Validation of a Probabilistic Prediction Model for Patients with Type 1 Diabetes Using Compositional Data Analysis

Abstract

Glycemia assessment in people with type 1 diabetes (T1D) has focused on the time spent in different glucose ranges. As this time reflects the relative contributions to the finite duration of a day, it should be treated as compositional data (CoDa) that can be applied to T1D data. Previous works presented a tool for the individual categorization of days and proposed a probabilistic transition model between categories, although validation has hitherto not been presented. In this study, we consider data from eight real adult patients with T1D obtained from continuous glucose monitoring (CGM) sensors and introduce a methodology based on compositional methods to validate the previously presented probability transition model. We conducted 5-fold cross-validation, with both the training and validation data being CoDa vectors, which requires developing new performance metrics. We design new accuracy and precision measures based on statistical error calculations. The results show that the precision for the entire model is higher than 95% in all patients. The use of a probabilistic transition model can help doctors and patients in diabetes treatment management and decision-making. Although the proposed method was tested with CoDa applied to T1D data obtained from CGM, the newly developed accuracy and precision measures apply to any other data or validation based on CoDa.

Individualized Prediction of Blood Glucose Outcomes Using Compositional Data Analysis

“…DSSs have proven to be useful tools for patients and physicians [2,46,47]. Although glucose profiles have been treated as CoDa vectors in previous studies [15][16][17], there is no application in this branch of mathematics that is focused on predicting the mean and the CV as an information system or DSS tool for patients with T1D at specific hours of the day oriented to wide PH (2 h and 4 h). In this work, CoDa variables and transformed scalars have been used to predict the mean and CV of glucose in patients with T1D.…”

“…The compositional input could contain zeros if some of the parts of the CoDa vector were zero; therefore, a pre-treatment was done because CoDa is based on log-ratios of parts. The detection matrix (dL) used in the imputation of the zeros was interpreted as in [17], taking into account the consecutive zeros. In this case, where we are only analyzing three parts, there could only be two consecutive zeros; the dL value will then be calculated by dividing 5 min (sensor measurement interval) by 120 min, which is the time analyzed from the previous 2 h, dL = 0.04166.…”

“…Compositional data (CoDa) are data that transmit information about the parts of a whole expressed in proportions or percentages, as is the case of the vector of daily times in each of the glucose ranges: time below range (TBR) (<70 mg/dL), TIR (70-180 mg/dL), and time above range (TAR) (>180 mg/dL) [14], where all the components are positive and of constant sum. Previous studies have treated the percentage of time in the glucose range as a composition, yielding favorable outcomes, and this variable is of paramount importance in this field [15][16][17]. Furthermore, regression models have demonstrated favorable results overall, both in scalar variables and CoDa, due to their simplicity of implementation and robustness in prediction outcomes.…”