effects of $(V,W)$ from both $Y$ and $X$. For each observation $i$, we compute the residual outcome and residual treatment, as in Equations (5) and (6):

$${\tilde{Y}}_i=Y_i-\widehat{g}\left(V_i,W_i\right)$$

(5)

$${\tilde{X}}_i=X_i-\widehat{h}\left(V_i,W_i\right)$$

(6)

where for $i=1,\dots ,n$. The vectors $\tilde{Y}=({\tilde{Y}}_1,\dots ,{\tilde{Y}}_n)$ and $\tilde{X}=({\tilde{X}}_1,\dots ,{\tilde{X}}_n)$ represent the parts of $Y$ and $X$ that are not explained by the confounders. By construction, $\tilde{Y}$ is uncorrelated with any function of $(V,W)$, and likewise, $\tilde{X}$ is purged of $(V,W)$ influences. Any dependence of $Y$ or $X$ on the adjustment variables is removed, so that what remains in $\tilde{Y}$ and $\tilde{X}$ should chiefly be the direct association between $Y$ and $X$ (including causality) and idiosyncratic noise.

Since $\tilde{Y}$ and $\tilde{X}$ have been stripped of confounding variation, a simple regression yields an unbiased estimate of the causal effect. In the simplest case (constant effect), we fit a linear model, as in Equation (7):

$${\tilde{Y}}_i={\beta }_0{\tilde{X}}_i+{{\beta }_1}^T\left({\tilde{X}}_i\cdot f\left(V_i\right)\right)+{\delta }_i$$

(7)

where $f(V_i)$ is a function of features derived from $V_i$ (such as a subset of confounders or basis functions encoding $V_i$). The coefficient vectors ${\beta }_0$ and ${\beta }_1$ can then be used to compute an estimated conditional average treatment effect. ${\delta }_i$ is the standard errors, which can be obtained for the coefficients to assess statistical significance.

To ensure the reliability and generalizability of our machine learning estimates, we conducted systematic sensitivity analyses regarding model hyperparameters. For the double machine learning framework, core hyperparameters of the embedded gradient boosting models, including the number of estimators, maximum search depth, and learning rate, were selected via grid search. This process entailed systematically exploring a predefined parameter space to identify the configuration that minimized out-of-sample prediction error through cross-validation, mitigating risks of overfitting or underfitting and enhancing reproducibility.

3.3.2. Average Treatment Effect and Conditional Average Treatment Effect

Given the learned DAG, we use do-calculus to define the causal effects of treatments as the average treatment effect (ATE) in Equation (8):

$$\mathrm{ATE}=\mathbb{E}\left[Y\left|do\left(X=x_1\right)\right.\right]-\mathbb{E}\left[Y\left|do\left(X=x_0\right)\right.\right]$$

(8)

The ATE in Equation (5) represents the average effect of setting treatment $X$ from value $x_0$ to $x_1$.

Meanwhile, the conditional average treatment effect (CATE) considers the causal effect in a specific context (i.e., for a subset of stations or conditions characterized by certain values of other variables), which can be defined as Equation (9):

$$\mathrm{CATE}\left(v,w\right)=\mathbb{E}\left[Y\left|do\left(X=x_1\right),V=v,W=w\right.\right]-\mathbb{E}\left[Y\left|do\left(X=x_0\right),V=v,W=w\right.\right]$$

(9)

Equation (9) captures treatment effects under specific contexts defined by values $V=v$ and $W=w$.

The causal effects uncovered by the analysis is then translates into targeted policy actions. For example, network centrality metrics such as betweenness and degree centrality inform the strategic deployment of backup bus rapid transit services and dynamic train rerouting plans, ensuring that stations with high through-traffic vulnerability receive priority capacity support. Built-environment variables, such as mixed-land-use intensity and pedestrian catchment patterns, identify nodes that require preemptive crowd management and adaptive service scheduling to mitigate severe ridership declines. Event characteristics including incident duration, time of day, and weather conditions are linked to parametric dispatch protocols and contingency staffing levels, thereby establishing a clear chain from empirical finding to operational recommendation.

