*Article* **Blood Glucose Level Time Series Forecasting: Nested Deep Ensemble Learning Lag Fusion**

**Heydar Khadem 1,\*, Hoda Nemat 1, Jackie Elliott 2,3 and Mohammed Benaissa <sup>1</sup>**


**\*** Correspondence: h.khadem@sheffield.ac.uk

**Abstract:** Blood glucose level prediction is a critical aspect of diabetes management. It enables individuals to make informed decisions about their insulin dosing, diet, and physical activity. This, in turn, improves their quality of life and reduces the risk of chronic and acute complications. One conundrum in developing time-series forecasting models for blood glucose level prediction is to determine an appropriate length for look-back windows. On the one hand, studying short histories foists the risk of information incompletion. On the other hand, analysing long histories might induce information redundancy due to the data shift phenomenon. Additionally, optimal lag lengths are inconsistent across individuals because of the domain shift occurrence. Therefore, in bespoke analysis, either optimal lag values should be found for each individual separately or a globally suboptimal lag value should be used for all. The former approach degenerates the analysis's congruency and imposes extra perplexity. With the latter, the fine-tunned lag is not necessarily the optimum option for all individuals. To cope with this challenge, this work suggests an interconnected lag fusion framework based on nested meta-learning analysis that improves the accuracy and precision of predictions for personalised blood glucose level forecasting. The proposed framework is leveraged to generate blood glucose prediction models for patients with type 1 diabetes by scrutinising two well-established publicly available Ohio type 1 diabetes datasets. The models developed undergo vigorous evaluation and statistical analysis from mathematical and clinical perspectives. The results achieved underpin the efficacy of the proposed method in blood glucose level time-series prediction analysis.

**Keywords:** deep learning; time-series forecasting; blood glucose; diabetes; ensemble learning; artificial neural network
