Title: Path-specific effects for pulse-oximetry guided decisions in critical care
Venue: NeurIPS 2025
Accepted: yes
Keywords: Causal inference

Computational healthcare

Algorithmic fairness
Abstract: Identifying and measuring biases associated with sensitive attributes is a crucial consideration in healthcare to prevent treatment disparities. One prominent issue is inaccurate pulse oximeter readings, which tend to overestimate oxygen saturation for dark-skinned patients and misrepresent supplemental oxygen needs. Most existing research has revealed *statistical disparities* linking device measurement errors to patient outcomes in intensive care units (ICUs) without causal formalization. This study *causally* investigates how racial discrepancies in oximetry measurements affect invasive ventilation in ICU settings. We employ a causal inference-based approach using *path-specific effects* to isolate the impact of bias by race on clinical decision-making. To estimate these effects, we leverage a doubly robust estimator, propose its self-normalized variant for improved sample efficiency, and provide novel finite-sample guarantees. Our methodology is validated on semi-synthetic data and applied to two large real-world health datasets: MIMIC-IV and eICU. Contrary to prior work, our analysis reveals minimal impact of racial discrepancies on invasive ventilation rates. However, path-specific effects mediated by oxygen saturation disparity are more pronounced on ventilation duration, and the severity differs across datasets. Our work provides a novel pipeline for investigating potential disparities in clinical decision-making and, more importantly, highlights the necessity of causal methods to robustly assess fairness in healthcare.

Path-specific effects for pulse-oximetry guided decisions in critical care

Abstract

Identifying and measuring biases associated with sensitive attributes is a crucial consideration in healthcare to prevent treatment disparities. One prominent issue is inaccurate pulse oximeter readings, which tend to overestimate oxygen saturation for dark-skinned patients and misrepresent supplemental oxygen needs. Most existing research has revealed statistical disparities linking device measurement errors to patient outcomes in intensive care units (ICUs) without causal formalization. This study causally investigates how racial discrepancies in oximetry measurements affect invasive ventilation in ICU settings. We employ a causal inference-based approach using path-specific effects to isolate the impact of bias by race on clinical decision-making. To estimate these effects, we leverage a doubly robust estimator, propose its self-normalized variant for improved sample efficiency, and provide novel finite-sample guarantees. Our methodology is validated on semi-synthetic data and applied to two large real-world health datasets: MIMIC-IV and eICU. Contrary to prior work, our analysis reveals minimal impact of racial discrepancies on invasive ventilation rates. However, path-specific effects mediated by oxygen saturation disparity are more pronounced on ventilation duration, and the severity differs across datasets. Our work provides a novel pipeline for investigating potential disparities in clinical decision-making and, more importantly, highlights the necessity of causal methods to robustly assess fairness in healthcare.

1 Introduction

Bias in medical devices can perpetuate disparities by impacting healthcare decisions. For example, pulse oximeters tend to overestimate blood oxygen saturation for dark-skinned patients [45, 50, 43, 21, 42, 15]. Such discrepancies can lead to 'hidden hypoxemia,' where a patient's true arterial oxygen saturation (SaO 2 ) is dangerously low, despite a reassuringly higher peripheral SpO 2 reading from the oximeter. Figure 1 demonstrates this using eICU data [40], where red dots ('H.H') highlight instances where low SaO 2 (< 88%) is masked by higher SpO 2 (> 88%). Such hidden hypoxemia can result in underestimated supplemental oxygen needs and delayed clinical interventions [50, 14, 12].

Prior studies have advanced our understanding of pulse oximeter inaccuracies and associated patient outcomes. For instance, Sjoding et al. [45] and Wong et al. [50] established links between race, hidden hypoxemia, and adverse outcomes like increased organ dysfunction and mortality in large

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ICU datasets (e.g., MIMIC-III/IV [22]). Similarly, Gottlieb et al. [14] examined racial differences in oxygen delivery rates using regression and simple mediation analysis in MIMIC-IV, while Henry et al. [18] and Fawzy et al. [12] reported delays in hypoxemia detection and treatment eligibility. These studies rely on statistical associations or canonical mediation analysis to highlight measurement bias. However, they fail to isolate causal pathways of disparities mediated only through oximeter discrepancies in the presence of other mediators, which requires more advanced causal mediation analysis.

Measuring fairness using path-specific causal analysis is an active research area [47, 49, 30, 6, 11, 39]. These methods isolate the influence of sensitive attributes, such as race, mediated through intermediate factors. In our context (Figure 2), we aim to quantify the causal effect of race on invasive ventilation specifically mediated by pulse oximetry discrepancies ( V ), which is distinct from the effect via other mediators ( W ). In complex systems with multiple mediators , techniques for identifying and robustly estimating effects along specific pathways have been developed [49, 30].

However, Table 1 illustrates several key gaps. While sophisticated path-specific methods exist, their applications to analyze racial bias in ICU settings are limited, with most applications in population health or survey data [34, 13]. Furthermore, there are no finite-sample guarantees for path-specific effect estimators, which are crucial for generating robust evidence with potentially constrained sample sizes, like in critical care. Thus, a framework applying path-specific causal analysis for ICU problems with robust estimation strategies and theoretical backing is necessary.

To address these identified gaps, this paper makes the following primary contributions.

We propose a causal pipeline to detect and quantify racial disparities in the ICU. Adapting a standard fairness model (Figure 2), we use path-specific analysis to isolate the impact of race mediated through oximeter discrepancies ( V ), called the V-specific Direct Effect (VDE) .

We present robust estimators for the VDE, including a doubly robust estimator, and propose a selfnormalized variant for improved sample variance, with novel finite-sample learning guarantees .

We apply our framework to analyze race-based disparities mediated by oximeter discrepancies on invasive ventilation (rate and duration) in MIMIC-IV [22] and eICU [40].

To the best of our knowledge, this is the first formal path-specific causal analysis of pulse oximetermediated bias on invasive ventilation using multiple mediators.

2 Preliminaries

We introduce preliminary notation and background in observational causal inference and fairness.

Notation. We use ( X , X , x , x ) to denote a random vector, variable, and their realized values, respectively. For a function f ( z ) , we use ∑ z f ( z ) to denote the summation/integration over discrete/continuous Z . For a discrete vector X , we denote 1[ X = x ] as an indicator function such that

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1[ X = x ] = 1 if X = x and 0 otherwise. P ( V ) denotes a distribution over V and P ( v ) a probability at V = v . We let E [ f ( V )] and V [ f ( V )] denote the mean and variance of f ( V ) relative to P ( V ) , and ∥ f ∥ P ≜ √ E [( f ( V )) 2 ] as the L 2 -norm of f with P . We use ̂ f -f = o P ( r n ) if ̂ f is a consistent estimator of f having rate r n , and ̂ f -f = O P ( r n ) if ̂ f -f is bounded in probability at rate r n . We will say ˆ f is L 2 -consistent if ∥ ˆ f -f ∥ P = o P (1) and ̂ f -f = O P (1) if ̂ f -f is bounded in probability. Let D ≜ { V i : i = 1, · · · , n } denote a set of n samples. The empirical average of f ( V ) over D is denoted as E D [ f ( V )] ≜ (1 / |D| ) ∑ i : V i ∈D f ( V i ) .

