Management insulin dosing for diabetes using a partially observable Markov decision process with missing data imputation

Missing data in continuous glucose monitoring (CGM) poses a significant challenge for applying sequential decision-making models to diabetes management. This study evaluates how missing-data imputation affects downstream Partially Observable Markov Decision Process (POMDP)-based policy outputs using real CGM trajectories from the Stanford Continuous Glucose Monitoring Database. Three imputation methods are compared: mean imputation, linear interpolation, and a bridge-based adjusted Metropolis-Hastings (M-H) algorithm. The adjusted M-H algorithm incorporates a local temporal bridge, Markovian state-transition information, and a smoothness constraint to generate model-compatible imputations. Numerical experiments are conducted under two missingness scenarios, random missingness and block missingness, with missing rates of 5%, 15%, and 25%. The methods are evaluated using mean squared imputation error (MSIE), policy disagreement rate, and absolute reward gap relative to the complete-data POMDP benchmark. The results show that mean imputation produces substantially larger reconstruction errors and greater downstream POMDP deviations across missingness scenarios. Linear interpolation and adjusted M-H both preserve CGM trajectories and POMDP-derived policy outputs much better than mean imputation. Linear interpolation achieves slightly lower global MSIE under random missingness, whereas adjusted M-H shows comparable POMDP-level performance and local advantages in nonlinear postprandial trajectories and block-missing segments. These findings suggest that temporally informed imputation methods are preferable to mean imputation for incomplete CGM data, and that adjusted M-H provides a model-compatible alternative for preserving sequential decision outputs under partially observed glucose trajectories.