Recognising, quantifying and accounting for classification uncertainty in type 2 diabetes subtypes

Abstract

Aims/hypothesis: Despite continued interest in precision diagnostics and type 2 diabetes subtypes, the challenge of uncertainty in the classification of individuals into subtypes remains. This study introduces a novel method for quantifying and accounting for classification uncertainty in type 2 diabetes subtypes.

Methods: Building on recommendations from the ADA/EASD Precision Medicine in Diabetes Initiative, we quantified classification uncertainty using the normalised relative entropy (NRE), computed from distances to cluster centroids. A lower NRE value indicates greater uncertainty in an individual's cluster assignment. We examined the NRE in a cohort of 859 individuals with recent-onset type 2 diabetes from the prospective, observational German Diabetes Study (GDS) and compared it across previously identified diabetes subtypes, defined by age, BMI, HbA_1c, HOMA-IR and HOMA-B. Predicted 10 year CVD risk (SCORE2-Diabetes) of the subtypes was evaluated with and without accounting for classification uncertainty.

Results: Individuals with mild age-related diabetes (n=395) and mild obesity-related diabetes (n=316) had a median NRE of 0.155 (95% CI 0.142, 0.177) and 0.119 (95% CI 0.107, 0.131), respectively. By contrast, individuals with severe insulin-resistant diabetes (n=130) and severe insulin-deficient diabetes (n=18) had a lower median NRE of 0.086 (95% CI 0.075, 0.108) and 0.082 (95% CI 0.071, 0.109), respectively. After weighting individuals by classification certainty, the proportion of variation in SCORE2-Diabetes explained by the subtypes (R²) increased from 17.4% (95% CI 12.8, 23.0) to 31.5% (95% CI 26.4, 37.1). The predicted 10 year CVD risk of the mild age-related diabetes subtype increased from 10.3% (95% CI 9.8, 10.7) to 11.6% (95% CI 11.2, 12.0).

Conclusions/interpretation: The NRE provides a means to quantify and compare individual classification uncertainty in type 2 diabetes subtypes. Classification uncertainty varied between subtypes and individuals with type 2 diabetes, and accounting for it improved the ability of the subtypes to predict 10 year CVD risk.

Keywords: Classification uncertainty; Clusters; German Diabetes Study; Precision medicine; Relative entropy; Subtypes; Type 2 diabetes mellitus.

Fig. 1

Spider charts of three individuals from the GDS classified as having MARD. The charts display their clinical profiles (dark purple/black) in comparison with the typical MARD profile from the nearest centroid algorithm (light purple). The individual in (a) closely aligns with the typical MARD profile, whereas the individual in (b) shows some deviations from it. The individual in (c) was assigned to the MARD subtype despite a younger age (40 years)

Fig. 2

Classification probabilities and NRE for three example individuals from Fig. 1 who were assigned to the MARD subtype by the nearest centroid algorithm. The NRE quantifies the classification uncertainty on a scale from 0 to 1, with higher values indicating greater certainty. The black dashed line indicates the classification probabilities in a reference setting with complete uncertainty regarding an individual’s cluster assignment. The individual in (a) has high classification probability of 97% for the MARD subtype, whereas the individual in (b) has a somewhat lower classification probability of 51%. The individual in (c) has a low classification probability of 34% for the MARD subtype

Fig. 3

Boxplots of the NRE and the classification probability for the assigned cluster of individuals with recent-onset type 2 diabetes in the GDS cohort. The midline of the boxplot shows the median and the box shows the lower and upper quartiles. The whiskers extend to the minimum and maximum values within 1.5 times the IQR from the lower and upper quartiles. Grey lines connect each individual’s NRE value to their classification probability, illustrating the relationship between the two measures. Note that the NRE takes into account not only the classification probability for the assigned cluster but also the classification probabilities for the remaining three clusters. While both measures share the same maximum possible value of 1 (red dashed line), the minimum value for the NRE is 0, and for the classification probability, it is 0.25

Fig. 4

Boxplots of the NRE for individuals with recent-onset type 2 diabetes in the GDS cohort, stratified by the type 2 diabetes subtypes: SIDD (n=18), SIRD (n=130), MOD (n=316) and MARD (n=395). The midline of the boxplot shows the median and the box shows the lower and upper quartiles. The whiskers extend to the minimum and maximum values within 1.5 times the IQR from the lower and upper quartiles. The red dashed line indicates the maximum possible NRE

Fig. 5

Association between the NRE and age across the different type 2 diabetes subtypes: (a) SIDD; (b) SIRD; (c) MOD; and (d) MARD. The black dashed line indicates the mean age of the respective subtype in the original ANDIS cohort. The solid line corresponds to a local polynomial regression fit separately for each subtype

Fig. 6

Predicted 10 year CVD risk (SCORE2-Diabetes) with 95% CIs for each subtype, based on a linear regression model with or without accounting for classification uncertainty via NRE-weighting. Predictions are derived from individuals with complete clinical data for SCORE2-Diabetes, with sample size as follows: SIDD (n=15); SIRD (n=111); MOD (n=256); and MARD (n=321)