Structural Causal Models. We use structural causal models (SCMs) [36] as our framework. An SCM M is a quadruple M = ⟨ U , V , P ( U ), F⟩ , where U is a set of exogenous (latent) variables following a joint distribution P ( U ) , and V is a set of endogenous (observable) variables whose values are determined by functions F = { f V i } V i ∈ V such that V i ← f V i ( pa V i , u V i ) where Pa V i ⊆ V and U V i ⊆ U . Each SCM M induces a distribution P ( V ) and a causal graph G = G ( M ) over V in which directed edges exist from every variable in Pa V i to V i and dashed-bidirected arrows encode common latent variables. An intervention is represented using the do-operator, do( X = x ) , which encodes the operation of replacing the original equations of X (i.e., f X ( pa X , u X ) ) by the constant x for all X ∈ X and induces an interventional distribution P ( V | do( x )) . For any Y ⊆ V , the potential response Y x ( u ) is defined as the solution of Y in the submodel M x given U = u , which induces a counterfactual variable Y x .

2.1 Related work

Algorithmic Fairness. Algorithmic fairness [16, 31, 2, 33] operationalizes computational methodologies to identify, measure, and address disparate behavior related to (automated or other) decisionmaking processes. One prominent line of work evaluates differential performance of machine learning models across subpopulations defined by any sensitive attribute, and proposes interventions to equalize performance or enforce specific conditional independence assumptions, such as equalized odds or opportunity [16], demographic parity [7], multicalibration [17], individual fairness [10], etc. Causal fairness is a complementary framework that assumes an underlying causal data-generating mechanism to operationalize fairness for predictive models [9, 26, 52, 39]. Principal fairness uses causal inference to enforce conditional independence of the sensitive attribute given counterfactual outcomes [20] and has been applied to coronary artery bypass grafting treatment allocation [53]. While algorithmic fairness frameworks have been used in healthcare [5, 29, 41, 38], their downstream utility has been low due to the systematic nature of statistical biases present in the data [4, 51, 46, 32].

Path-specific Effects. Path-specific effects are a broad class of causal effects that measure the influence of a treatment X on an outcome Y through specific causal pathways [37, 1, 44]. The Total Effect (TE), defined as TE( x 1 , x 0 ) ≜ E [ Y | do( x 1 )] -E [ Y | do( x 0 )] , captures the influence transmitted through all causal paths connecting the treatment and the outcome. The total effect is decomposed into the direct effect and the indirect effect , where the latter is an effect mediated through intermediate variables. For example, in the scenario depicted by Fig. 2a, the Natural Direct Effect (NDE) [36] of X on Y is NDE( x 1 , x 0 ) ≜ E [ Y x 1 , W x 0 , V x 0 ] -E [ Y x 0 ] , which captures variation in Y if X changes from x 0 to x 1 , while the mediators W and V hypothetically remain the same. The Natural Indirect Effect (NIE) is NIE( x 1 , x 0 ) ≜ E [ Y x 1 ] -E [ Y x 1 , W x 0 , V x 0 ] . This quantity represents the change in outcome due to the mediators shifting in response to the change in X from x 0 to x 1 .

Much of the literature has focused on estimating NDE and NIE under single-mediator settings (e.g., [47, 11]). Motivated by the presence of multiple mediators, contemporary research on pathspecific analysis has broadened its scope to investigate effects transmitted along particular, often complex, paths within multi-mediator systems. For instance, effects acting through the colored path in Fig. 2a might be characterized by the nested counterfactual quantity E [ Y x 1 , V x 0 , Wx 1 ] in statistics and algorithmic fairness [49, 30, 52, 6, 8]. Specifically, [30] developed a robust estimator for measuring path-specific effects transmitted through a particular mediator in the presence of other mediators.

3 Pulse-oximetry bias using path-specific analysis

We define path-specific effects within the standard fairness model (SFM), illustrated by the DAG in Figure 2, which represents a broad class of clinical problems. In our setup, X is a binary indicator of race, Y represents ventilation-related outcomes, and Z denotes the pre-admission statistics. The mediator W represents post-admission measurements, while the mediator V includes variables related to oxygen saturation, such as the peripheral oxygen saturation reading from a pulse oximeter SpO 2 , the more accurate arterial blood gas measurement (SaO2), and the discrepancy ∆ = SpO 2 -SaO2. We examine two primary outcomes: (1) the rate of invasive ventilation, defined as the proportion of patients who receive any invasive ventilation procedure during their ICU stay, and (2) the duration of invasive ventilation, measured as the length of the first invasive ventilation event.

We study the direct effect of X on V which then affects Y , termed the V-specific Direct Effect (VDE):

This path-specific effect, which isolates the influence mediated through V given W x 1 (the mediators W as they would be under exposure x 1 ), corresponds to estimands discussed in prior work (e.g., Miles et al. [30]). Within our SFM, we specifically term this as the VDE. As an example, suppose x 0 = White , x 1 = Black , and Y is the rate of invasive ventilation. The VDE captures the difference in expected invasive ventilation rate ( Y ) if post-admission measurements ( W ) and the ventilation decision were made as if the patient were Black ( x 1 ), while oxygen saturation readings (SpO 2 , SaO 2 , ∆ ) were measured as if the patient were White ( x 0 ). This effect isolates treatment rate heterogeneity due to discrepancies in oxygen saturation measurements. The SFM in Figure 2 captures plausible associations between the mediators W and V in which the VDE is identifiable (see proof in Appendix A). Table 2 contextualizes and compares all causal effects of interest within our framework.

3.1 Estimating path-specific effects

This section presents identifiability conditions for the VDE (Eq. (1)) and then develops its doubly robust estimator. Our approach integrates key insights from Miles et al. [30], who addressed similar path-specific effects often under parametric assumptions, and Jung et al. [25], who provided a general non-parametric framework for complex estimands involving conditional expectations. By synthesizing these, we develop a doubly robust VDE estimator that, crucially, does not require parametric modeling. This allows for the flexible use of machine learning methods to estimate these functions, which improves robustness to model misspecification. Under the SFM in Figs. (2a, 2b), the VDE is identifiable as follows.