4. Study Area and Dataset

4.1. Study Area

The analysis encompasses the entire Shanghai municipal area, defined by the administrative boundaries of the Shanghai Municipality. All 409 urban rail transit stations across 20 metro lines within these limits are included. Built-environment and bus-connectivity data were collected for each station using circular buffers of 500 m with robustness checks at 1 km and 2 km around the station centroid, ensuring that only features and bus stops physically located within the Shanghai city proper were considered. The spatial distribution is presented in Figure 2.

The complexity of the network, characterized by dense station coverage and intricate connectivity, presents unique challenges when addressing issues of emergency management, particularly concerning station-level passenger flow forecasting during incidents.

4.2. Dataset

The dependent variable in this study is the station-level ridership dynamics between the incident scenario and the general scenario, while the independent variable includes three main groups: URT network structure factors, station-level built environment factors, incident, and external factors.

The URT network structure factors include station degree and betweenness centrality, which are key metrics in network analysis. Station degree reflects the local complexity of the network, particularly whether a station acts as a transfer point, while betweenness centrality measures a station’s importance in connecting different parts of the network. Both of these indicators were derived from the latest topological structure from OpenStreetMap. These network metrics are essential for understanding how the spatial configuration of the network influences station-level ridership, particularly under emergency conditions.

The station-level built environment factors provide context-specific information for understanding station-level ridership dynamics. These factors include land use entropy, which captures the diversity of land uses surrounding a station; job accessibility, which measures the density of employment opportunities in the vicinity; and job–housing balance, which indicates the equilibrium between residential and employment areas. Additionally, binary variables indicate the presence of key urban features, such as universities, central business districts (CBDs), and transportation hubs, within a 500 m radius of each station. The buffer radius of 500 m was selected to balance spatial resolution against overlap of adjacent station catchments. To assess robustness, parallel analyses employed 1000 m and 2000 m buffers. As buffer size increases, aggregation of heterogeneous land-use attributes leads to attenuated effect estimates, indicating that finer-scale catchments better capture localized built-environment influences. The bus connectivity metric measures the number of bus stations within the same radius. These built environment variables were sourced from OpenStreetMap APIs.

This study further employs the Shanghai Metro’s incident data, which specifically includes disruption duration (the time between service interruption and restoration), as well as indicators for different types of incidents, such as power failures, intrusions, and signal- or train-related issues. We also include variables reflecting whether the incident occurred during a weekday or peak-hour period and whether the station in question was directly affected or near the disruption. Weather variables, encompassing precipitation, snowfall, fog, and severe wind events, were collapsed into a binary indicator of favorable versus adverse conditions. This binarization reduces model complexity by limiting the number of external covariates, thereby enhancing the interpretability and stability of estimates for built-environment and operational factors.

It should be noted that emergency and external factors were chosen to represent the principal causes and contextual conditions known to affect service stability and passenger behavior during urban rail disruptions. Incident types such as power failures, intrusions, signal malfunctions, train equipment faults, and door equipment faults were selected based on their prevalence and impact. These categories capture both system-level failures and station-level malfunctions. Temporal dummies for weekday and peak-hour distinguish periods of elevated ridership pressure and correspondingly different response protocols. The accident-station indicator isolates events directly impacting the station infrastructure versus those on adjacent segments. Weather was binarized into favorable versus adverse conditions because severe weather events are documented to degrade repair crew access and passenger flow simultaneously. It is acknowledged that other unobserved factors such as large special-event crowds, scheduled maintenance windows or operational adjustments may also influence both disruption characteristics and ridership responses. The causal framework rests on an assumption of causal sufficiency among the observed covariates. To mitigate bias, all known confounders for which consistent station-level data were available have been included; variables lacking uniform coverage were excluded to preserve estimation stability.

