Uncertainty quantification in neural-network based pain intensity estimation

Improper pain management leads to severe physical or mental consequences, including suffering, a negative impact on quality of life, and an increased risk of opioid dependency. Assessing the presence and severity of pain is imperative to prevent such outcomes and determine the appropriate intervention. However, the evaluation of pain intensity is a challenging task because different individuals experience pain differently. To overcome this, many researchers in the field have employed machine learning models to evaluate pain intensity objectively using physiological signals. However, these efforts have primarily focused on pain point estimation, disregarding inherent uncertainty and variability in the data and model. A point estimate, which provides only partial information, is not sufficient for sound clinical decision-making. This study proposes a neural network-based method for objective pain interval estimation, and quantification of uncertainty. Our approach, which enables objective pain intensity estimation with desired confidence probabilities, affords clinicians a better understanding of a person's pain intensity. We explored three distinct algorithms: the bootstrap method, lower and upper bound estimation (LossL) optimized by genetic algorithm, and modified lower and upper bound estimation (LossS) optimized by gradient descent algorithm. Our empirical results demonstrate that LossS outperforms the other two by providing narrower prediction intervals. For 50%, 75%, 85%, and 95% prediction interval coverage probability, LossS provides average interval widths that are 22.4%, 7.9%, 16.7%, and 9.1% narrower than those of LossL, and 19.3%, 21.1%, 23.6%, and 26.9% narrower than those of bootstrap. As LossS outperforms, we assessed its performance in three different model-building approaches: (1) a generalized approach using a single model for the entire population, (2) a personalized approach with separate models for each individual, and (3) a hybrid approach with models for clusters of individuals. Results demonstrate that the hybrid model-building approach provides the best performance.