PREBA: Surgical Duration Prediction via PCA-Weighted Retrieval-Augmented LLMs and Bayesian Averaging Aggregation

Accurate prediction of surgical duration is pivotal for hospital resource management. Although recent supervised learning approaches-from machine learning (ML) to fine-tuned large language models (LLMs)-have shown strong performance, they remain constrained by the need for high-quality labeled data and computationally intensive training. In contrast, zero-shot LLM inference offers a promising training-free alternative but it lacks grounding in institution-specific clinical context (e.g., local demographics and case-mix distributions), making its predictions clinically misaligned and prone to instability. To address these limitations, we present PREBA, a retrieval-augmented framework that integrates PCA-weighted retrieval and Bayesian averaging aggregation to ground LLM predictions in institution-specific clinical evidence and statistical priors. The core of PREBA is to construct an evidence-based prompt for the LLM, comprising (1) the most clinically similar historical surgical cases and (2) clinical statistical priors. To achieve this, PREBA first encodes heterogeneous clinical features into a unified representation space enabling systematic retrieval. It then performs PCA-weighted retrieval to identify clinically relevant historical cases, which form the evidence context supplied to the LLM. Finally, PREBA applies Bayesian averaging to fuse multi-round LLM predictions with population-level statistical priors, yielding calibrated and clinically plausible duration estimates. We evaluate PREBA on two real-world clinical datasets using three state-of-the-art LLMs, including Qwen3, DeepSeek-R1, and HuatuoGPT-o1. PREBA significantly improves performance-for instance, reducing MAE by up to 40% and raising R^2 from -0.13 to 0.62 over zero-shot inference-and it achieves accuracy competitive with supervised ML methods, demonstrating strong effectiveness and generalization.