Multiple Linear regression of 1,5-AG, HbA1c and CGM data

To determine the potential role of 1,5-AG in monitoring glycaemic variability we collected data from 29 Australian DM patients and 49 French DM patients for whom CGM data was available. Patients had a median age of 32.45 years, a median BMI of 24.72 kg/m2, a median 1,5-AG of 3.5 µg/mL and a median HbA1c of 7.4% (Supplementary Table 1).

A MLR was subsequently performed to assess the association between 1,5-AG/HbA1c and percentage time in range, percentage time very high, percentage time low and GRI. Percentage time very low was not included in the analysis as it failed the assumption of residual homoscedasticity (data not shown). In light of the potential confounding effects of age, sex, BMI and site these factors were included as covariates. Importantly, and consistent with prior reports [11], 1,5-AG and HbA1c were highly correlated (Fig. 1). Therefore, including the variables HbA1c and 1,5-AG in the same MLR would violate the assumption of limited multicollinearity upon which a MLR is based [24]. Accordingly, two separate MLR models for 1,5-AG and HbA1c were created (Supplementary Tables 2 and 3). Both 1,5-AG and HbA1c levels had a significant association with percentage time in range, percentage time very high, percentage time high, percentage time low and GRI when controlling for the aforementioned covariates (Supplementary Tables 2 and 3).

Fig. 1

HbA1c and 1, 5-AG are highly correlated in patients with type 1 diabetes. Data was obtained from 49 type 1 diabetes patients recruited from France and 29 recruited from Australia. Statistical significance was determined with Person’s correlation coefficient where p < 0.0001(****)

Regression tree analysis of GRI

The above data indicate a strong linear relationship between both 1,5-AG and HbA1c and CGM-derived measures of glycaemic variability. However, these data do not indicate whether the addition of 1,5-AG provides increased insight into a patient’s glycaemic variability compared to measuring HbA1c alone. To answer this question, we turn to methods in machine learning. Specifically, we developed a regression tree for a patient’s GRI (Fig. 2). A regression tree is a predictive model that splits data into progressively smaller groups based on input features. At each split, it chooses a feature and value that best separates the data to minimize prediction errors. Such a model can thus be used clinically in a predictive context, where the flowchart can be followed and the GRI of a patient without a CGM can be predicted based on the features of the tree. However, to develop such a model for robust GRI prediction in the clinic it would be necessary to divide data into a training and test set, which is not possible with the n number of the present study. Rather, here we sought to use a regression tree to simply determine if 1,5-AG offers any additional predictive power on the estimated value of GRI over HbA1c alone. In this context, it is appropriate to test the validity of the model using 10-fold cross-validation, with a 90% training set and 10% validation set. With this in mind we created three different regression trees – one including just HbA1c (in addition to age, sex, BMI and site), one including just 1,5-AG (in addition to age, sex, BMI and site) and one including both HbA1c and 1,5-AG (in addition to age, sex, BMI and site) (Table 1). To compare the performance across each tree, the mean squared error is calculated for GRI prediction on each fold iteration and averaged over all folds (Table 1). In this context, a lower average mean square indicates improved GRI prediction (Table 1). Consistent with an additive role of 1,5-AG and HbA1c in diabetes management the best performing model was Model 1, which included age, sex, site, BMI, HbA1c and 1,5-AG (Table 1). Surprisingly, model 2 (1,5-AG, age, sex, site and BMI) had a lower average mean square error than Model 3 (HbA1c, age, sex, site and BMI) (Table 1). To explore these data further we assessed the importance of each feature (e.g. HbA1c, age, sex etc.) in Model 1 using the CART method [25]. Figure 3 shows that HbA1c and 1,5-AG were the features with the highest predictive value, with HbA1c classified at a higher importance over 1,5-AG.

Fig. 2

Regression tree for GRI incorporating age, sex, site, HbA1c and 1,5-AG. Numbers at the end of each node indicate the predicted GRI

Table 1 Regression tree analysis with both HbA1c and 1,5-AG, 1,5-AG alone or HbA1c aloneFig. 3

Feature importance in model 1 (HbA1c, 1,5-AG, age, sex, site and BMI)

These data (Fig. 3) contrast with those shown in Table 1 where the model using 1,5-AG alone (Model 2) better predicts GRI compared to the HbA1c alone model (Model 3). To explore this discrepancy further we examined the predictive capacity of the three different models across the range of GRIs recorded herein (Fig. 4). Here, we show that Model 3 (HbA1c alone) is best able to predict the values of GRI from individuals whose GRI falls in zone B (21–40), zone C (41–60) and zone D (61–80) [26]. This reflects the majority of the individuals in the cohort and is hence in agreement with the greater importance of HbA1c as a feature (Fig. 3). In contrast, 1,5-AG is able to more accurately predict values of GRI that fall in zone A (0–20) and zone E (81+)28 (Fig. 4), allowing 1,5-AG to contribute significantly to the decrease in mean sqaured error of the model (Table 1). Taken together, these data indicate that 1,5-AG provides additional predictive information to determine a patient’s GRI above that offered by HbA1c alone. The inclusion of 1,5-AG is particularly important for individuals with a GRI that falls within zone A or zone E.