For the dependent variable calculation, the URT ridership data includes two key variables: non-incident URT ridership, which represents the hourly ridership at each station under normal conditions, and incident URT ridership decline, which measures the drop in passenger flow within one hour of an incident. These ridership variables are central to the analysis of how disruptions affect station-level flow. The descriptive statistics for the variables used in this study are provided in

Table 1. Descriptive statistics of urban rail transit network structure, station-level built environment, incident and external factors, and urban rail transit ridership.

Variable	Type	Unit	Mean	Std	Min	Max
URT network structure factors
Degree	Discrete	-	2.855	1.352	1.000	8.000
Betweenness	Continuous	-	0.047	0.051	0.000	0.256
Station-level built environment factors
Land use entropy	Continuous	-	0.895	0.114	0.348	1.172
Job accessibility	Continuous	hundred jobs	3.364	2.851	0.037	12.399
Job–housing balance level	Continuous	-	1.209	0.980	0.210	7.424
University dummy	Discrete	-	0.224	0.417	0.000	1.000
CBD dummy	Discrete	-	0.304	0.460	0.000	1.000
Transportation hub dummy	Discrete	-	0.151	0.358	0.000	1.000
Bus connectivity	Discrete	stations	6.769	7.889	0.000	56.000
Incident andexternal factors
Disruption duration	Continuous	minutes	27.398	14.035	5.500	67.200
Power incident dummy	Discrete	-	0.100	0.300	0.000	1.000
Intrusion incident dummy	Discrete	-	0.142	0.349	0.000	1.000
Line incident dummy	Discrete	-	0.174	0.380	0.000	1.000
Signal incident dummy	Discrete	-	0.224	0.417	0.000	1.000
Train incident dummy	Discrete	-	0.249	0.433	0.000	1.000
Door incident dummy	Discrete	-	0.111	0.314	0.000	1.000
Weekday dummy	Discrete	-	0.184	0.388	0.000	1.000
Peak-hour dummy	Discrete	-	0.394	0.489	0.000	1.000
Accident station dummy	Discrete	-	0.273	0.446	0.000	1.000
Weather dummy	Discrete	-	0.405	0.491	0.000	1.000
URT ridership
Non-incident URT ridership	Continuous	hundred people/hour	25.507	32.976	0.770	245.570
Incident URT ridership decline	Continuous	hundred people/hour	10.737	18.594	0.058	216.155

.

5. Results

5.1. Causal Effect Analysis

The causal DAG is identified from the NOTEARS algorithm and depicted in Figure 3. The station-level built environment factors influence urban rail transit (URT) ridership dynamics through two primary pathways, sharping the non-incident URT ridership while influences the availability of alternate transportation options such as bus which can buffer the impact of an incident by diverting passengers to other modes. Complex network metrics such as degree and betweenness modulate how severely an incident curtails ridership, while incident characteristics such as incident type and spatiotemporal factors determine the duration and scale of service interruptions.

Built environment factors show significant effects on both non-incident URT ridership and bus connectivity. Stations in more mixed land-use areas with higher land use entropy have substantially higher non-incident URT ridership, with an ATE of +16.6. Stations around a transportation hub are also associated with a large causal relation on non-incident URT ridership, with an ATE of +19.6. Built environment factors affect the station’s integration with the bus network. Urban rail transit stations around transportation hubs demonstrate an ATE of +4.7 in the bus connectivity, and stations near a university have about +4.8 ATE of bus connectivity. It should be noted that higher job accessibility and job–housing balance level increase the bus connectivity with the ATE of 0.813 and 1.357, suggesting that more job accessibility and balanced job–housing distribution boost ridership demand while promoting bus service concentration. Built environment factors create higher routine ridership levels, thereby increasing the potential exposure to an incident, whereas they also tend to improve inter-modal connectivity, which can mitigate that exposure.

The network structure, bus connectivity, and non-incident URT ridership greatly affect the incident URT ridership decline. The impact of urban rail network betweenness metrics on incident URT ridership decline is extremely high, with an ATE of +78.0, indicating that an incident at a highly central station or the network bottleneck triggers an outsized drop in ridership. The local connectivity represented by degree centrality has a small negative effect on ridership decline, with an ATE of –0.14, meaning stations with more line interconnections experience slightly less passenger loss, probably because passengers can reroute via alternative lines at those transfer stations. The availability of bus alternatives also significantly cushions the impact, confirming the second pathway in the causal diagram, where robust bus connectivity at a station directly enhances resilience by retaining more riders during a rail service outage. The non-incident URT ridership contributes to a greater absolute decline under incident conditions with an ATE of +0.47, as would be expected when more travelers are exposed to the disruption.

