A Leakage-Aware Multimodal Evaluation Framework for Early Intraoperative Acute Kidney Injury Prediction

# A Leakage-Aware Multimodal Evaluation Framework for Early Intraoperative Acute Kidney Injury Prediction
Source: [https://arxiv.org/html/2609.26848](https://arxiv.org/html/2609.26848)
Quang Minh Nguyen\[0009\-0006\-1135\-5861\]and Duc Minh Le\[0009\-0007\-2269\-5949\]and Ho Nhat Minh Nguyen\[0009\-0008\-4290\-0759\]and Thuy Quynh Nguyen\[0009\-0000\-1241\-5666\]and Trong Nghia Nguyen\[0000\-0003\-1888\-0117\]Affiliation:National Economics University, Hanoi, Vietnam,E\-mail:[11247324@st\.neu\.edu\.vn](mailto:[email protected])Affiliation:National Economics University, Hanoi, Vietnam,E\-mail:[11247320@st\.neu\.edu\.vn](mailto:[email protected])Affiliation:National Economics University, Hanoi, Vietnam,E\-mail:[11247321@st\.neu\.edu\.vn](mailto:[email protected])Affiliation:National Economics University, Hanoi, Vietnam,E\-mail:[11247346@st\.neu\.edu\.vn](mailto:[email protected])Affiliation:National Economics University, Hanoi, Vietnam,E\-mail:[nghiant@neu\.edu\.vn](mailto:[email protected])

###### Abstract

Postoperative acute kidney injury \(AKI\) after major non\-cardiac surgery carries substantial morbidity, yet early intraoperative risk stratification remains difficult\. In this retrospective cohort study, we propose SynerT, a waveform\-only hybrid temporal backbone that combines a causal dilated TCN with a hierarchy of dilated recurrent layers to encode early intraoperative physiologic trajectories for AKI risk prediction\. Building on SynerT, we further design two model variants that extend the backbone with structured clinical context: SynerT\-MM, a late\-fusion multimodal extension that integrates hemodynamic burden summaries and preoperative covariates, and SynerT\-Stack, a leakage\-safe stacked ensemble that combines cross\-validated predictions from SynerT\-MM with strong tabular baselines at the meta\-learning stage\. All models are evaluated under a strict leakage\-aware framework on VitalDB, a high\-fidelity perioperative database, with prediction restricted to information available within the first 60 intraoperative minutes\. Among 2,413 waveform\-usable cases \(180 AKI\-positive; 7\.46% prevalence\), SynerT fell well below strong structured\-data baselines, demonstrating that waveform\-only temporal modeling is insufficient under strict early constraints\. SynerT\-MM recovered discrimination by incorporating hemodynamic burden summaries and preoperative covariates, and SynerT\-Stack achieved the best overall performance across AUROC, AUPRC, and F1\-max\. Cross\-fitted Platt recalibration substantially corrected calibration defects in both multimodal variants, and decision\-curve analysis confirmed the recalibrated stacked model delivered the strongest net clinical benefit across low\-to\-intermediate thresholds\. These findings indicate that credible early perioperative AKI risk stratification requires structured multimodal context, calibration\-aware estimation, and transport robustness evaluation rather than waveform modeling complexity alone\.

###### Keywords:

acute kidney injury, perioperative prediction, intraoperative vital signs, leakage\-aware evaluation

## 1Introduction

Postoperative acute kidney injury \(PO\-AKI\) is a common complication after major non\-cardiac surgery, associated with substantial short\-term morbidity and long\-term mortality\[[1](https://arxiv.org/html/2609.26848#bib.bib1),[5](https://arxiv.org/html/2609.26848#bib.bib5)\]\. Clinically, the optimal AKI prediction system must identify elevated risk early enough during the operation to allow for proactive intraoperative and postoperative management\. However, this is technically challenging because perioperative kidney injury emerges from the interaction between baseline patient vulnerability and evolving physiologic stress\. Recent VitalDB\-based studies have demonstrated the feasibility of AKI prediction using both interpretable ensembles and temporal deep\-learning models\[[4](https://arxiv.org/html/2609.26848#bib.bib4),[8](https://arxiv.org/html/2609.26848#bib.bib8)\], yet the evidence base remains methodologically uneven, often lacking strict leakage control for early\-prediction constraints and rigorous ablation of waveform\-only versus multimodal designs\[[7](https://arxiv.org/html/2609.26848#bib.bib7),[6](https://arxiv.org/html/2609.26848#bib.bib6)\]\. Rather than claiming a fundamentally novel architecture, this study contributes a disciplined, leakage\-aware evaluation framework for multimodal fusion under strict early\-prediction constraints, with SynerT as the proposed waveform\-only temporal backbone at its core\.

The contributions of this paper are as follows\. First, we establish a strict leakage\-aware early\-prediction framework that restricts dynamic inputs to the first 60 intraoperative minutes, applies fold\-specific preprocessing, and builds stacked predictions only from out\-of\-fold outputs \(i\)\. Second, within this framework, we show that waveform\-only temporal modeling is insufficient for reliable early PO\-AKI prediction, as the original SynerT underperforms strong structured\-data baselines \(ii\)\. Third, we show that adding structured perioperative context and leakage\-safe stacking improves performance, with SynerT\-MM and especially SynerT\-Stack yielding stronger discrimination and clinical utility after cross\-fitted Platt recalibration \(iii\)\. Finally, we provide a clinically oriented evaluation that includes calibration diagnostics, decision\-curve analysis, and a cross\-setting transport stress test on eICU\-CRD Demo\. We hypothesized that early intraoperative waveform dynamics alone would be insufficient for clinically meaningful PO\-AKI prediction, and that integrating structured perioperative context via leakage\-safe ensembling is required for superior discrimination and calibrated risk estimation \(iv\)\.