Fig. 4

1,5-AG provides the greatest predictive value for individuals with a GRI is Zone A and E. Zones were defined according to [26]. True GRI values are shown in black. Predicted values from Model 1 (1,5-AG, HbA1c, BMI, Age, Site and Sex) are shown in red circles. Predicted values from Model 2 (1,5-AG, BMI, Age, Site and Sex) are shown with a blue cross. Predicted values from Model 3 (HbAc1, BMI, Age, Site and Sex) are shown with a purple asterisk. Individual Index refers to the donor ID number. MSE = Average Mean Square Error

1,5-AG and the CD4 + T cell cytokine responses to ex vivo stimulation with influenza virus in individuals with a matched HbA1c

Glycaemic variability, rather than just HbA1c, is important in predicting the micro and macrovascular complications of diabetes [1] as well as the immune impairment/susceptibility to respiratory virus infection seen in patients with DM [1,2,3]. We thus sought to explore if 1,5-AG provided any additional information (above that of HbA1c) to predict the anti-viral immune response in patients with DM. As described above, this analysis could not be performed using MLR with HbA1c and 1,5-AG as covariates as these values are highly correlated (Fig. 1) and thus violate the assumptions of multiple linear regression. Instead, individuals from the Australian cohort were classified as having a ‘low’ or ‘high’ 1,5-AG. There is currently no accepted clinical definition of a ‘low’ or ‘high’ 1,5-AG for patients with DM. Rather individuals were classified as having a ‘low’ 1,5-AG if the 1,5-AG levels were lower than the range observed for 368 patients with DM (i.e. 1,5-AG ≤ 1.1)29. This categorical grouping allowed us to match individuals with ‘low’ and ‘high’ HbA1c based on their HbA1c (< 1% difference; HbA1c < 10), age (< 40 years difference) and sex (identical) and assess their ex vivo immune response to influenza virus. Supplementary Table 4 demonstrates that 7 matched individuals were selected who had a significant difference in 1,5-AG levels but no significant difference in HbA1c, age, sex or BMI.

To evaluate if 1,5-AG could provide any insight into T cell function, in the presence of matched HbA1c, the cytokine response of CD4 + T cells to ex vivo stimulation with influenza virus in the 7 matched donors was assessed (Fig. 5). Cytokine production by CD4 + T cells is an essential part of the anti-viral immune response as CD4 + T cell derived cytokines play a key role in activating CD8 + T cells and B cells, whilst also recruiting and activating innate antigen presenting cells such as dendritic cells. HbA1c matched individuals with a lower 1,5-AG had a significantly lower percentage of CD4 + IFNγ+TNF−MIP1β−, CD4 + IFNγ−TNF+MIP1β− and CD4 + IFNγ−TNF−MIP1β+ cells in response to influenza virus stimulation (Fig. 5). Consistent with these data, matched individuals with type 1 DM and a lower 1,5-AG also had a significantly lower percentage of total CD4 + IFNγ+, CD4 + TNF+ and CD4 + MIP1β+ cells in response to influenza virus stimulation (Fig. 5). These differences were specific to influenza virus stimulation, as the 7 matched individuals with a lower 1,5-AG did not have a significantly lower CD4 + T cell cytokine positive cells in response to stimulation with PMA/I (Fig. 6) or CD3/CD28 beads (Fig. 7). Taken together, these data indicate that 1,5-AG can provide additional insight as to CD4 + T cell function above that which is provided by HbA1c alone. Specifically, these data suggest that low 1,5-AG can reduce the number of CD4 + T cell cytokine producing cells in response to influenza virus.

Fig. 5

Low 1,5-AG is associated with reduced CD4 + T cell cytokine production in response to ex vivo stimulation with influenza virus. (A) Polyfunctional analysis of CD4 + T cells. (B) Total percentage of MIP1β, IFNγ or TNFα positive CD4 + T cells. Statistical significance was assessed using a paired t-test (normally distributed data) or a Wilcoxon test (not normally distributed data). *p < 0.05 1,5-AG ≤ 1.1 is shown in light blue squares whilst 1,5-AG > 1.1 is shown in dark blue circles

Fig. 6

Low 1,5-AG is not associated with reduced CD4 + T cell cytokine production in response to ex vivo stimulation with PMA/I. (A) Polyfunctional analysis of CD4 + T cells. (B) Total percentage of MIP1β, IFNγ or TNFα positive CD4 + T cells. Statistical significance was assessed using a paired t-test (normally distributed data) or a Wilcoxon test (not normally distributed data). *p < 0.05

Fig. 7

Low 1,5-AG is not associated with reduced CD4 + T cell cytokine production in response to ex vivo stimulation with CD3/CD28 magnetic beads. (A) Polyfunctional analysis of CD4 + T cells. (B) Total percentage of MIP1β, IFNγ or TNFα positive CD4 + T cells. Statistical significance was assessed using a paired t-test (normally distributed data) or a Wilcoxon test (not normally distributed data). *p < 0.05