The incident characteristics also strongly influence outcomes via the disruption duration. Severe incident types that tend to cause prolonged outages show large positive ATEs on the length of service interruption. Longer disruptions in turn lead to larger ridership declines with an ATE of +0.76. Meanwhile, incidents during weekdays and peak hours tend to have longer disruption durations than those off-peak, reflecting operational difficulties in clearing incidents at busy times. The specific average treatment effect estimates for each causal edge are summarized in

Table 2. Average treatment effect of each causal edge in the DAG.

Treatment Variable	Outcome Variable	Average Treatment Effect
Land use entropy	Bus connectivity	−1.128
Job accessibility	Bus connectivity	0.813
Job–housing balance level	Bus connectivity	1.357
University dummy	Bus connectivity	4.788
CBD dummy	Bus connectivity	1.250
Transportation hub dummy	Bus connectivity	4.655
Land use entropy	Non-incident URT ridership	16.558
Job accessibility	Non-incident URT ridership	3.788
Job–housing balance level	Non-incident URT ridership	6.477
University dummy	Non-incident URT ridership	2.441
CBD dummy	Non-incident URT ridership	8.955
Transportation hub dummy	Non-incident URT ridership	19.556
Weather dummy	Non-incident URT ridership	−3.280
Power incident dummy	Disruption duration	40.552
Intrusion incident dummy	Disruption duration	25.334
Line incident dummy	Disruption duration	17.974
Signal incident dummy	Disruption duration	2.038
Train incident dummy	Disruption duration	−2.509
Door incident dummy	Disruption duration	−24.286
Weekday dummy	Disruption duration	11.37
Peak-hour dummy	Disruption duration	11.028
Accident station dummy	Disruption duration	20.018
Weather dummy	Disruption duration	−12.448
Degree	Incident URT ridership decline	−0.135
Betweenness	Incident URT ridership decline	77.991
Bus connectivity	Incident URT ridership decline	−0.304
Non-incident URT ridership	Incident URT ridership decline	0.467
Disruption duration	Incident URT ridership decline	0.761

.

The distribution of individual treatment effects (ITEs) provides insight into how uniformly these causal mechanisms manifest across different stations and incidents. Figure 4, Figure 5 and Figure 6 illustrate the spread of ITEs for key variables. For most causal edges, the ITEs are roughly unimodal and centered around the ATE, indicating that the effect is relatively consistent across the majority of stations. For example, the influence of non-incident URT ridership or bus connectivity on incident decline exhibits a single-peaked distribution, suggesting a homogeneous treatment effect where nearly all stations experience a similar per-unit effect of those factors.

In contrast, the ITE distributions for certain incident-type variables are distinctly bimodal, implying the presence of two subgroups of incidents with markedly different outcomes. Specifically, some incidents even of the same category result in only minimal service disruption, while others lead to extreme delays, creating two clusters of effect sizes. For instance, the causal effect of a power incident on disruption duration may either be relatively small if the failure is quickly resolved or very large if it causes an extensive outage, with few incidents in between, thus yielding a two-peaked ITE distribution. Such patterns underscore that not all incidents labeled under a common type have identical impacts; contextual factors or secondary failures likely divide them into minor vs. major events.

5.2. Heterogeneous Causal Effect Analysis

While the estimated ATEs provide an average picture of causal effects, it is crucial to recognize that these effects can vary depending on the station context and incident circumstances. The conditional average treatment effects (CATEs) are calculated for key causal edges across different built environment and external conditions. The incident datasets are stratified by these conditions, with continuous variables split into low/medium/high groups corroding to quantile and discrete variables split into categorizations. The ATEs are re-estimated depending on the magnitude of selected causal effects within each subgroup.