## 2Related Work

The clinical framing of this study follows established PO\-AKI literature\. KDIGO remains the standard basis for AKI definition\[[1](https://arxiv.org/html/2609.26848#bib.bib1)\], although perioperative studies must specify which criteria are operationalized\. In the present study, the endpoint is restricted to creatinine\-based postoperative AKI because urine\-output data were unavailable\. Prowle et al\.\[[5](https://arxiv.org/html/2609.26848#bib.bib5)\]emphasized that PO\-AKI after non\-cardiac surgery reflects interactions among baseline susceptibility, operative stress, and postoperative renal assessment, which motivates combining structured renal\-risk context with intraoperative physiologic trajectories\.

Among direct machine\-learning comparators, Peng et al\.\[[4](https://arxiv.org/html/2609.26848#bib.bib4)\]provide the closest AKI\-specific VitalDB\-linked reference for the waveform baseline considered here\. Their CISS 2021 study evaluated both interpretable ensemble learning on structured perioperative variables and an attention\-weighted CNN–LSTM for temporal perioperative signals, showing that intraoperative sequence modeling is clinically informative while strong tabular models remain difficult to outperform\. Park et al\.\[[8](https://arxiv.org/html/2609.26848#bib.bib8)\]likewise showed that preoperative context and intraoperative physiologic signals are complementary rather than interchangeable, while Lee et al\.\[[9](https://arxiv.org/html/2609.26848#bib.bib9)\]demonstrated that boosting\-based tabular models remain highly competitive when perioperative summary variables are available\. Building on these studies, the present work asks how much performance can be recovered when structured context and leakage\-safe ensembling are added to waveform\-first modeling\.

The rationale for multimodal integration is also consistent with broader precision\-health literature\. Kline et al\.\[[6](https://arxiv.org/html/2609.26848#bib.bib6)\]reviewed multimodal machine learning in precision health and found that data fusion often improves predictive performance, but also noted limited evidence on deployment, subpopulation robustness, and clinically meaningful evaluation\. Similar concerns have been raised for perioperative AKI prediction\[[7](https://arxiv.org/html/2609.26848#bib.bib7)\]\. Because AKI prediction models may function as clinical risk scores rather than only ranking systems, calibration and clinical utility are central evaluation components\. Prior work has emphasized the importance of calibration assessment, transparent reporting, and decision\-curve analysis for clinically meaningful prediction models\[[10](https://arxiv.org/html/2609.26848#bib.bib10),[11](https://arxiv.org/html/2609.26848#bib.bib11),[14](https://arxiv.org/html/2609.26848#bib.bib14),[15](https://arxiv.org/html/2609.26848#bib.bib15)\]\.

Taken together, prior studies support the feasibility of perioperative AKI prediction and the complementary value of multimodal perioperative information, while also showing that strong tabular baselines are difficult to surpass\. However, the literature still incompletely characterizes how much early predictive signal arises from waveform trajectories alone versus structured renal\-risk context under strict leakage\-control settings\. This gap motivates the present ablation\-focused evaluation of waveform\-only modeling, multimodal fusion, leakage\-safe stacking, calibration, and transport robustness within a unified early\-prediction framework\.

## 3Methodology

![Refer to caption](https://arxiv.org/html/2609.26848v1/figure/synert_pipeline.png)Figure 1:Overview of the SynerT\-MM pipeline with leakage\-aware stacking: temporal waveform preprocessing, temporal encoding, structured feature embedding, late fusion, and meta\-learner ensemble for final AKI risk\. The original SynerT backbone is the waveform\-only temporal branch, while SynerT\-MM and SynerT\-Stack extend that backbone with structured context and leakage\-safe ensembling, respectively\.### 3\.1Notation

In the Methods,iiindexes surgical cases andttindexes seconds within the early intraoperative window\.TiT\_\{i\}denotes the valid sequence length for caseii;𝐱i,t∈ℝC\\mathbf\{x\}\_\{i,t\}\\in\\mathbb\{R\}^\{C\}the resampled physiologic value vector;𝐦i,t∈\{0,1\}C\\mathbf\{m\}\_\{i,t\}\\in\\\{0,1\\\}^\{C\}the corresponding observation\-mask vector;𝐳i,t∈ℝ2​C\\mathbf\{z\}\_\{i,t\}\\in\\mathbb\{R\}^\{2C\}the concatenated value\-indicator input;𝐙i∈ℝTi×2​C\\mathbf\{Z\}\_\{i\}\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\}the full temporal sequence;𝐬i∈ℝds\\mathbf\{s\}\_\{i\}\\in\\mathbb\{R\}^\{d\_\{s\}\}the structured static covariate vector; andai,ta\_\{i,t\}the intraoperative mean arterial pressure \(MAP\) series\. We writeτ∈\{65,60\}\\tau\\in\\\{65,60\\\}for the MAP hypotension thresholds used for burden summaries\. The target is a binary postoperative AKI labelyi∈\{0,1\}y\_\{i\}\\in\\\{0,1\\\}, and model outputs are scalar probabilitiesp^i∈\(0,1\)\\hat\{p\}\_\{i\}\\in\(0,1\)\.