Proposition 1 ( Identifiability [30]) . Under the SFMs in Fig. 2, the VDE E [ Y x 1 ] -E [ Y x 1 , V x 0 , Wx 1 ] is identifiable and is given as follows: E [ Y x 1 ] = ∑ z E [ Y | x 1 , z ] P ( z ) and

We focus on estimating the nested counterfactual term of the VDE, E [ Y x 1 , V x 0 , Wx 1 ] represented in Eq. (2), since estimating E [ Y x 1 ] using the back-door adjustment [35] is well-known.

To construct the estimator, we will parameterize Eq. (2) using the following:

Definition 1 ( Nuisance Parameters [30]) . Two sets of nuisance parameters µ 0 ≜ { µ 1 0 , µ 2 0 , µ 3 0 } and π 0 ≜ { π 1 0 , π 2 0 , π 3 0 } are defined as shown in the following table, where ˇ µ 3 0 ≜ µ 3 0 ( V , W , x 1 , Z ) and ˇ µ 2 0 ≜ µ 2 0 ( W , x 0 , Z ) .

Then, the VDE in Eq. (2) can be parametrized as follows.

Lemma 1 ( Parametrization ) .

Among all parametrizations of Eq. (2), we use the one with the double robustness property:

The functional φ is a valid representation since E [ φ (( Y , V , W , X , Z ); µ 0 , π 0 )] = Eq. (2). Moreover, φ exhibits the following robustness property:

Lemma 2 ( Double Robustness Property ) . Let V = ( Y , V , W , X , Z ) . For any arbitrary vectors µ , π , the functional φ satisfies the following double robustness property:

Eq. (7) shows debiasedness because whenever ˆ µ i , ˆ π i converges to µ i 0 , π i 0 with rate n -1 / 4 , then the error in φ converges at a much faster n -1 / 2 rate. We construct the following doubly robust estimator.

Definition 2 ( Doubly Robust VDE Estimator ) . Given a sample D i . i . d . ∼ P , the doubly robust VDE estimator ˆ ψ is constructed as follows:

( Sample-Splitting ) Take any L -fold random partition for the dataset D ≜ ( V 1 , · · · , V n ) ; i.e., D = ∪ L ℓ =1 D ℓ where the size of the partitioned dataset D ℓ is equal to n/L .

( Learning by Partitions ) For each ℓ = 1, 2, · · · , L , construct the estimator ˆ µ i ℓ , ˆ π i ℓ using D\D ℓ for i = 1, 2, 3 and compute ˆ ψ ℓ ≜ E D ℓ [ φ ( Y , V , W , X , Z ); ˆ µ , ˆ π ]

( Aggregation ) The one-step estimator ˆ ψ is an average of { ˆ ψ ℓ } L ℓ =1 ; i.e., ˆ ψ ≜ 1 L ( ˆ ψ 1 + · · · , ˆ ψ L ) .

Following the analysis from [Theorem 4 in 25], we provide novel finite-sample learning guarantees: Theorem 2 ( Finite-Sample Analysis ) . Suppose ˆ µ i ℓ , µ i 0 < ∞ and 0 < ˆ π i ℓ , π i 0 < ∞ almost surely for i = 1, 2, 3 . Suppose the third moment of φ exists. Let R 1 ≜ (1 /L ) ∑ L ℓ =1 ( E D ℓ [ ˆ φ ℓ ] -E P [ φ 0 ]) . Let ρ 2 0 ≜ V [ φ 0 ] . Let κ 3 0 ≜ E [ | φ | 3 ] . Let Φ( x ) denote the standard normal CDF. Then,

where, with probability greater than 1 -ϵ ,

Theorem 2 demonstrates that the error can be decomposed into two terms. The term R 1 closely approximates a standard normal distribution variable, and the remaining term exhibits the doublyrobustness behavior. This is formalized in the corresponding asymptotic analysis.

Corollary 2 ( Asymptotic error ) . Assume µ i 0 , ˆ µ i ℓ < ∞ and 0 < π i 0 , ˆ π i ℓ < ∞ almost surely. Suppose ˆ µ i ℓ and ˆ π i ℓ are L 2 -consistent. Then,

and √ nR 1 converges in distribution to Normal (0, ρ 2 k ,0 ) .

To estimate ˆ π i ∈ ˆ π , we can rewrite the nuisance expressions using Bayes' rule to avoid computing densities in high dimensions. However, estimation can still be challenging because propensities in the denominator may cause the variance to explode. Since E [ π i 0 ] = 1 , we can improve the estimation stability using self-normalization (SN) by setting ˆ π i SN ← ˆ π i / E D [ˆ π i ] . This technique is known to reduce the variance [19]. The self-normalized estimator for the NDE/NIE is outlined in Appendix B. Theoretical results follow analogously for the self-normalized doubly-robust estimator.

4 Experiments

We evaluate our proposed canonical and self-normalized doubly robust estimators for computing the fairness effects in Table 2 across synthetic, semi-synthetic, and real-world settings. Like most causal inference literature, we validate our methodology using synthetic and semi-synthetic data, which provide access to the true data-generating mechanisms and counterfactual outcomes.

We then apply our methodology to two real-world ICU datasets to estimate the path-specific effect of race (specifically mediated by discrepancies in pulse oximetry measurements) on the rate and duration of invasive treatment. Note that unlike previous studies which examine patient outcomes, we study decision-making regarding invasive ventilation procedures in the ICU.

For all experiments, we perform sample-splitting with L = 5 folds and clip propensities within the range [ ε , 1 -ε ] , where ε = 10 -4 . All propensity and outcome models are trained using XGBoost. Details on hyperparameter selection are provided in Appendix D and code credits are in Appendix L.

4.1 Synthetic data

In this experiment, we demonstrate the finite-sample behavior of the canonical and self-normalized doubly robust estimator. We validate convergence of causal estimands using a linear synthetic setting, where Z and W are multi-dimensional continuous vectors.

We generate samples from a linear SCM with randomly initialized weights, where Z , V are 3dimensional, W is 10-dimensional, and X , Y are single-dimensional. These dimensionalities are chosen to be similar to the real-world data. We estimate all causal queries for computing fairness effects in Table 2, namely: E [ Y x 0 ] , E [ Y x 1 ] , E [ Y x 1 , M x 0 ] , and E [ Y x 1 , V x 0 , Wx 1 ] . To show the convergence, we vary the sample size from 1,000 to 32,000, which roughly matches the number of eICU samples.

In Figures 3a and 3b, we report the mean and 95% confidence interval of the relative error for each causal query across 100 bootstraps using the standard doubly robust (non-SN) and self-normalized (SN) estimator. While both estimators converge to the true causal quantities, the errors without self-normalization exhibit significantly higher variance. In Appendix E, we demonstrate that this difference primarily occurs because the empirical mean of the nuisance parameters deviates from one.