The CATE of non-incident URT ridership on disruption impact under different built environment conditions is demonstrated in

Table 3. CATE distribution of ‘non-incident URT ridership–incident URT ridership decline’ causal edge under different continuous built environment conditions.

Built Environment Conditions	CATE of the Low Group	CATE of the Medium Group	CATE of the High Group
Land use entropy	0.407	0.454	0.519
Job accessibility	0.441	0.463	0.488
Job–housing balance level	0.423	0.471	0.495

and

Table 4. CATE distribution of ‘non-incident URT ridership–incident URT ridership decline’ causal edge under different discrete built environment conditions.

Built Environment Conditions	Treatment Group (Dummy = 1)	Control Group (Dummy = 0)
University dummy	0.477	0.462
CBD dummy	0.485	0.446
Transportation hub dummy	0.527	0.391

. Stations situated in more urbanized or diverse environments exhibit a stronger marginal effect of non-incident URT ridership on incident URT ridership decline. In areas with high land use mix, each additional unit of non-incident URT ridership contributes about 0.519 units of incident ridership decline, compared to only 0.407 in low-mix areas. A similar upward trend is observed with job accessibility and balance. High-accessibility stations demonstrate a larger per-rider impact, with a CATE of +0.49, than low-accessibility ones, with a CATE of +0.44. In highly accessible urban settings, the existing ridership is more vulnerable in aggregate, likely due to these stations serving as major trip generators, where a disruption affects many interdependent passengers. A similar trend is also found in discrete built environment conditions, with the CATE of the university dummy, CBD dummy, and transportation hub dummy in the treatment group being +0.477, +0.485, and +0.527, generally higher than that of the control group.

A similar context-dependence for the causal effect of bus connectivity on incident outcomes is observed, as presented in

Table 5. CATE distribution of ‘bus connectivity–incident URT ridership decline’ causal edge under different continuous built environment conditions.

Built Environment Conditions	CATE of the Low Group	CATE of the Medium Group	CATE of the High Group
Land use entropy	−0.267	−0.339	−0.310
Job accessibility	−0.299	−0.305	−0.312
Job–housing balance level	−0.287	−0.301	−0.323

and

Table 6. CATE distribution of ‘bus connectivity–incident URT ridership decline’ causal edge under different discrete built environment conditions.

Built Environment Conditions	Treatment Group (Dummy = 1)	Control Group (Dummy = 0)
University dummy	−0.341	−0.264
CBD dummy	−0.315	−0.282
Transportation hub dummy	−0.339	−0.272

. Across different built environment factor groups, the magnitude of the bus connectivity benefit can vary. In moderately mixed land use contexts, adding bus connections yields the strongest mitigation of ridership loss with a CATE of –0.34, whereas in low-mix areas the effect is weaker, with a CATE of –0.27. The highest land use entropy stations also demonstrate a slightly reduced benefit with a CATE of –0.3, hinting at a non-linear pattern where, beyond a certain point, perhaps in very dense city centers, additional bus routes face diminishing returns in offsetting rail disruptions. Trends for job accessibility and job–housing balance are more monotonic. Stations in highly accessible or well-balanced areas have a greater negative effect, with a CATE of –0.31, than those in low-accessibility areas, with a CATE of –0.29. A similar trend is observed under discrete built environment conditions, where, in the presence of certain built environment factors around URT stations, the negative causal effect of bus connectivity on incident URT ridership decline generally exceeds that of the control group. This finding indicates that in environments where proper bus connectivity exists, buses can more effectively substitute for rail service during an incident.

