Longitudinal Modeling of the Relationship Between Mean Plasma Glucose and HbA1c Following Antidiabetic Treatments

Abstract

Late-phase clinical trials within diabetes generally have a duration of 12-24 weeks, where 12 weeks may be too short to reach steady-state glycated hemoglobin (HbA1c). The main determinant for HbA1c is blood glucose, which reaches steady state much sooner. In spite of this, few publications have used individual data to assess the time course of both glucose and HbA1c, for predicting HbA1c. In this paper, we present an approach for predicting HbA1c at end-of-trial (24-28 weeks) using glucose and HbA1c measurements up to 12 weeks. The approach was evaluated using data from 4 trials covering 12 treatment arms (oral antidiabetic drug, glucagon-like peptide-1, and insulin treatment) with measurements at 24-28 weeks to evaluate predictions vs. observations. HbA1c percentage was predicted for each arm at end-of-trial with a mean prediction error of 0.14% [0.01;0.24]. Furthermore, end points in terms of HbA1c reductions relative to comparator were accurately predicted. The proposed model provides a good basis to optimize late-stage clinical development within diabetes.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e82; doi:10.1038/psp.2013.58; advance online publication 30 October 2013.

Figure 1

The model is an indirect response model where the production of HbA1c is stimulated by mean plasma glucose (MPG) through the parameter k_{in_HbA1c} that is fixed to 0.081%/mmol/l per week. The model is initialized in steady state, at the time of the screening visit, where MPG_ss is the value for MPG (see Table 2 for parameter values). MPG is assumed to change during a washout/run-in period toward MPG_base typically obtained at the baseline visit. MPG_{posttreatment} is the stable glucose value obtained after introducing the experimental treatment. k_{out_MPG} is the rate constant defining the rate of treatment onset on MPG. The parameter k_{out_HbA1c} defines the output rate constant for HbA1c and is fixed to 0.226 per week. The present model further introduces a parameter β that allows an offset in the linear relationship between MPG and HbA1c in steady state. Thus, k_{in_HbA1c} is stimulated by MPG + β (see model code in Supplementary Material online).

Figure 2

Visual predictive checks for mean plasma glucose (MPG) over time (left) and HbA1c (right) of each arm of the insulin studies^, presented in Table 1. The arm numbers are followed from left to right, so left is arm 1 and right arm 2. Further descriptions can be found in Table 1. Solid gray (light) line presents median of predictions and shaded area presents 95% confidence interval for predictions as predicted without uncertainty in parameter estimates. Median and 95% confidence interval of observations are presented by black dots and whiskers. Week 0 corresponds to the week of randomization.

Figure 3

Visual predictive checks for mean plasma glucose over time (left) and HbA1c (right) in each arm of the glucagon-like peptide-1 analogue studies^, presented in Table 1. The arm numbers are followed from left to right and top to bottom and descriptions are found in Table 1. Solid gray (light) line presents median of predictions and shaded area presents 95% confidence interval for predictions as predicted without uncertainty in parameter estimates. Median and 95% confidence interval of observations are presented by black dots and whiskers. Week 0 corresponds to the week of randomization.

Figure 4

Overview of prediction performance in each arm. Abscissa presents the percentage change in HbA1c (ΔHbA1c) following 24–28 weeks of treatment compared with main comparator (see description in Table 1). Each line presents 95% confidence interval for treatment effect vs. comparator calculated from observations (black) and predictions from 12 weeks (gray). Dots present mean difference in ΔHbA1c between comparator and the specific arm.