4.2 ICU cohort selection

To conduct semi-synthetic/real-world experiments, we use two large, publicly available critical care datasets: the eICU Collaborative Research Database (eICU) with ICU admissions from hospitals across the continental U.S. [40], and Medical Information Mart for Intensive Care (MIMIC-IV), with ICU data from the Beth Israel Deaconess Medical Center in Boston [22].

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We are interested in investigating the causal effect of race on invasive ventilation rate and duration mediated by oxygen saturation discrepancy. If a patient undergoes multiple intubations over the course of a single ICU admission, only the first is considered. We treat gender, age, and comorbidity scores as confounders, representing patient characteristics available before ICU admission and prior to any clinical procedures or measurements. Comorbidity is quantified using the Charlson Comorbidity Index and the pre-ICU OASIS score, both of which summarize baseline health status.

The mediators W consist of post-admission measurements: arterial blood gas (ABG) results excluding SpO2 and SaO2, laboratory values such as creatinine and lactate, and periodic vital signs (e.g., temperature, respiratory rate). The V mediators include any SpO2 and SaO2 values within the range [70%, 100%] , as well as the measurement discrepancy ∆ = SpO 2 -SaO2. For computing ∆ , we match each SpO2 reading with an SaO2 measurement taken within the next five minutes if available.

Note that our V mediators include not only the discrepancy, but also SaO 2 and SpO 2 , because race influences the discrepancy through oxygen saturation measurements. Although V includes patient variables that are not intrinsically unfair, incorporating all oximetry-related variables captures the mechanism by which racial bias in pulse oximetry mediates clinical decisions more comprehensively.

To summarize measurement trajectories over time, we compute an exponentially weighted average from ICU admission up to the time of first ventilation (or discharge if the patient was not intubated). For a sequence of observations x 1 , . . . , x n taken t 1 , . . . , t n minutes before the first ventilation or discharge, the aggregated value is x = ∑ i w i x i /∑ i w i , where w i = exp( -γt i ) is an exponentially decaying weight and γ is a smoothing parameter. We restrict the analysis to stays lasting at least 24 hours and with at least one recorded measurement of SpO2, SaO2, and a matched discrepancy value. The final cohort consists of 37,222 admissions from eICU and 4,897 admissions from MIMIC-IV. Figure 4 presents the distribution of ICU stays by race, ventilation status, and treatment duration. Details on the distribution of pre-admission severity scores are included in Appendix C.

4.3 Semi-synthetic eICU experiments

We create a semi-synthetic cohort by leveraging real-data patterns to construct a synthetic SCM. Semi-synthetic data allows us to evaluate our methodology in a more realistic setting while retaining access to ground-truth effects for error analysis.

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To generate the cohort, we use the real-world eICU dataset to train separate XGBoost models to predict each variable in the set { X , W , V , Y } given its observed parents. In the semi-synthetic setting, Y is a binary variable indicating whether the patient received an invasive ventilation procedure during the stay. These trained models serve as the true causal mechanisms when generating samples. We use the eICU dataset due to its larger sample size compared to MIMIC-IV.

Following the setup in the synthetic experiment, we compute the relative error for E [ Y x 0 ] , E [ Y x 1 ] , E [ Y x 1 , M x 0 ] , and E [ Y x 1 , V x 0 , Wx 1 ] across varying sample sizes in Figures 3c and 3d. Similar to the synthetic experiments, our proposed self-normalized variant exhibits significantly lower variance in a healthcare-grounded setting with complex relationships between variables. This behavior is consistent with results using MIMIC-based semi-synthetic data, which we include in Appendix G. Additionally, we compare our estimators with state-of-the-art effect estimation baselines in Appendix I and demonstrate their robustness to imbalance between x 0 and x 1 subpopulations in Appendix J.

Results on semi-synthetic data support our approach over other methods in Table 1. Most prior work only allow for a single mediator, which could be applicable in other ICU settings, but is limited for our pulse oximetry application because relevant patient variables beyond oxygen discrepancy must be taken into consideration for valid and unbiased estimates of fairness. While Miles et al. [30] use multiple mediators, their estimator is conceptually analogous to our non-self-normalized variant, which exhibits high variance in small-sample settings like ours. Based on these considerations, we adopt the self-normalized estimator for quantifying path-specific effects in real-world data.

4.4 Real-world eICU and MIMIC-IV experiments

We estimate the effects in Table 2 using x 0 = White as the baseline (reflecting the majority demographic of the cohort) and x 1 = Black . Additionally, we compute the NIE as if we entirely ignored W and denote this effect as NIE ∗ . This alternative effect allows for comparison with existing research, as prior studies have quantified the effect of race mediated by measurement discrepancy without accounting for other post-admission mediators (denoted as W in our setup). For example, Gottlieb et al. [14] used NIE ∗ in the context of pulse oximetry to quantify the effect of the discrepancy on oxygen supplementation levels, but did not account for the impact of other potential mediators on the outcome. In contrast, our methodology explicitly models these mediators using W .

We compute all causal effects over 500 bootstrap iterations and report the mean and 95% confidence intervals. Figure 5 shows the effects for the rate and duration of ventilation. A positive-valued effect indicates that the corresponding pathway contributes to more frequent or longer invasive ventilation treatments for Black patients relative to White patients. We include the results using the canonical doubly robust estimator in Appendix H. All of our analysis and conclusions are consistent between the self-normalized and the canonical doubly robust estimators, with some slight differences in the effect magnitudes.

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Analysis of ventilation rates. Figure 5a suggests that the overall total effect varies across the two datasets, which indicates baseline practice differences. While the negative TE indicates baseline ventilation rates are higher for White patients compared to Black patients, these differences do not indicate unfairness without studying the decomposed effects. A negative NDE in eICU versus a positive NDE in MIMIC-IV suggests direct discrepancy adjusted only for baseline patient confounders, but not ICU-specific patient condition. Much of the total variation in both eICU and MIMICIV is dominated by the NIE, suggesting potential differences in White vs. Black patient health conditions influencing ventilation rates. The VDE for invasive ventilation rates for both eICU ( -0.21 percentage points, 95% CI [ -0.23 to -0.19 ]) and MIMIC-IV ( -0.46 percentage points, 95% CI [ -0.56 to -0.36 ]) datasets is relatively small, indicating low unfairness mediated by oxygen saturation discrepancy. In addition, the NIE* shows that ignoring W mediators for this problem can exacerbate the estimated scale of unfairness and potentially flip the direction of disparity.