An examination of the land-use entropy stratification reveals that stations within the medium-entropy band experience the most pronounced causal effects because they occupy a transitional zone between overly homogenous and highly fragmented urban fabrics. In low-entropy contexts, limited functional mix constrains both baseline ridership and the network of alternative trip attractors, dampening the marginal impact of additional non-incident riders or bus connections. Conversely, in high-entropy areas, extreme diversification often correlates with highly multimodal infrastructures and redundant travel options, which diffuse passenger flows and attenuate sensitivity to individual factors. Medium-entropy zones, however, strike an optimal balance: sufficient land-use diversity generates appreciable baseline demand, while network complexity remains moderate enough that disruptions or service enhancements translate into clearer shifts in passenger behavior. This synergy of demand density and network metrics underpins the elevated conditional average treatment effects observed in the medium-entropy subgroup.

Table 7. CATE distribution of ‘disruption duration–incident URT ridership decline’ causal edge under different incident and external factors conditions.

Incident and External Factors Conditions	Treatment Group (Dummy = 1)	Control Group (Dummy = 0)
Power incident dummy	1.117	0.536
Intrusion incident dummy	1.029	0.524
Line incident dummy	0.997	0.505
Signal incident dummy	0.919	0.633
Train incident dummy	0.728	0.774
Door incident dummy	0.680	0.793
Weekday dummy	0.825	0.732
Peak-hour dummy	0.821	0.745
Accident station dummy	0.986	0.671
Weather dummy	0.702	0.793

reports how the impact of disruption duration on ridership loss varies with incident and external conditions. Every additional minute of service interruption does not translate into the same ridership loss in all scenarios; instead, the per-minute damage is amplified or dampened by the nature of the incident. Major technical failures, such as power outages or intrusions, exhibit significantly higher sensitivity. Under those incident types, the CATE is around 1.0–1.1, roughly double the effect of other incident types. This stark difference implies that these severe disruptions not only tend to last longer, but each minute of delay during them causes disproportionate ridership loss, perhaps because they often halt service completely over a large area, leaving passengers with few immediate alternatives. In contrast, minor malfunctions like train car or door issues show a lower per-minute impact, with a CATE of 0.68–0.73, even when they do cause delays. Similarly, the data indicate higher vulnerability during high-demand periods. On weekdays and especially during peak hours, each minute of disruption translates to a greater ridership drop than during weekends or off-peak times. One minute of disruption in rush hour causes about 0.82 units of loss versus 0.75 in off-peak. This reflects the concentration of travelers during peak periods. When service is interrupted, more people are immediately affected per unit time. Another notable distinction is whether an incident occurs at the current station or adjacent stations. If the incident is at the current station, the per-minute impact on ridership loss is much higher than if it happens at adjacent stations. These heterogeneous effect analyses reveal a non-linear pattern of vulnerability and resilience in the URT system. The influence of a given factor on ridership loss is not fixed but, rather, contingent on contextual variables.

5.3. Policy Discussion

The conditional effect estimates indicate that the ten percent of stations with the highest betweenness centrality contribute to more than half of the total ridership loss when disruptions occur. This non-uniform vulnerability suggests that resilience investments should concentrate on modal interchange hubs. Transit agencies can establish bus-bridging corridors anchored at these transfer nodes, pre-deploying shuttle vehicles in nearby layover yards and linking them via a dedicated high-occupancy bus lane. Real-time platform density sensors allow the operation’s control center to enforce crowd-level thresholds: when passenger counts exceed a predetermined safety limit, automated alerts trigger the dispatch of additional buses. GPS-assisted dynamic routing ensures that shuttle services replicate the suspended rail line’s alignment, minimizing detour delays and maintaining headways that prevent platform overcrowding.

The CATE analysis also reveals that the buffering impact of supplementary bus services is maximized in districts with intermediate land-use entropy, whereas overly homogeneous or excessively fragmented precincts yield diminishing returns. Urban planning departments should therefore recalibrate zoning around critical stations to mandate a balanced mix of residential, commercial, and institutional land uses. This can be achieved through floor-area-ratio stipulations, such as requiring at least 30% and no more than 50% commercial floor space within a 500 m radius and offering expedited permitting or density bonuses for projects that meet these criteria. By nurturing calibrated mixed-use catchments, planners create contiguous urban fabrics that sustain high baseline demand while preserving clear routing corridors for emergency bus mobilization, as evidenced by the –0.339 CATE in medium-entropy contexts, as presented in Table 5.

