Proposing a RAG-Based System for Context-Aware Healthcare Monitoring

Proposing a RAG-Based System for Context-Aware Healthcare Monitoring

System-Level Validation and Mathematical Justification of Retrieval Superiority in Clinical AI

Om Patil

Electronics and Telecommunication department COEP Technological University

Pune, India

Raj Dhapse

COEP Technological University Pune, India

Bhavan Kore

COEP Technological University Pune, India

AbstractModern healthcare continuous patient monitoring

systems frequently rely on static threshold-based alerting mechanisms, which lack personalization and contribute to high false alarm rates. Conventional predictive models primarily utilize structured electronic health record (EHR) data but often fail to adapt in real-time to diverse and evolving patient contexts.

In this work, we propose an intelligent healthcare monitoring architecture that mathematically grounds the integration of Retrieval-Augmented Generation (RAG) with agentic Large Language Models (LLMs). Our system not only enables context- aware knowledge retrieval and reasoning, but also empowers LLMs to autonomously invoke external tools and services, including alert triggers and diagnostic recommendations.

We introduce a rigorous mathematical formulation to model retrieval entropy, decision utility, and policy regret minimization, thereby providing formal justification for our design. This framework supports real-time vitals monitoring, adaptive risk stratification, and context-sensitive decision-making.

By tightly integrating retrieval, reasoning, and tool-calling into a unified system, we aim to transform healthcare monitoring from passive threshold-based alerts to proactive, action-oriented decision support systems. We present the architecture, discuss optimization strategies for knowledge chunking and contextual retrieval, and outline a pathway toward fully autonomous and mathematically interpretable clinical assistants.

KeywordsRAG, Healthcare Monitoring, AI Agents, Tool- Calling, Reasoning, LLMs, NLP in Healthcare, Chain of Thought, Mathematical Formulation, Entropy Reduction, Context-Aware Decision Support, Clinical Automation.

1. INTRODUCTION

   Modern clinical monitoring remains bounded within deterministic rule-based alert systems (e.g., NEWS2, MEWS), inherently limited by static thresholds and rigid decision trees. Language models, while powerful generative engines, are epistemologically bounded: their knowledge is frozen at training time and may hallucinate when extrapolating.

   RAG architectures partially address this by retrieving dynamic contextual information [1]. However, they remain largely reactive rather than action-oriented.

   Recent advancements in tool-enabled AI agents offer the possibility of autonomous clinical actions a transition from suggestive to operational AI in healthcare [3], [4].

   In this work, we propose and mathematically construct an autonomous, retrieval-grounded, agentic healthcare system that:

   • Continuously monitors patient vitals through IoT-enabled sensing hardware [6].

   • Dynamically augments model context using real-time semantic retrieval from medical databases and structured EHRs [1], [2].

   • Performs tool-enabled reasoning to invoke critical clinical actions such as diagnosis support, risk stratification, and emergency alerting.

   • Optimizes a multi-objective clinical utility function, balancing timeliness, specificity, risk minimization, and decision interpretability.

2. MATHEMATICAL FOUNDATIONS

   1. Problem Formulation

      Let XtRn represent the state vector of patient vitals at time t. Let D denote the corpus of external knowledge (medical guidelines, EHRs, drug interaction databases).

      Define the retrieval operator:

      R(x) = {di D similarity(x, di) }

      where is a dynamic similarity threshold determined via a learned scoring function.

      The conditional probability of generating a response y and invoking an action a given input x is:

      p(y, ax) = dR(x)p(y, ax, d)p(dx) [1], [2]

   2. Classical LLM Limitation Without retrieval:

      p(yx)=p(y)

      where are frozen parameters. Thus:

      • No adaptation to real-time vitals.

      • No contextualization to patient-specific or latest medical protocols.

      • No external decision invocation.

   3. Proposed RAG-Agent Augmentation Our system instead optimizes:

      maxR,aEx[U(y,a,x)]

      where U is a clinical utility function incorporating:

      • Diagnostic accuracy.

      • Time-to-intervention.

      • Risk mitigation.

   4. Proposed Retrieval-Augmented Clinical Risk Score Define RACRS as:

   RACRS=×Sensitivity+×Specificity+×Actionability where ,, are clinician-set importance weights [2]

3. COMPARATIVE ANALYSIS: LLM VS RAG VS RAG+IOT

   TABLE 1: Comparative analysis

   We aim to show:

   EQ[Acc(P(YQ,RQ))] > EQ[Acc(P(YQ))]

   1. Sketch of the Argument

      1. Retrieval-Constrained MDP

         Let Vt be patient vitals at time t, and Rt be the retrieved context. We define an action policy:

         (Rt,Vt)=argmaxaE[U(aRt,Vt)] [2]

         This transforms healthcare decision-making into a retrieval-constrained Markov Decision Process (MDP), allowing adaptive, context-grounded interventions.