Analysis of ventilation duration. Figure 5b shows significant differences in the duration of ventilation between eICU and MIMIC-IV, which is largely indicative of baseline distribution shifts in both ICU datasets (see Appendix C). The flipped signs of NDE specify that across multicenter eICU data, Black patients are ventilated for longer, while in MIMIC-IV, White patients are ventilated for longer, when adjusting for pre-admission covariates. The NIE is the primary pathway influencing the total effect, however the effect severity drastically shifts when considering only a subset of mediators (i.e. NIE*), which suggests the need to decompose NIE further to assess VDE. We observe slightly longer durations of invasive ventilation among Black over White patients in eICU ( 2.3 hrs, 95% CI [ 2.2 to 2.5 ]) and significantly longer durations in MIMIC-IV ( 7.4 hrs, 95% CI [ 6.9 to 7.9 ]), mediated by pulse oximetry discrepancies. The MIMIC-IV bias in duration is broadly in line with some reported differences in levels of end-of-life care by race [24, 23], but requires further investigation to attribute observed VDE differences to meaningful causes.

To better understand how oxygen discrepancy influences the VDE, we present the effect conditioned on both the discrepancy ∆ and the SpO2 value. Training a regression model for the VDE proved challenging due to small sample sizes in certain regions; therefore, we compute averages over discrete binned intervals of ∆ and SpO2. The conditional effects are shown in Figure 6.

While MIMIC-IV samples are sparse, the eICU conditional VDE suggests that under hypoxemia (SpO 2 ≤ 85% and ∆ ≥ 0% ), higher rates of ventilation tend to occur for Black compared to White patients. However, the effect flips when 85% ≤ SpO 2 ≤ 90% and 10% ≤ ∆ ≤ 20% . The conditional VDE for ventilation duration is relatively small and uniform when there is little oxygen discrepancy ( | ∆ | ≤ 10% ). Meanwhile, Black patients experience significantly longer ventilation times when 90% ≤ SpO 2 ≤ 95% and 10% ≤ ∆ ≤ 20% (hidden hypoxemia) in both datasets. This pattern also persists when 80% ≤ SpO 2 ≤ 90% and -20% ≤ ∆ ≤ -10% (moderate hypoxemia), but the effect flips in the region 90% ≤ SpO 2 ≤ 95% for eICU samples.

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eICU

10

10

0

-10

8

2

-20

0

-30

6

a

S

4

30

2

I

20

MIMIC-IV

2

0

10

P

0

0

S

-10

-20

2

-30

70

75

80

85

90

95

100

Sp02 (%)

Rate of ventilation (%)

30

20

eICU

0.5

10

-10

0

0.0

2

-20

-30

a

-0.5

S

2

I

30

20

MIMIC-IV

-1.0

0

10

P

0

S

-10

-20

-30

-1.5

70

75

80

85

90

95

100

Sp02 (%)

5 Discussion

In this work, we introduce the V -specific Direct Effect (VDE) to quantify racial biases in critical care decision-making that are mediated by measurement discrepancies from pulse oximeter devices. While previous studies have documented disparate outcomes for Black patients, our approach is the first to apply a path-specific causal framework to examine heterogeneity by race in a clinically actionable healthcare process. We develop a doubly robust estimator and a self-normalized variant for the VDE, provide favorable finite-sample guarantees, and demonstrate strong empirical performance on both synthetic and semi-synthetic health data.

In two publicly available ICU datasets, we find negligible disparities in invasive ventilation rates indicating slightly less frequent treatment for Black patients relative to White patients mediated by oxygen saturation discrepancy. Both datasets also show longer treatment durations for Black compared to White patients with different effect severities. We consistently observe that the canonical NIE exacerbates the magnitude of disparity while the NIE ∗ may potentially flip the direction. This highlights the necessity of our path-specific causal framework to accurately examine fairness.

For assessing clinical decision-making, our findings indicate that bias arising from pulse oximetry measurements primarily affects the duration of invasive ventilation rather than initiation of treatment. This pattern suggests that clinicians may effectively integrate additional patient information beyond oxygen saturation when deciding whether to ventilate. Alternatively, the bias may manifest through pathways not captured within our current framework, such as through unmeasured variables or outcomes. Understanding the mechanisms underlying such bias remains an active area of research.

Limitations. As with most causal inference methods, our framework relies on a specified causal graph and thus depends on assumptions about the data-generating process that can be challenging to verify in practice. Consequently, it shares common limitations related to potential misspecification of the causal structure. For example, if there is strong reason to believe that W and V have a latent common cause in a given application, any estimated path-specific effect for the VDE would be inaccurate because the true effect is not identifiable.

Our causal graph reflects generally plausible mechanisms by ensuring clinically relevant quantities reported in the datasets are modeled, while making the minimal assumptions required for identifiability of the causal effects of interest. The graph explicitly captures these underlying assumptions, which is an important advantage highlighted in critical care literature [27].

We only consider the first invasive ventilation and do not explicitly model temporality in our analysis. Additionally, sparse SaO2 measurements limit the frequency of matched oxygen saturation discrepancy measurements, further affecting sample size. However, we emphasize that this is a limitation with the dataset and not inherent to our method.

Broader Impact. Several clinical problems can be framed using the multiple-mediation analyses. Our contributions are intended to provide a practical algorithm for computing particular path-specific effects more broadly. The methods provide a more nuanced understanding of heterogeneity in current healthcare practices.

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A Proofs

A.1 Identifiability of VDE in Figures (2a, 2b)

Figures (2a, 2b) imply the following conditional independences between counterfactual variables:

These conditional independences lead to the following derivation:

where

Since W x ⊥ ⊥ X | Z , we have P ( W x 1 = w | z ) = P ( w | x 1 , z ) .

Since V x 0 , w ⊥ ⊥ W x 1 | Z , we have P ( V x 0 , w = v | W x 1 = w , z ) = P ( V x 0 , w = v | z ) .

Since Y x 1 , v ⊥ ⊥ V x 0 , w | Z , W x 1 , we have

A.2 Non-identifiability of VDE in Figures (7a, 7b)

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Whenever there exist unmeasured confounders between W and V , the VDE is not identifiable. Specifically, we can write the counterfactual nested term P ( Y x 1 , V x 0 , Wx 1 = y ) as follows using the

identification algorithm proposed by [8]:

This reduces the problem to identifying P ( V x 0 , w , z = v , W x 1 , z = w ) . By [Theorem 3 in 8], this term is not identifiable because of inconsistency (where X = 0 in the counterfactual V x 0 , w , z while X = 1 in W x 1 , z ).

A.3 Proof of Lemma 1

We note that

and

Therefore,

Furthermore,

Also,

Finally,

This completes the proof.