Stations embedded in mixed-use environments and those with high job accessibility exhibit the greatest surge of passengers during service interruptions, underscoring the need for station-specific crowd management protocols aligned with built-environment characteristics. Platform screen doors should be integrated with passenger counting modules so that, upon reaching specified occupancy thresholds, doors operate in a staggered sequence to regulate boarding flow. Dynamic wayfinding panels fed by real-time congestion maps guide commuters to alternative egress paths, while station staff, equipped with handheld crowd-control devices, can redirect flows to less congested stairwells. Regular simulation exercises, run jointly by operations and safety teams, will validate evacuation timings against these built-environment profiles, ensuring that dwell times remain within safe limits even under peak-period disruptions.

The differentiated severity of incident types such as power failures and trespass events, each carrying disruption-duration CATEs exceeding one minute of additional ridership loss, demands a tiered incident-management framework. Upon classification of an outage as high-severity, the dispatch system automatically notifies specialty maintenance crews, activates standby rolling stock pools at designated depots, and recalibrates downstream train schedules to minimize network bottlenecks. Minor incidents, such as door malfunctions or signal glitches, follow a streamlined protocol that leverages remote diagnostics and rapid-response teams stationed within the network. Embedding these tiered procedures in an integrated asset-management and dispatch platform ensures that field deployments align precisely with the empirically derived impacts of each failure class, optimizing both service restoration speed and cost efficiency.

The heterogeneous effect analysis reveals that bus connectivity yields the greatest marginal reduction in ridership loss at high-betweenness stations during peak hours in Table 5. Bus-bridging services should be pre-positioned and dynamically scaled at these network pivots when commuter flows are highest, ensuring rapid substitution for disrupted rail segments. The non-monotonic relationship between land-use entropy and mitigation benefit strongest in the medium-entropy band suggests that urban design around core nodes should aim for balanced mixed-use patterns. Zoning regulations should thus encourage a calibrated mix of residential, commercial, and institutional uses to achieve intermediate entropy levels, where bus interventions deliver maximal resilience returns without suffering diminishing marginal effects in overly diversified or overly homogeneous settings. This approach aligns emergency transit planning with the nonlinear causal pathways uncovered in this study, enhancing system robustness under stress.

While the recommended measures such as dynamic bus bridging, calibrated mixed-use zoning, and tiered incident management offer strong potential for improving URT resilience, their large-scale deployment may be constrained by financial, institutional, and operational factors. For instance, the upfront capital investment required for platform sensor upgrades, real-time GPS-based dispatch, or dedicated bus lanes may exceed available budgets, especially in cities with competing infrastructure needs. Policymakers must therefore weigh these investments against projected reductions in passenger delays, safety incidents, and indirect economic losses.

Institutional coordination presents another critical barrier, as effective emergency response requires seamless cooperation among transit operators, municipal agencies, law enforcement, and urban planners. Without clear delineation of responsibilities and real-time information sharing, even well-designed protocols can face delays in execution or gaps in coverage. Pilot programs with phased implementation, performance monitoring, and adaptive funding mechanisms are recommended to lower risks and build inter-agency trust. Rigorous cost–benefit analyses quantifying both direct operational savings, such as reduced service interruption durations, and broader social benefits, such as passenger time savings and improved safety, should guide the prioritization of interventions.

To maximize practical impact, the findings of this study should be communicated to policymakers and transit operators through multiple audience-tailored channels. Policy briefs that summarize the main causal mechanisms, highlight priority intervention points, and translate technical metrics into operational guidelines can be developed for decision-makers. Interactive visualization tools such as web-based dashboards can display real-time station vulnerability profiles, simulate the effects of various interventions, and support scenario planning for emergency responses. Regular stakeholder workshops, co-organized with municipal agencies and transit operators, can facilitate two-way communication: presenting evidence in accessible formats while also gathering practitioner feedback on implementation feasibility. Collaborations with professional associations and participation in national transportation forums can further promote the uptake of research-based recommendations.

