Identification of physiological shock in intensive care units via Bayesian regime switching models

stat.AP stat.ME stat.ML stat.OT Emmett B. Kendall, Jonathan P. Williams, Curtis B. Storlie, Misty A. Radosevich, Erica D. Wittwer, Matthew A. Warner · Mar 23, 2026
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What it does
This paper addresses the critical challenge of detecting occult hemorrhage (internal bleeding) in intensive care units, where delayed diagnosis leads to preventable physiological shock and death. The authors develop a Bayesian regime...
Why it matters
The authors develop a Bayesian regime switching model (RSM) that tracks five latent physiological states—including stable, hemorrhage, and recovery—using longitudinal vital signs (heart rate, MAP, hemoglobin, lactate) and medication...
Main concern
The paper presents a methodologically sophisticated Bayesian approach to an important clinical problem. The novel state-sampling algorithm is a genuine contribution to computational statistics, offering orders-of-magnitude speedup over...
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Plain-language introduction

This paper addresses the critical challenge of detecting occult hemorrhage (internal bleeding) in intensive care units, where delayed diagnosis leads to preventable physiological shock and death. The authors develop a Bayesian regime switching model (RSM) that tracks five latent physiological states—including stable, hemorrhage, and recovery—using longitudinal vital signs (heart rate, MAP, hemoglobin, lactate) and medication history. Applied to 33,924 Mayo Clinic ICU encounters, the model aims to provide interpretable, probabilistic early warnings that outperform standard vital sign monitoring by accounting for autoregressive trends and pre-admission physiological changes.

Critical review
Verdict
Bottom line

The paper presents a methodologically sophisticated Bayesian approach to an important clinical problem. The novel state-sampling algorithm is a genuine contribution to computational statistics, offering orders-of-magnitude speedup over standard Gibbs approaches. However, the clinical validation is preliminary at best—relying on only five manually annotated test cases—and the model exhibits fundamental ambiguity between hemorrhagic shock and other shock etiologies (septic, cardiogenic), which limits its utility as a specific diagnostic tool for bleeding.

“state 2 was suggested when septic and cardiogenic shock were present and progressing rapidly. This is likely due to the overlap in the presentation of different shock types”
Kendall et al., Sec. 5.2 · Page 28
What holds up

The statistical methodology is rigorous and innovative. The authors' Algorithm 1 reduces the computational complexity of state sampling from $\mathcal{O}(5^p)$ to $\mathcal{O}(5(p-2) + 5^2)$, achieving a 36,394× speedup over Gibbs sampling with $p=8$ while improving state identification accuracy to 87.66% (Table 2). The handling of pre-ICU admission physiological changes via the approximation $g(\alpha^{(i)}, b_1^{(i)}) \approx y_1^{(i)} - D_{\omega,1}^{(i)}\omega - X_1^{(i)}\beta$ is clever and validated in supplementary simulations. The incorporation of 84 distinct medication effects and state-dependent autocorrelation matrices $A_1, \dots, A_5$ demonstrates thoughtful attention to clinical realism.

“Algorithm 1 achieves complexity O(5(p −2) + 52)”
Kendall et al., Sec. 3.4 · Page 19
“Algorithm 1 0.0729 0.8766 ... B (p = 8) 2653.1* 0.8392*”
Kendall et al., Table 2 · Page 20
Main concerns

The clinical validation rests on a vanishingly small test set of only five patients (Subjects A–E), with mixed results: while the model correctly identified bleeding in Subjects A and D, it generated false positives for Subject B (no bleed) and confused septic shock with hemorrhage in Subjects C and E. This reveals a fundamental limitation: State 2 captures generic shock physiology rather than hemorrhage-specific patterns, as the authors acknowledge that heart rate, MAP, and lactate trends overlap across shock types. The recommended probability threshold $\hat{c} = 0.0465$ for bleeding alerts is extremely low, suggesting the model functions more as a sensitive shock detector than a specific hemorrhage classifier. Additionally, the assumption that a patient's shock phenotype ($\alpha^{(i)}$) remains constant across multiple bleeding events is clinically questionable.

“Figure 5 appears to reflect the patient's dynamic course... state 2 was suggested when septic and cardiogenic shock were present”
Kendall et al., Sec. 5.2 · Page 28
“threshold value c ... 0.0465”
Kendall et al., Sec. 4.2 · Page 23
“our approach requires assuming that the shock phenotype for an individual is the same over time”
Kendall et al., Sec. 6 · Page 29
Evidence and comparison

The simulation study (100 datasets, 1,000 patients each) demonstrates good discriminative ability with median AUC of 0.8419 for detecting state 2. However, the paper lacks direct comparison to baseline methods—no black-box ML models (e.g., random forests, LSTMs) are trained on the same data, despite claims that the RSM offers superior interpretability. The comparison to existing state-sampling methods (Table 2) is limited to computational efficiency rather than clinical utility. The real-world case studies, while illustrative, do not establish superiority over simple heuristic rules (e.g., MAP < 65 mmHg + rising lactate) and highlight the model's propensity for false alarms when patients experience non-hemorrhagic shock states.

“median out-of-sample AUC ... is 0.8419”
Kendall et al., Sec. 4.2 · Page 23
“Figure 3 suggested a likely bleeding event ... the patient did not suffer a bleeding event. This may represent over-detection”
Kendall et al., Sec. 5.2 · Page 54
Reproducibility

Reproduction of this work would be extremely challenging. No code, scripts, or software implementation are provided. The data are restricted ('available from the corresponding author upon reasonable request'), and the MCMC sampling involves complex custom algorithms (Algorithms 1–3) with numerous hyperparameters and strong informative priors (e.g., $\nu_R = 2 \cdot \sum n_i$ degrees of freedom for the Inverse-Wishart on $R$) that are only fully detailed in supplementary materials. The case study required 2,000,000 MCMC iterations with the last 500,000 used for inference, suggesting substantial computational costs that would hinder independent validation without significant computational resources and the authors' specific implementation details.

“The data that support the findings of this study are available from the corresponding author [EBK] upon reasonable request”
Kendall et al., Sec. 7 · Page 30
“we set the Inverse-Wishart prior degrees of freedom for R to $\nu_R = 2 \cdot \sum_{i=1}^N n_i$”
Kendall et al., Sec. 3.3 · Page 15
“The MCMC routine is run for 2,000,000 iterations”
Kendall et al., Sec. 5.2 · Page 27
Abstract

Detection of occult hemorrhage (i.e., internal bleeding) in patients in intensive care units (ICUs) can pose significant challenges for critical care workers. Because blood loss may not always be clinically apparent, clinicians rely on monitoring vital signs for specific trends indicative of a hemorrhage event. The inherent difficulties of diagnosing such an event can lead to late intervention by clinicians which has catastrophic consequences. Therefore, a methodology for early detection of hemorrhage has wide utility. We develop a Bayesian regime switching model (RSM) that analyzes trends in patients' vitals and labs to provide a probabilistic assessment of the underlying physiological state that a patient is in at any given time. This article is motivated by a comprehensive dataset we curated from Mayo Clinic of 33,924 real ICU patient encounters. Longitudinal response measurements are modeled as a vector autoregressive process conditional on all latent states up to the current time point, and the latent states follow a Markov process. We present a novel Bayesian sampling routine to learn the posterior probability distribution of the latent physiological states, as well as develop an approach to account for pre-ICU-admission physiological changes. A simulation and real case study illustrate the effectiveness of our approach.

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