A.4 Proof of Lemma 2

We will first use the following helper lemma:

Lemma 3 ( Helper Lemma ) . For any functional ( a 0 ( W ), b 0 ( W )) and ( a ( W ), b ( W )) , for any W ⊆ V , the following holds:

Proof. Define F ( W ) as a function satisfying the following equation:

We will omit W for notational convenience for now. The above equation shows that

Then,

By the definition of F , we have

This completes the proof.

Based on this helper lemma, for i = 1, 2, 3 , we have

Then, consider

Combining,

where the equation holds since E [ π 3 0 µ 3 0 ] = ψ 0 ≜ Eq. (2), and by the law of the total expectation.

Next, define µ 2 ∗ ≜ µ 2 ∗ [ µ 3 ] ≜ E [ µ 3 ( V , W , x 1 , Z ) | W , X , Z ] for any fixed µ 3 . Then,

Next, define µ 1 ∗ ≜ µ 1 ∗ [ µ 2 ] ≜ E [ µ 1 ( W , x 0 , Z ) | X , Z ] for any fixed µ 2 . Then,

Then, since

Therefore, E [ π 3 0 µ 3 ] in the first term and -E [ π 2 0 µ 2 ∗ ] in the second term can be canceled out. Furthermore,

since

Therefore, E [ π 2 0 µ 2 ] in the second term and -E [ π 1 0 µ 1 ∗ ] in the third term can be canceled out. Therefore, we can conclude that

This completes the proof.

A.5 Proof of Theorem 2

A.5.1 Proof of Eq. (8) in Theorem 2

Let V = { Y , V , W , X , Z } . We note that the doubly robust estimator is given as

Then,

Define

Then, with the proof of Lemma 3, we observe that Eq. (8) holds.

A.5.2 Proof of Eq. (9) in Theorem 2

Let or equivalently,

We first study the term ( E D -E P )[ ϕ 0 ( V )] . By Chebyshev's inequality,

where n ≜ |D| . Equivalently,

Choose

Then, with a probability greater than 1 -ϵ ,

A.5.3 Proof of Eq. (10) in Theorem 2

From the previous proof, we have

By choosing we have

Define

Here,

Then,

Then,

This completes the proof.

B Self-normalized estimators for the NDE and NIE

Wefocus on estimating the counterfactual term for the NDE and NIE, E [ Y x 1 , W x 0 , V x 0 ] , since estimating E [ Y x 0 ] and E [ Y x 1 ] using the back-door adjustment [35] is well-known. Let M = { W , V } be the combined set of mediators. The counterfactual quantity is identifiable in Figure 2 using the formula:

Following the recipe in [25], the expression for ψ 0 = E [ Y x 1 , M x 0 ] can be parameterized using the following nuisance parameters:

where ˇ µ 2 0 ≜ µ 2 0 ( M , x 1 , Z ) . The doubly robust estimator for ψ 0 is

We estimate the nuisance parameters using the same sample-splitting procedure as for the VDE. To estimate ˆ π i ∈ ˆ π , we can rewrite the expressions using Bayes' rule to avoid computing highdimensional densities. Since E [ π i 0 ] = 1 , the self-normalized variant uses ˆ π i SN ← ˆ π i / E D [ˆ π i ] .

C Additional data analysis

All analysis is restricted to adult patients. To better understand the distribution of patients in our datasets, we analyze baseline characteristics and pre-admission severity scores across datasets and racial groups. Figure 8 shows the distribution of age and sex, stratified by race. To assess pre-ICU severity, we use two measures: the OASIS score and the Charlson Comorbidity Index. Both are integer-based scores, with higher values indicating greater clinical severity. These distributions are shown in Figure 9.

We observe that the distribution of patient severity remains consistent across different racial groups. Moreover, baseline patient conditions tend to be more severe in the eICU dataset, which explains the longer ventilation times in Figure 4b.

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D Hyperparameter selection

In this section, we outline our approach for selecting the hyperparameters of the XGBoost models to compute E [ Y x 1 , W x 0 , V x 0 ] and E [ Y x 1 , V x 0 , Wx 1 ] . For both the synthetic and semi-synthetic settings, we generate a random dataset consisting of 32,000 samples and perform a separate grid search for each propensity model and each outcome model. For the real-world setting, we perform the hyperparameter search using the eICU and MIMIC-IV datasets.

The grid search optimizes three hyperparameters: the number of estimators from the set { 20, 50, 100, 200 } , the maximum tree depth from the set { 3, 4, 5, 6 } , and the ℓ 2 -regularization penalty from the set { 0.5, 1, 2, 5 } , using 5 -fold cross-validation. For propensity models, we select the hyperparameter configuration according to the Brier score, which evaluates prediction calibration. For outcome models, we select the configuration using the mean squared error. The chosen hyperparameters remain fixed across all bootstraps and sample sizes throughout the corresponding experimental setting.

E VDE nuisance parameter analysis

We demonstrate that the improved variance of our proposed self-normalized estimator, as shown in Figures 3, can be attributed to better nuisance estimates when the sample size is small. In Figure 10, we present the mean and 95% confidence interval across 100 bootstraps for the empirical average of the VDE nuisance parameters ˆ π 3 , ˆ π 2 , and ˆ π 1 .

As the number of samples increases, the empirical mean converges to the true value of one. For smaller sample sizes, the nuisance parameters tend to be large, which causes greater variance in the standard doubly robust estimator. In contrast, our self-normalized variant scales the nuisance parameters so that the empirical average is one, which reduces the variance in the estimation. In the semi-synthetic setting, the nuisance parameters exhibit slow convergence or a small bias due to propensity clipping.

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F Synthetic binary setting

In addition to the synthetic experiment with continuous variables, we also analyze a synthetic setting with singleton binary variables. This experiment aims to demonstrate the convergence of causal effects and nuisance parameter estimates. By choosing a simplified setting, we illustrate that when the nuisance parameters are accurate, the standard and self-normalized estimators produce approximately identical results.

We generate data according to the following model, where all observed variables take singleton binary values and the unobserved variables are U X , U XZ , U W , U V , U Y ∼ N (0, 1) :

We estimate the causal queries necessary to compute fairness effects: E [ Y x 0 ] , E [ Y x 1 ] , E [ Y x 1 , M x 0 ] , and E [ Y x 1 , V x 0 , Wx 1 ] . Like the synthetic setting with continuous variables, we vary the sample size from 1,000 to 32,000.

We report the mean and 95% confidence intervals across 100 bootstraps of the relative error on each causal query and the empirical mean of the nuisance parameters in Figure 11. As the sample size increases, our estimates converge to the true causal quantities. Due to the simplicity of the singleton binary variables in this experiment, the empirical mean of the nuisance parameters is always close to one. Consequently, the estimates obtained with the self-normalized estimator are nearly identical to those shown in Figure 11a.