### 3\.2Data Source, Cohort, and Outcome Definition

We used the VitalDB perioperative database, which contains synchronized waveform, numeric, clinical, and laboratory records from surgical patients\[[2](https://arxiv.org/html/2609.26848#bib.bib2)\]\. The primary creatinine\-labeled cohort contained 3,242 cases, of which 2,413 passed waveform\-availability and quality screening for waveform\-based development and evaluation; 180 were AKI\-positive \(7\.46%\)\.

The target was creatinine\-based postoperative AKI aligned with the creatinine component of KDIGO\[[1](https://arxiv.org/html/2609.26848#bib.bib1)\]\. For caseii, letcibasec\_\{i\}^\{\\text\{base\}\}denote the most recent preoperative creatinine within 30 days before surgery, and letcipostc\_\{i\}^\{\\text\{post\}\}denote the maximum postoperative creatinine within 7 days\. The binary endpoint was defined as

yi=\[cipost≥1\.5cibase∨\(cipost−cibase\)≥0\.3mg/dL\]\.y\_\{i\}=\\mathbf\{1\}\\\!\\left\[c\_\{i\}^\{\\text\{post\}\}\\geq 1\.5\\,c\_\{i\}^\{\\text\{base\}\}\\;\\lor\\;\\bigl\(c\_\{i\}^\{\\text\{post\}\}\-c\_\{i\}^\{\\text\{base\}\}\\bigr\)\\geq 0\.3~\\text\{mg/dL\}\\right\]\.\(1\)

### 3\.3Input Representation

#### Dynamic Physiologic Signals

Dynamic inputs were constructed from the first 60 intraoperative minutes and resampled to a 1 Hz grid, yielding at mostTi≤3,600T\_\{i\}\\leq 3\{,\}600time steps per case\. For each caseiiand secondtt,𝐱i,t∈ℝC\\mathbf\{x\}\_\{i,t\}\\in\\mathbb\{R\}^\{C\}denotes the resampled physiologic values acrossC=7C=7monitoring channels, and𝐦i,t∈\{0,1\}C\\mathbf\{m\}\_\{i,t\}\\in\\\{0,1\\\}^\{C\}denotes the matched observation indicators\. The retained channels were invasive mean arterial pressure, plethysmographic pulse rate, peripheral oxygen saturation, invasive systolic arterial pressure, invasive diastolic arterial pressure, heart rate, and end\-tidal carbon dioxide\.

Each time step is represented by value\-indicator concatenation,

𝐳i,t=\[𝐱i,t;𝐦i,t\]∈ℝ2​C,t=1,…,Ti,\\mathbf\{z\}\_\{i,t\}=\\bigl\[\\mathbf\{x\}\_\{i,t\};\\,\\mathbf\{m\}\_\{i,t\}\\bigr\]\\in\\mathbb\{R\}^\{2C\},\\qquad t=1,\\ldots,T\_\{i\},\(2\)
and the full temporal input sequence for caseiiis

𝐙i=\(𝐳i,1,…,𝐳i,Ti\)∈ℝTi×2​C,2​C=14\.\\mathbf\{Z\}\_\{i\}=\\bigl\(\\mathbf\{z\}\_\{i,1\},\\ldots,\\mathbf\{z\}\_\{i,T\_\{i\}\}\\bigr\)\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\},\\qquad 2C=14\.\(3\)
This representation preserves missingness explicitly rather than masking it through imputation alone\. Linear interpolation was applied only within each channel’s observed support; outside that support, the value channel was zeroed and the mask channel recorded absence of measurement\. Value channels were normalized using per\-fold scalers fitted on training\-fold data only to prevent leakage, using standardzz\-score normalization for most channels and robust scaling for the skewed vasopressor infusion rate\.

#### Structured Context and Hemodynamic Burden

To represent baseline renal\-risk context, the multimodal models additionally used a static covariate vector𝐬i∈ℝds\\mathbf\{s\}\_\{i\}\\in\\mathbb\{R\}^\{d\_\{s\}\}containing preoperative demographic, laboratory, and comorbidity information\. We also derived hemodynamic burden summaries from intraoperative MAPai,ta\_\{i,t\}at the common hypotension thresholdsτ∈\{65,60\}\\tau\\in\\\{65,60\\\}mmHg\. On the 1 Hz grid, three burden statistics were computed for each thresholdτ\\tau:

Bτ,itime=∑t=1Ti𝟏\[ai,t<τ\],Bτ,ifrac=1Ti∑t=1Ti𝟏\[ai,t<τ\],B\_\{\\tau,i\}^\{\\text\{time\}\}=\\sum\_\{t=1\}^\{T\_\{i\}\}\\mathbf\{1\}\[a\_\{i,t\}<\\tau\],\\qquad B\_\{\\tau,i\}^\{\\text\{frac\}\}=\\frac\{1\}\{T\_\{i\}\}\\sum\_\{t=1\}^\{T\_\{i\}\}\\mathbf\{1\}\[a\_\{i,t\}<\\tau\],\(4\)Bτ,iauc=∑t=1Ti\(τ−ai,t\)\+,B\_\{\\tau,i\}^\{\\text\{auc\}\}=\\sum\_\{t=1\}^\{T\_\{i\}\}\(\\tau\-a\_\{i,t\}\)\_\{\+\},\(5\)whereBτ,itimeB\_\{\\tau,i\}^\{\\text\{time\}\}is the total seconds below thresholdτ\\tau,Bτ,ifracB\_\{\\tau,i\}^\{\\text\{frac\}\}is the corresponding fraction of the observation window, andBτ,iaucB\_\{\\tau,i\}^\{\\text\{auc\}\}is the area under the MAP\-deficit curve\. These features were supplemented by episode counts, longest hypotensive run duration, and short\-term MAP variability statistics\. Burden summaries are interpreted here as clinically motivated exposure descriptors rather than causal threshold claims\.

### 3\.4SynerT: Waveform\-Only Temporal Backbone

We first describe SynerT, the original waveform\-only backbone, because the remaining model families either extend this encoder or act as stand\-alone tabular baselines\. SynerT takes as its sole input the value\-indicator sequence

𝐙i∈ℝTi×2​C⏟input​Xi→SynerTp^iSynerT∈\(0,1\)⏟output​Yi\\underbrace\{\\mathbf\{Z\}\_\{i\}\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\}\}\_\{\\text\{input \}X\_\{i\}\}\\xrightarrow\{\\text\{SynerT\}\}\\underbrace\{\\hat\{p\}\_\{i\}^\{\\text\{SynerT\}\}\\in\(0,1\)\}\_\{\\text\{output \}Y\_\{i\}\}\(6\)with no access to static clinical covariates or hemodynamic burden summaries\. The backbone consists of four stages\.

#### Stage 1: Channel Projection

The input sequence is transposed from time\-major to channel\-major format,𝐙i∈ℝTi×2​C→𝐙i⊤∈ℝ2​C×Ti\\mathbf\{Z\}\_\{i\}\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\}\\to\\mathbf\{Z\}\_\{i\}^\{\\top\}\\in\\mathbb\{R\}^\{2C\\times T\_\{i\}\}, and projected into adhd\_\{h\}\-dimensional latent space via a pointwise \(1×11\\times 1\) convolution:

𝐇i\(0\)=Conv1D1×1⁡\(𝐙i⊤\)∈ℝdh×Ti\.\\mathbf\{H\}\_\{i\}^\{\(0\)\}=\\operatorname\{Conv1D\}\_\{1\\times 1\}\\\!\\bigl\(\\mathbf\{Z\}\_\{i\}^\{\\top\}\\bigr\)\\in\\mathbb\{R\}^\{d\_\{h\}\\times T\_\{i\}\}\.\(7\)This step performs cross\-channel mixing before temporal modeling in a uniformdhd\_\{h\}\-dimensional feature space\.

#### Stage 2: Causal Dilated TCN

𝐇i\(0\)\\mathbf\{H\}\_\{i\}^\{\(0\)\}is passed throughLTCNL\_\{\\text\{TCN\}\}residual TCN blocks with exponentially increasing dilation\. Each block applies two causal 1\-D convolutions \(kernel sizekk, dilationdℓ=2ℓ−1d\_\{\\ell\}=2^\{\\ell\-1\}\), each followed by ReLU and dropout, with a residual skip connection:

𝐇i\(ℓ\)=𝐇i\(ℓ−1\)\+ϕTCN\(ℓ\)\(𝐇i\(ℓ−1\)\),ℓ=1,…,LTCN,\\mathbf\{H\}\_\{i\}^\{\(\\ell\)\}=\\mathbf\{H\}\_\{i\}^\{\(\\ell\-1\)\}\+\\phi\_\{\\text\{TCN\}\}^\{\(\\ell\)\}\\\!\\bigl\(\\mathbf\{H\}\_\{i\}^\{\(\\ell\-1\)\}\\bigr\),\\qquad\\ell=1,\\ldots,L\_\{\\text\{TCN\}\},\(8\)where

ϕTCN\(ℓ\)​\(⋅\)=Drop⁡\(ReLU⁡\(CausalConvk,dℓ⁡\(Drop⁡\(ReLU⁡\(CausalConvk,dℓ⁡\(⋅\)\)\)\)\)\)\.\\phi\_\{\\text\{TCN\}\}^\{\(\\ell\)\}\(\\cdot\)=\\operatorname\{Drop\}\\\!\\Bigl\(\\operatorname\{ReLU\}\\\!\\Bigl\(\\operatorname\{CausalConv\}\_\{k,\\,d\_\{\\ell\}\}\\\!\\Bigl\(\\operatorname\{Drop\}\\\!\\bigl\(\\operatorname\{ReLU\}\\\!\\bigl\(\\operatorname\{CausalConv\}\_\{k,\\,d\_\{\\ell\}\}\(\\cdot\)\\bigr\)\\bigr\)\\Bigr\)\\Bigr\)\\Bigr\)\.\(9\)Causality is enforced by left\-padding each convolution by\(k−1\)​dℓ\(k\-1\)d\_\{\\ell\}positions and trimming the future\-facing outputs, so that𝐇i,t\(ℓ\)\\mathbf\{H\}\_\{i,t\}^\{\(\\ell\)\}depends only on𝐳i,1,…,𝐳i,t\\mathbf\{z\}\_\{i,1\},\\ldots,\\mathbf\{z\}\_\{i,t\}\. With doubling dilation across levels, the TCN captures multi\-scale temporal patterns within the 60\-minute observation window\.