      2. EntropyRegret Trade-off

         Let Q be a clinical query, Y the output space, and RQ

         retrieved context. We observe:

         H(YQ) > H(YQ,RQ)

         Metric	Architecture Used
         	Pure LLM	RAG-Only	RAG+IoT
         Sensitivity (early deterioration detection)	Low ( 60%)	Moderate (6575%)	High (80 90%)
         Specificity (false alert reduction)	Low ( 50%)	Moderate (6070%)	High (80 85%)
         Latency (time to action)	High	Moderate	Low
         Explainability	Poor	Good	Excellent
         Personalization	None	Partial	Full (patient- specific)
         Knowledge Freshness	Frozen	Retrieval- based	Dynamic IoT + Retrieval

         R(T)=

         T(UU(a ))

         t-1 t

         Where, U is optimal utility, at is action at time t, U(at) is the utility of chosen action .

      3. Adaptive & Cross-Modal Retrieval

         Using a severity-aware granularity function G(Vt), retrieval spans vitals, clinical text, and sensor inputs:

         Rt = Retrieve(Vt, textt, sensort) [5], [6]

         C. Conclusion: Lemma 1 (Retrieval Improves Recall)

         Given two systems S1 (pure LLM) and S2 (RAG-enhanced) over a corpus D, if:

4. MATHEMATICAL PROOF SKETCH: RETRIEVAL

   DOMINANCE

   In healthcare applications, traditioal LLMs generate outputs solely from their static training priors, limiting adaptability to

   then:

   x, d D: p(dx)>0

   Recall(S2) Recall(S1)

   evolving clinical data and patient-specific contexts. Retrieval- Augmented Generation (RAG) addresses this by conditioning generation on dynamically retrieved external knowledge. We sketch a proof to show that retrieval inclusion leads to performance dominance in such settings.

   A. Formal Setup

   Let:

   • Q: input query (e.g., symptom description),

   • Y: target output (e.g., diagnosis),

   • RQ: retrieved documents relevant to Q,

     Proof: Retrieval enlarges the effective context window, reducing the chance of missing relevant information.

     Corollary 1: Actionability is a monotonic function of retrieval depth.

5. RESULTS AND SIMULATIONS

   1. Simulation Setup

      To evaluate the clinical effectiveness of the proposed RAG + AI Agent architecture, we designed a synthetic simulation using simulated ICU patient data [1], [4], [6]

      • Dataset: Synthetic time-series vital signs generated for 500 virtual patients, each simulated over a 48-hour hospital stay window.

      • Signals Generated: Heart Rate (HR), Blood Pressure (BP), Respiratory Rate (RR), SpO, Body Temperature [6].

      • Event of Interest: Onset of sepsis-like deterioration, simulated using multi-parametric deviation patterns from healthy ranges.

      • Simulated Triggers:

        • Increase in heart rate (> 110 bpm)

        • Drop in systolic BP (< 90 mmHg)

        • RR > 24

        • Temperature spike or drop (> 38.3°C or < 36°C)

   2. RAG System testing configurations

      • LLM-Only: Static model without dynamic retrieval.

      • RAG: With document/contextual retrieval but no real-time sensor integration.

      • RAG + IoT + Tools: Complete system with IoT data, context retrieval, reasoning, and tool invocation [4], [5].

   3. Metrics Measured

   • Time to Detection (TTD): How early the system identifies clinical deterioration.

   • False Alarm Rate (FAR): Percentage of alerts triggered for stable patients.

   • RACRS: Retrieval-Augmented Clinical Risk Score (weighted blend of sensitivity, specificity, and actionability)

     TABLE 2: Output Metrics

6. DISCUSSION

   This work extends the traditional scope of Retrieval- Augmented Generation into a more dynamic and clinically applicable Agentic Intelligence Framework for healthcare [1], [3].

   Key outcomes of the proposed system include:

   • Dynamic Patient-State Adaptation: The system reasons over real-time inputs and not just static queries, enabling more personalized diagnostics.

   • Autonomous Decision Chains: Tool invocation (like alert triggering, test recommendation) adds operational intelligence, not just textual response.

   • Clinician Trust and Explainability: Every action is traceable to the patients real-time vitals and retrieved clinical history, reducing cognitive load and false alarms.

   • Mathematical Perspective: The system builds a 3-space basis:

     • Retrieval vector space

     • Reasoning path space (diagnostic logic)

     • Tool projection space (action selection over utility surfaces)

       This architecture transforms passive monitoring systems into context-aware, proactive clinical agents

7. CONCLUSION AND FUTURE WORK

We proposed a novel, clinically oriented AI framework that merges RAG, tool-calling AI agents, and IoT-based patient monitoring, creating an end-to-end autonomous decision system for modern healthcare. Our architecture shows improvements in diagnostic responsiveness, reduced false alarms, and actionable explainability through tool-chains.

Future Work Includes:

• Real-world ICU Deployments: Integrating with hospital EHRs via FHIR for pilot validation.

• Multimodal Retrieval: Including images, speech, waveform.

• Agent Policy Learning: Reinforcement-based tuning of agent actions.

• Mathematical Convergence Proofs: Validate regret minimization and utility optimization bounds.

ACKNOWLEDGMENT

We sincerely thank our mentor, Associate Professor Dr. Nilima Kolhare, Department of Electronics and Telecommunication Engineering, COEP Technological University, for their invaluable guidance, insights, and mentorship throughout the course of this project and paper.

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