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G Semi-synthetic MIMIC-IV results

We show the experimental results for our estimators on semi-synthetic data based on patterns in the MIMIC-IV dataset. Following the setup in the semi-synthetic eICU setting, we train an XGBoost model to predict each variable in the set { X , W , V , Y } given its observed parents in the real-world data. We fix Y to be a binary variable indicating whether the patient received an invasive ventilation procedure during the stay.

We report the mean and 95% confidence interval across 100 bootstraps of the relative error for each causal query across varying sample sizes in Figure 12. Like for the semi-synthetic eICU setting, we observe that our estimands approximately converge to the true value, however, the convergence is slow for E [ Y x 1 , V x 0 , Wx 1 ] using the canonical doubly robust estimator.

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H Canonical doubly robust estimator results on real-world data

We compute the causal effects in Table 2 using the canonical doubly robust estimator. We report the mean and 95% confidence intervals for the rate and duration of invasive ventilation in Figure 13. The VDE for invasive ventilation rates for eICU ( -0.21 percentage points, 95% CI [ -0.23 to -0.19 ]) and MIMIC-IV ( -0.47 percentage points, 95% CI [ -0.57 to -0.36 ]) datasets is relatively small. Moreover, the VDE indicates slightly longer ventilation durations for Black relative to White patients in eICU data ( 2.4 hrs, 95% CI [ 2.2 to 2.5 ]) and significantly longer durations in MIMIC-IV data ( 8.1 hrs, 95% CI [ 7.5 to 8.7 ]).

The direction and statistical significance of all causal fairness measures obtained using the selfnormalized estimator (Figure 5) and canonical estimator are in agreement. Furthermore, we observe that the canonical estimator typically predicts wider confidence intervals across all effects, which is consistent with our experimental results in the synthetic and semi-synthetic settings.

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I State-of-the-art comparison

We compare our proposed canonical doubly robust estimator and its self-normalized variant against several state-of-the-art and baseline methods. To the best of our knowledge, no prior work directly targets the VDE beyond the canonical estimator. Therefore, we include the following (somewhat misspecified) baselines: (1) the X -learner, which estimates the ATE without accounting for mediation; (2) a single-mediator estimator, which treats W and V as a single merged mediator (i.e., NIE ∗ from Section 4.4); and (3) the nested regression estimator, corresponding to µ 1 0 in Equation 6.

Table 4 presents the comparison of VDE prediction errors. Our results show that the self-normalized estimator consistently achieves the lowest error while maintaining valid 95% confidence intervals. Although the nested regression estimator performs similarly on semi-synthetic data, its confidence intervals are overly narrow. State-of-the-art methods for similar effect estimation tasks, such as the X -learner, have large error in all settings since they do not account for the correct mediation structure.

J Group imbalance experiments

In the real-world data, the eICU cohort comprises approximately 31,000 White and 4,000 Black patients, while MIMIC-IV includes around 4,000 White and 400 Black patients. These distributions reveal a substantial group imbalance between White and Black patients, which is approximately preserved in our semi-synthetic experiments.

Although our self-normalized estimator demonstrates strong convergence properties despite this imbalance, we further examine its performance under varying degrees of group imbalance. Using the eICU-based and MIMIC-based semi-synthetic datasets, we control the imbalance by thresholding the predictions of X at different values to induce varying proportions of x 0 and x 1 subgroups. To quantify the imbalance, we define η = # of x 1 samples # of total samples . We assess performance using the relative error for each causal query in Figure 14.

As expected, both the relative error and variance of the estimators tend to increase as the imbalance between the x 0 and x 1 subgroups grows. Nevertheless, the overall variation in estimator performance across different values of η remains modest, with relative errors increasing by only a few percentage points. These findings suggest that our estimator is moderately robust to the group imbalance present in the real-world experiments.

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K Compute resources

All models were trained on a single NVIDIA RTX A6000 GPU, 32 CPU cores, 256GB of system RAM, running Ubuntu 22.04 with kernel 5.15. The synthetic and semi-synthetic experiments compute 100 bootstraps for all sample sizes in two hours, while the real-world experiments require two hours to compute 500 bootstraps for each dataset and ventilation-based outcome.

L Experiment assets

In our experiments, we use the eICU [40] v2.0 and MIMIC-IV [22] v3.1 datasets, both publicly available under the PhysioNet Credentialed Health Data License 1.5.0. Data processing is performed using the eICU-CRD Code Repository 4 and the MIMIC Code Repository 5 , both under the MIT License. For eICU ventilation outcomes, we follow the data extraction procedure described in [48]. For Charlson Comorbidity Scores in the eICU dataset, we follow the process in [3] provided in the code implementation under the MIT License. 6 All the code and instructions for reproducing our experiments are available at https://github.com/reAIM-Lab/PSE-Pulse-Oximetry .