#### Stage 3: Dilated RNN Hierarchy and Fusion

The TCN output𝐇i\(LTCN\)\\mathbf\{H\}\_\{i\}^\{\(L\_\{\\text\{TCN\}\}\)\}is transposed back to time\-major format and processed by a hierarchy ofLRNNL\_\{\\text\{RNN\}\}dilated recurrent layersϕRNN\(1\),…,ϕRNN\(LRNN\)\\phi\_\{\\text\{RNN\}\}^\{\(1\)\},\\ldots,\\phi\_\{\\text\{RNN\}\}^\{\(L\_\{\\text\{RNN\}\}\)\}\. Each layer operates on a temporally sub\-sampled input, expanding effective sequential context without proportionally increasing recurrent steps\. The outputs of the TCN and RNN branches are then fused through a learned gating mechanismϕfuse\\phi\_\{\\text\{fuse\}\}:

𝐇~i=ϕfuse​\(\[𝐇i\(LTCN\),ϕRNN\(1\)​\(𝐙i\),…,ϕRNN\(LRNN\)​\(𝐙i\)\]\)∈ℝTi×dh,\\tilde\{\\mathbf\{H\}\}\_\{i\}=\\phi\_\{\\text\{fuse\}\}\\\!\\Bigl\(\\bigl\[\\mathbf\{H\}\_\{i\}^\{\(L\_\{\\text\{TCN\}\}\)\},\\;\\phi\_\{\\text\{RNN\}\}^\{\(1\)\}\(\\mathbf\{Z\}\_\{i\}\),\\;\\ldots,\\;\\phi\_\{\\text\{RNN\}\}^\{\(L\_\{\\text\{RNN\}\}\)\}\(\\mathbf\{Z\}\_\{i\}\)\\bigr\]\\Bigr\)\\in\\mathbb\{R\}^\{T\_\{i\}\\times d\_\{h\}\},\(10\)This fused representation combines local multi\-scale pattern extraction from the TCN with longer\-range sequential dependencies from the recurrent hierarchy\.

#### Stage 4: Masked Temporal Pooling and Classification Head

𝐇~i\\tilde\{\\mathbf\{H\}\}\_\{i\}is reduced to a fixed\-length case embedding by masked mean pooling over the valid temporal extentTiT\_\{i\}, excluding zero\-padded positions:

𝐡itemp=1Ti​∑t=1Ti𝐇~i,t∈ℝdh\.\\mathbf\{h\}\_\{i\}^\{\\text\{temp\}\}=\\frac\{1\}\{T\_\{i\}\}\\sum\_\{t=1\}^\{T\_\{i\}\}\\tilde\{\\mathbf\{H\}\}\_\{i,t\}\\;\\in\\;\\mathbb\{R\}^\{d\_\{h\}\}\.\(11\)Dividing byTiT\_\{i\}rather than padded batch length avoids penalizing cases with shorter valid observation windows\. The pooled embedding is then passed through dropout and a linear projection to produce the AKI risk probability:

p^iSynerT=σ⁡\(𝐰⊤​𝐡itemp\+b\)∈\(0,1\),\\hat\{p\}\_\{i\}^\{\\text\{SynerT\}\}=\\sigma\\\!\\bigl\(\\mathbf\{w\}^\{\\top\}\\mathbf\{h\}\_\{i\}^\{\\text\{temp\}\}\+b\\bigr\)\\in\(0,1\),\(12\)whereσ⁡\(⋅\)\\sigma\(\\cdot\)is the sigmoid function\. In summary, SynerT maps𝐙i∈ℝTi×2​C⟶p^iSynerT∈\(0,1\)\\mathbf\{Z\}\_\{i\}\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\}\\;\\longrightarrow\\;\\hat\{p\}\_\{i\}^\{\\text\{SynerT\}\}\\in\(0,1\)using waveform data alone\.

### 3\.5Model Families and Variants

The analysis centers on three model families\. The first is the original waveform\-only SynerT backbone, which tests whether early physiologic trajectories are sufficient on their own\. The second is a late\-fusion multimodal extension \(SynerT\-MM\) that adds structured clinical covariates and hemodynamic burden summaries\. The third is a leakage\-safe stacked ensemble \(SynerT\-Stack\) that combines cross\-validated predictions from SynerT\-MM with strong tabular baselines at the meta\-learning stage\.

