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Clinical researchers use prognostic modeling techniques to identify a-prior patient health status and characterize progression patterns. It is highly desirable to predict future health condition especially to implement preventive and intervention strategies in pre-diabetic individuals. Hidden Markov Model (HMM) and its variants are a class of models that provide predictions concerning future condition by exploiting sequences of clinical measurements obtained from a longitudinal sample of patients. Despite the advantages of using these models for prognostic modeling, it still face barriers and significant challenges, to effectively learn dynamic interactions, when using irregularly sampled longitudinal Electronic Medical Records (EMRs) data. Newton's divide difference method (NDDM) is a classical approach for handling irregular data in terms of divided difference. However, as it is polynomial approximation technique, it suffers with Runge Phenomenon. The problem can be even more severe when the interval is a bit extended. Therefore, to tackle this problem, we proposed a novel approximation method based on NDDM as a component with HMM in order to estimate the 8 years risk of developing Type 2 Diabetes Mellitus (T2DM) in a particular individual. The proposed method is evaluated on real world clinical data obtained from CPCSSN. The results demonstrated that our proposed technique has the ability to exploit the available irregularly sampled EMRs data for effective approximation and improved prediction accuracy.