6. Conclusions

This study explores the nonlinear causal relationships among the built environment, urban rail transit network structure, and station-level ridership dynamics under emergency conditions. The primary contribution of this research lies in its ability to integrate causal machine learning methods to identify and quantify the factors influencing ridership shifts during service disruptions. This approach allows for a more nuanced understanding of the nonlinear and threshold effects that shape passenger flow during emergencies. The findings reveal that the built environment, including land-use diversity, job accessibility, job–housing balance level, and proximity to transportation hubs, significantly impacts both non-incident ridership levels and the resilience of stations during disruptions. Stations located in areas with high land-use entropy and strong transport connectivity experience higher non-incident ridership while facing greater potential passenger flow loss during incidents. The availability of alternative transportation modes, such as bus connectivity, also proves crucial in mitigating the impact of service interruptions.

The study further demonstrates that the network centrality plays a pivotal role in determining the extent of ridership loss during disruptions. Central stations with high betweenness centrality contribute to disproportionately higher ridership declines when affected by incidents. This highlights the importance of ensuring the resilience of critical nodes within the network to minimize the cascading effects of service disruptions. The policy implications of these findings are significant for urban planners and transportation managers. By understanding the causal factors that influence ridership resilience, more targeted interventions can be designed. For instance, enhancing the intermodal connectivity between rail and bus networks, particularly in areas with high ridership potential, can reduce the severity of disruptions. Attention should also be focused on improving the resilience of stations in central locations to prevent widespread network incidents.

Several limitations of this study should be addressed in future research.

The current approach does not integrate causal discovery and causal effect estimation with deep learning techniques, which could enhance the precision of the estimates. Incorporating advanced deep learning models would allow for better capturing of the complex, nonlinear relationships in the data and provide more accurate causal effect estimates. Future research could leverage advanced spatial–temporal deep learning architectures to refine causal discovery and effect estimation. In particular, sparse graph attention networks (SGAT) can efficiently model station-to-station dependencies by focusing attention on key edges in the transit graph, while temporal graph convolutional networks (T-GCN) capture dynamic ridership patterns over time. Hybrid architectures combining graph neural network layers with temporal transformer modules can further encode sequence dynamics and threshold effects. These models promise both the representational richness needed for complex, nonlinear urban mobility data and the computational scalability required for large-scale transit networks.

This study relies on cross-sectional observations of discrete disruption events, precluding examination of longer-term adaptation and resilience dynamics. Future research should integrate panel data frameworks with repeated post-incident measurements to trace recovery trajectories, validate resilience metrics over time, and examine how repeated exposures shape ridership responses and network robustness.

This study focuses exclusively on the Shanghai urban rail transit network, a large, densely populated system with mature multimodal connections and distinctive land-use patterns. The estimated effect sizes and resilience pathways identified here may not directly translate to cities with different urban forms, transit modal splits, or passenger demand profiles. Future research should apply the proposed causal discovery and estimation framework to rail systems in varied geographic and socio-economic environments. Comparation analyses across small, medium, and megacity networks will help delineate which causal mechanisms are universally operative and which are context-specific, thereby refining both theoretical insights and policy prescriptions for global urban transit resilience. It is also worthwhile to apply the combined causal discovery and double machine learning framework to additional URT systems, ideally contrasting a developed-city network such as Tokyo or London with a rapidly expanding system in a developing-country context such as Delhi or São Paulo, illuminating how regional variations in urban design, modal integration, and passenger behavior shape nonlinear causal mechanisms and enable the derivation of context-specific resilience strategies.

An important avenue for extending this framework lies in its integration with real-time operational decision-support systems. By coupling the structure learning and effect estimation components with streaming ridership and incident data feeds, the model could continuously update its causal DAG and DML estimates as new information arrives. This would enable transit operators to trigger automated bus-bridging deployments, adjust platform dwell protocols, and reallocate maintenance resources based on live causal impact assessments. Achieving this will require scalable streaming architectures, online learning algorithms for low-latency model retraining, and user-friendly dashboards to translate causal outputs into actionable directives for control-center staff.