#### SynerT\-MM

The input to SynerT\-MM is the pair

XiMM:=\(𝐙i,𝐬i\),X\_\{i\}^\{\\text\{MM\}\}:=\\bigl\(\\mathbf\{Z\}\_\{i\},\\;\\mathbf\{s\}\_\{i\}\\bigr\),\(13\)where𝐙i∈ℝTi×2​C\\mathbf\{Z\}\_\{i\}\\in\\mathbb\{R\}^\{T\_\{i\}\\times 2C\}is the temporal waveform sequence and𝐬i∈ℝds\\mathbf\{s\}\_\{i\}\\in\\mathbb\{R\}^\{d\_\{s\}\}is the structured static feature vector\. The temporal branch encodes𝐙i\\mathbf\{Z\}\_\{i\}through the SynerT backbone, producing𝐡itemp∈ℝdh\\mathbf\{h\}\_\{i\}^\{\\text\{temp\}\}\\in\\mathbb\{R\}^\{d\_\{h\}\}as in Equations \([7](https://arxiv.org/html/2609.26848#Ch0.E7)\)–\([11](https://arxiv.org/html/2609.26848#Ch0.E11)\)\. The structured branch independently encodes𝐬i\\mathbf\{s\}\_\{i\}via a learned projectionϕstat:ℝds→ℝdh\\phi\_\{\\text\{stat\}\}:\\mathbb\{R\}^\{d\_\{s\}\}\\to\\mathbb\{R\}^\{d\_\{h\}\}\. Late fusion is performed by concatenation after separate encoding,

𝐡iMM=\[𝐡itemp;ϕstat​\(𝐬i\)\]∈ℝ2​dh,\\mathbf\{h\}\_\{i\}^\{\\text\{MM\}\}=\\bigl\[\\mathbf\{h\}\_\{i\}^\{\\text\{temp\}\};\\;\\phi\_\{\\text\{stat\}\}\(\\mathbf\{s\}\_\{i\}\)\\bigr\]\\in\\mathbb\{R\}^\{2d\_\{h\}\},\(14\)and the combined representation is passed through a classification head:

YiMM:=p^iMM=σ⁡\(ψMM​\(𝐡iMM\)\)∈\(0,1\),Y\_\{i\}^\{\\text\{MM\}\}:=\\hat\{p\}\_\{i\}^\{\\text\{MM\}\}=\\sigma\\\!\\bigl\(\\psi\_\{\\text\{MM\}\}\(\\mathbf\{h\}\_\{i\}^\{\\text\{MM\}\}\)\\bigr\)\\in\(0,1\),\(15\)whereψMM:ℝ2​dh→ℝ\\psi\_\{\\text\{MM\}\}:\\mathbb\{R\}^\{2d\_\{h\}\}\\to\\mathbb\{R\}is the fusion classification head\. Late fusion lets the temporal and structured branches be encoded separately before prediction\.

#### SynerT\-Stack

SynerT\-Stack does not operate on raw temporal sequences directly\. Its input consists of out\-of\-fold base\-model probability estimates together with leakage\-safe static features:

XiStack:=\(p^iMM,OOF,p^iRF,OOF,p^iLR,OOF,𝐬i\),X\_\{i\}^\{\\text\{Stack\}\}:=\\Bigl\(\\hat\{p\}\_\{i\}^\{\\text\{MM,OOF\}\},\\;\\hat\{p\}\_\{i\}^\{\\text\{RF,OOF\}\},\\;\\hat\{p\}\_\{i\}^\{\\text\{LR,OOF\}\},\\;\\mathbf\{s\}\_\{i\}\\Bigr\),\(16\)wherep^iMM,OOF\\hat\{p\}\_\{i\}^\{\\text\{MM,OOF\}\},p^iRF,OOF\\hat\{p\}\_\{i\}^\{\\text\{RF,OOF\}\}, andp^iLR,OOF\\hat\{p\}\_\{i\}^\{\\text\{LR,OOF\}\}are out\-of\-fold probability estimates from SynerT\-MM, random forest, and logistic regression, respectively\. A logistic meta\-learner is fit as

YiStack:=p^iStack=σ⁡\(β0\+β1​p^iMM,OOF\+β2​p^iRF,OOF\+β3​p^iLR,OOF\+𝜸⊤​𝐬i\)∈\(0,1\),Y\_\{i\}^\{\\text\{Stack\}\}:=\\hat\{p\}\_\{i\}^\{\\text\{Stack\}\}=\\sigma\\\!\\Bigl\(\\beta\_\{0\}\+\\beta\_\{1\}\\hat\{p\}\_\{i\}^\{\\text\{MM,OOF\}\}\+\\beta\_\{2\}\\hat\{p\}\_\{i\}^\{\\text\{RF,OOF\}\}\+\\beta\_\{3\}\\hat\{p\}\_\{i\}^\{\\text\{LR,OOF\}\}\+\\boldsymbol\{\\gamma\}^\{\\top\}\\mathbf\{s\}\_\{i\}\\Bigr\)\\in\(0,1\),\(17\)whereβ0∈ℝ\\beta\_\{0\}\\in\\mathbb\{R\}is the meta\-learner intercept,β1,β2,β3∈ℝ\\beta\_\{1\},\\beta\_\{2\},\\beta\_\{3\}\\in\\mathbb\{R\}are the base\-model coefficients, and𝜸∈ℝds\\boldsymbol\{\\gamma\}\\in\\mathbb\{R\}^\{d\_\{s\}\}is the coefficient vector for the static safe features retained at the meta\-learning stage\. Because the meta\-learner is trained only on out\-of\-fold predictions, SynerT\-Stack avoids meta\-level information leakage by construction\.

The main text retains only the strongest or literature\-grounded comparators: the Peng\-style CNN\-LSTM baseline and high\-capacity tree ensembles \(random forest, extra trees, and CatBoost\-style boosting\), aligned with recent perioperative AKI baselines\[[4](https://arxiv.org/html/2609.26848#bib.bib4),[8](https://arxiv.org/html/2609.26848#bib.bib8),[9](https://arxiv.org/html/2609.26848#bib.bib9)\]\.[Table1](https://arxiv.org/html/2609.26848#Ch0.T1)summarizes the information sources available to the main model families\.