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper considers the fairness issues in Healthcare scenarios and aims for investigating the influence of racial bias in oximetry measurements on invasive ventilation in Intensive Care Units (ICU) settings from a causal perspective. Specifically, it leverages path-specific analysis to detect the causal effects of sensitive attribute (race) on invasive ventilation mediated by pulse oximetry discrepancies. To quantify such path-specific effects, it proposes a doubly robust estimator and a self-normalized variant, with fine-sample guarantees. Experiments on synthetic and real-world datasets showcase the effectiveness of the proposed method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The authors address a nice and importance fairness problem in this work.\n2. The authors propose a novel doubly robust estimator and self-normalized variant for quantifying V-specific direct effects.\n3. Theoretically sound. The proposed method is built upon existing theoretical results while also providing rigorous theoretical analysis.\n4. The experiments results demonstrate that the proposed method can effectively assess V-specific direct effects.\n\nWeaknesses:\n1. The presentation in articulating the research gap is not so clear. More explanations about how existing path-specific methods can be adapted or applied to ICU settings would help in understanding the flexibility and integration potential of them, e.g., Reference [27].\n2. In Table 1, Reference [46] also focuses on multiple mediators settings.\n3. The proposed V-specific direct effect is a special case of path-specific effects.\n4. The validity of the proposed method relies on the assumptions of the causal models illustrated in Figure 2. However, the rationale behind data generation mechanism aligning with these causal models is not clearly presented. For example, X, representing race as an inherent characteristic of individuals, raises questions regarding why it is caused by Z. The authors do not provide any explanations where these causal models may hold, thus making it difficult to justify the assumptions.\n5. There is a lack of comparison with SOTA methods in the experiments. More SOTA methods should be considered.\n\nQUESTIONS:\n1. What are the unique challenges of the ICU settings compared to other healthcare applications scenarios?\n2. Please refer to the weaknesses.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors focus on tackling the problem of racial bias on ICU settings, where medical device bias can lead to delaying clinical interventions for certain sensitive groups. To this end, the authors introduce the V-specific direct effect to estimate the racial biases in the ICU. Subsequently, the authors propose a doubly robust estimator and a self-normalized variant for the V-specific direct effect with theoretical guarantees. Experimental results show the effectiveness of the proposed method in analyzing the causal effects of pulse oximeter mediated bias on invasive ventilation.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The first causal analysis method to investigate the racial biases in ICU settings.\n2. The authors propose a theoretically sound estimator to quantify the path-specific causal effects of racial bias on invasive ventilation.\n3. The writing is clear and easy to follow.\n\nWeaknesses:\n1. The unique challenges of addressing fairness issues in ICU settings are not sufficiently discussed. In addition, it is unclear why existing causal analysis methods, such as [27], [44], and [46] shown in Table 1, are not applicable to ICU data.\n2. The proposed method relies on several implicit assumptions to ensure the identifiability of the V-specific direct effect, e.g., the absence of hidden confounders. However, the plausibility of these assumptions in real ICU settings is not sufficiently discussed.\n3. The numerical experiments lack comparisons with state-of-the-art methods, including those based on statistical correlations, to demonstrate the advantages of the proposed approach.\n4. How does the proposed method performs under imbalanced sensitive group distributions, as is often the case in practice where black patients are underrepresented compared to white patients.\n\nQUESTIONS:\nPlease refer to the weaknesses.\n\nLIMITATIONS:\nYes, the authors have discussed the limitations of the proposed method.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors employ a causal inference framework to isolate the specific impact of pulse oximeter measurement discrepancies on invasive ventilation rates and duration. As key contributions, the authors propose a method using path-specific effects to quantify racial disparities in ICU decision-making. They define a specific causal query, the V-specific Direct Effect (VDE), to isolate the influence of race that is mediated specifically through oxygen saturation measurement discrepancies. They also present a doubly robust estimator for the VDE and introduces a self-normalized variant to improve sample efficiency and reduce variance, providing novel finite-sample guarantees for the estimator.\n\nThe methodology is validated on semi-synthetic data and then applied to two large ICU datasets, MIMIC-IV and eICU. Contrary to prior work suggesting significant disparities, this causal analysis finds a minimal impact of the measurement bias on invasive ventilation rates. However, the study does reveal a more pronounced and varied effect on the duration of ventilation, highlighting different outcomes between the two datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\nNovel causal inference framework applied to real-world dataset with insightful analysis. \n\nWeakness\nThe authors acknowledge as a limitation that they only consider the first invasive ventilation and do not explicitly model temporality. They aggregate time-series data using an exponentially weighted average.\n\nQUESTIONS:\nThe paper finds a negligible effect of oximetry bias on the  rate of ventilation, which seems counterintuitive. Does this finding imply that for the critical decision of initiating ventilation, clinicians are successfully integrating a wide array of data beyond the pulse oximeter, effectively mitigating the device's known racial bias? Or could the bias be manifesting in ways not captured by this outcome, such as delays in receiving non-invasive oxygen support before a decision to intubate is made?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe manuscript describes a methodology to estimate path-specific causal effects in the presence of multiple mediators, with application to a fairness analysis in ICU data. In terms of the methodology, the authors develop a doubly robust estimator for the path-specific effect of a treatment on the outcome via one particular mediator. They provide a theoretical analysis of the properties of this estimator (identifiability, double robustness property, finite-sample behavior, asymptotic behavior) and verify its behavior in synthetic as well as semi-synthetic experiments. They then proceed to apply this estimator to the task of assessing whether measurement biases in pulse oximeters (which are known to produce mistakenly low measurements for Black patients at a higher rate than for white patients) have a specific effect on race-specific ventilation-related outcomes. This study is conducted in two ICU datasets, eICU and MIMIC-IV. The results indicate that following their methodology, the effect of these race-specific measurement discrepancies on ventilation outcomes appears to be small.\n\nSTRENGTHS AND WEAKNESSES:\nThe manuscript is very well-written, thorough, and dense. The development of a novel, doubly robust path-specific effect estimator in the presence of multiple mediators is an essential contribution and presented very thoroughly. The provided theoretical analysis and empirical experiments (confirming the validity of the theoretical results) further strengthen this contribution. Finally, the case study alone is already very interesting and well-conducted, and moves far beyond the prototypical standard bias case studies presented in many papers. The topic of the case study is also very timely; I believe the manuscript really adds something to the ongoing debate about these measurement discrepancies.\n\nI essentially don't see any major weaknesses - I just have some questions or very minor suggestions which I am leaving below.\n\nQUESTIONS:\n- One thing left me a bit puzzled, but maybe I just missed a discussion of this somewhere? The authors estimate the V-specific effect, but V includes SpO2, SaO2, and the discrepancy between the two. In terms of the fairness question the authors are posing, it seems to me to make a crucial difference whether the authors are estimating an effect race -> SaO2 -> ventilation, or rather race -> (SpO2-SaO2) -> ventilation. The latter path would be unfair (and what the authors are really after, I believe) while the former path might be considered acceptable. Could the authors clarify this? E.g., which of these effects are the \"VDEs\" in Fig. 5?\n- Possibly related to my previous question: in the same figure (5b), it appears highly unlikely that the effect of the measurement discrepancy would be positive in one study and negative in another. Is this because - as indicated in my previous question - the VDE here is actually *not* just the effect of the measurement discrepancy? In any case, the result as presented here would seem to indicate that the uncertainty estimation probably yields highly optimistic bounds, no? (Assuming that the true effect of measurement discrepancies should have the same directionality in both studies, the confidence intervals should at least cover the null in both studies.)\n- In Fig. 3 top right panel, the variance actually does not appear to converge to 0, or at least *very* slowly. Is there a reason for this? Could the efficiency be improved somehow?\n- In the causal graph, why is race (X) affected by pre-admission statistics (Z)? That seems at least very curious.\n- The authors write that \"Algorithmic fairness [15, 28, 2, 30] operationalizes evaluation of differential performance of machine learning models across subpopulations\" - this is a very reductive description of the AF field. Not all AF conceptions are about subpopulations, and even of those not all are about differential performance. Some would say that AF also encompasses ethical questions beyond those that can be answered by looking at csv files with model predictions and \"ground truths\". (For one: what the authors are doing in this manuscript does not fall under the above description but would surely be classified as \"algorithmic fairness\".)\n\nLIMITATIONS:\nI would like to see the limitations of this approach presented more clearly, specifically the dependence on a rather large range of complex assumptions about the data-generating process that may be difficult to understand in detail and even more difficult to verify for a given application. One obvious risk is that people might misapply this method and conclude that something is \"fair\", when really it is not.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-04"}