In this work the real-time estimation of plasma insulin concentration (PIC) to quantify the insulin in the bloodstream in patients with type 1 diabetes mellitus (T1DM) is presented. To this end, Hovorkas model, a glucose-insulin dynamics model, is incorporated with various estimation techniques, including continuous-discrete extended Kalman filtering, unscented Kalman filtering, and moving horizon estimation, to provide an estimate of PIC. Furthermore, due to the considerable variability in the temporal dynamics of patients, some uncertain model parameters that have significant effects on PIC estimates are considered as additional states in Hovorkas model to be simultaneously estimated. Latent variable regression models are developed to individualize the PIC estimators by appropriately initializing the time-varying model parameters for improved convergence. The performance of the proposed methods is evaluated using clinical data sets from subjects with T1DM, and the results demonstrate the accurate estimation of PIC.