Table 1:Information sources used by the main model families\. Bold entries highlight the components that distinguish the multimodal and stacked variants from the original waveform\-only model\.Model familyTemporal physiologyObservation indicatorsStructured covariatesBurden summariesCross\-validated model scoresOriginal SynerTYesYesNoNoNoRF baselineNoNoYesYesNoSynerT\-MMYesYesYesYesNoSynerT\-StackNoNoYesYesYes

### 3\.6Evaluation Design and Leakage Control

All experiments used fold\-specific preprocessing with scalers fitted on training folds only, and stacked predictions were constructed exclusively from out\-of\-fold base\-model outputs to prevent meta\-level leakage\. Performance was evaluated by five\-fold cross\-validation using AUROC and AUPRC as the primary discrimination metrics, with particular emphasis on AUPRC given the 7\.46% event prevalence\. Additional evaluation included operating\-point metrics at 95% specificity, pooled out\-of\-fold calibration diagnostics \(Brier score, ECE, reliability plots, calibration intercept and slope\), and decision\-curve analysis over threshold probabilities from 0\.02 to 0\.25\[[10](https://arxiv.org/html/2609.26848#bib.bib10),[11](https://arxiv.org/html/2609.26848#bib.bib11),[14](https://arxiv.org/html/2609.26848#bib.bib14),[15](https://arxiv.org/html/2609.26848#bib.bib15)\]\. For SynerT\-MM and SynerT\-Stack, absolute\-risk calibration was further improved via leakage\-safe cross\-fitted Platt recalibration\. The eICU\-CRD Demo cohort served as a transport stress test, scored without refitting\[[12](https://arxiv.org/html/2609.26848#bib.bib12),[13](https://arxiv.org/html/2609.26848#bib.bib13)\]\.

## 4Experiments and Results

### 4\.1Main Model Comparison

[Table2](https://arxiv.org/html/2609.26848#Ch0.T2)shows a clear progression across model families\. The original SynerT remained well below the strongest structured\-data baselines, confirming that waveform\-only temporal modeling is insufficient under strict early\-prediction constraints\. Adding structured clinical context and hemodynamic burden summaries improved discrimination in SynerT\-MM, though the gain over random forest was directional rather than statistically significant at the five\-fold level\. SynerT\-Stack achieved the highest AUROC, AUPRC, and F1\-max across all models, making leakage\-safe stacking the clearest supported improvement in the main comparison\. Secondary tabular baselines and additional waveform backbones did not surpass SynerT\-MM or SynerT\-Stack, reinforcing that the core gain came from multimodal context and stacking rather than broader backbone search\.

Table 2:Main five\-fold performance results centered on the strongest and literature\-grounded comparators\. Values are mean±\\pmstandard deviation across validation folds\. Boldface marks the best value in each column\.
### 4\.2Cross\-Setting Transport Stress Test on eICU\-CRD Demo

A preliminary cross\-setting transport stress test on eICU\-CRD Demo suggested substantial degradation for most standalone models under setting shift\. However, SynerT\-Stack retained the strongest discrimination \(AUROC 0\.831±\\pm0\.026; AUPRC 0\.555±\\pm0\.177\)\. Because the cohort was small and not a matched intraoperative surgical population, these findings should be interpreted only as a proxy transport result rather than definitive external validation\.

![Refer to caption](https://arxiv.org/html/2609.26848v1/figure/revision_transport_shift.png)Figure 2:Cross\-setting transport stress test comparing internal VitalDB and eICU Demo performance\.
### 4\.3Statistical Testing of the Main Contribution

[Table3](https://arxiv.org/html/2609.26848#Ch0.T3)reports the pre\-specified paired AUPRC comparisons, using fold\-paired Wilcoxon signed\-rank tests together with paired bootstrap deltas from aligned out\-of\-fold predictions\. Because random forest was the strongest AUROC baseline and one of the base learners in SynerT\-Stack, the comparison path was anchored on the random\-forest baseline\. The results support three conclusions: random forest significantly outperformed the original waveform\-only SynerT; SynerT\-MM improved over random forest in point estimate but not at a statistically significant level in the current five\-fold evaluation; and SynerT\-Stack significantly improved over both SynerT\-MM and random forest, making stacking the most statistically secure gain in the main analysis\.

Table 3:Paired statistical testing for the main contribution\-focused AUPRC comparisons\. Fold\-level significance uses a Wilcoxon signed\-rank test with one\-sided alternative*model A*\>\>*model B*\.
### 4\.4Calibration Assessment

[Table4](https://arxiv.org/html/2609.26848#Ch0.T4)summarizes pooled out\-of\-fold calibration diagnostics for the main contribution path\. Among the raw models, random forest showed the best calibration, whereas both SynerT\-MM and SynerT\-Stack were substantially miscalibrated\. Cross\-fitted Platt recalibration largely corrected this defect, reducing ECE from 0\.350 to 0\.005 for SynerT\-MM and from 0\.316 to 0\.027 for SynerT\-Stack while leaving discrimination largely unchanged\. Thus, SynerT\-Stack remained the best discriminator, but clinically interpretable absolute\-risk use should rely on post\-hoc recalibration\.

Table 4:Calibration diagnostics on pooled out\-of\-fold predictions for the main contribution path\. Lower Brier and ECE are better; calibration intercept00and slope11are ideal\. Boldface marks the best value in each column\.
### 4\.5Decision\-Curve Analysis

[Figure3](https://arxiv.org/html/2609.26848#Ch0.F3)shows decision\-curve analysis for the deployment\-ready probabilities: raw random\-forest scores and cross\-fitted Platt\-recalibrated SynerT\-MM and SynerT\-Stack probabilities\. Both recalibrated multimodal models maintained positive net benefit across the examined threshold range of 0\.02 to 0\.25, whereas the random\-forest baseline fell below the treat\-none strategy at approximately the 0\.10 threshold\. Across most low\-to\-intermediate thresholds, the recalibrated SynerT\-Stack model provided the highest net benefit, supporting it as the most defensible candidate for risk\-guided use after leakage\-safe recalibration\.

t\]![Refer to caption](https://arxiv.org/html/2609.26848v1/figure/revision_internal_dca.png)

Figure 3:Decision\-curve analysis comparing random forest, recalibrated SynerT\-MM, recalibrated SynerT\-Stack, and treat\-all or treat\-none strategies across threshold probabilities from 0\.02 to 0\.25\.
### 4\.6ROC, Precision\-Recall, and Operating\-Point Evaluation

[Figure4](https://arxiv.org/html/2609.26848#Ch0.F4)provides threshold\-dependent ROC discrimination views for the principal model families\.[Table5](https://arxiv.org/html/2609.26848#Ch0.T5)summarizes clinically oriented operating\-point performance at 95% specificity\. At this operating point, SynerT\-Stack achieved the highest sensitivity and positive predictive value, with SynerT\-MM ranking next among the neural variants\.

Out\-of\-fold ROC curve panel for the principal model families\.![Refer to caption](https://arxiv.org/html/2609.26848v1/figure/main_results_roc_overlay.png)

Figure 4:Out\-of\-fold ROC curves for the principal model families\. SynerT\-Stack provides the strongest threshold\-agnostic discrimination, with SynerT\-MM consistently above the waveform\-only SynerT model\.Table 5:Clinically oriented operating\-point metrics for the leading models and strongest tabular baselines\. Values are mean±\\pmstandard deviation across five folds\. Boldface marks the best value in each column\.

## 5Discussion

This study demonstrates that strict leakage\-aware evaluation is essential for credible early PO\-AKI prediction, because without such constraints the apparent performance of waveform\-only models can be overstated\. Under controlled early prediction settings, waveform\-only temporal modeling was insufficient for reliable risk stratification, whereas integrating physiologic trajectories with structured renal\-risk context and hemodynamic burden summaries through leakage\-safe stacking produced the strongest overall results, supporting a multimodal information\-fusion view of the task rather than a purely architectural one\. The eICU\-CRD Demo analysis should be interpreted as a transport stress test rather than definitive external validation given its small, ICU\-based, and mismatched cohort\[[3](https://arxiv.org/html/2609.26848#bib.bib3),[12](https://arxiv.org/html/2609.26848#bib.bib12),[13](https://arxiv.org/html/2609.26848#bib.bib13)\], yet it still suggests that the stacked ensemble is less brittle under setting shift than standalone models\. At the same time, improved discrimination alone was not sufficient for deployment\-ready risk estimation, because the multimodal models required leakage\-safe Platt recalibration to correct important calibration defects, after which decision\-curve analysis showed superior net benefit for the stacked model across low\-to\-intermediate thresholds\. Clinically, prediction within the first 60 intraoperative minutes may support earlier hemodynamic optimization and ICU triage, but the present study remains limited by creatinine\-only AKI labeling without urine\-output ascertainment\[[1](https://arxiv.org/html/2609.26848#bib.bib1)\]and by the small unmatched external cohort, so validation on larger perioperative datasets remains necessary\. Overall, these findings suggest that credible early PO\-AKI prediction depends more on multimodal context, calibration, and robustness assessment than on temporal\-model complexity alone\.

## 6Conclusion

In this leakage\-aware intraoperative prediction study, waveform\-only temporal modeling was insufficient for postoperative AKI discrimination\. Performance improved when dynamic vital\-sign trajectories were combined with structured renal\-risk context and clinically motivated hemodynamic burden summaries, and improved further through leakage\-safe stacking of complementary learners\. The strongest supported result is therefore the advantage of the stacked model, not a generic claim of waveform\-only deep\-learning superiority\. Calibration and decision\-curve analysis refined that conclusion: the stacked model delivered the best ranking performance, cross\-fitted Platt recalibration improved the absolute\-risk behavior of both multimodal models, and the recalibrated stacked model provided the most favorable clinical\-utility profile across low\-to\-intermediate thresholds\. The eICU\-CRD Demo analysis adds a stress test, showing that this advantage is less brittle under cross\-setting shift while motivating matched surgical cohorts for external validation\. More broadly, the leakage\-aware multimodal evaluation framework presented here offers a transferable template for early intraoperative risk stratification studies that disentangle the contributions of dynamic waveform data, structured clinical context, and calibration\-aware ensemble design under strict clinical deployment constraints\.

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