# DDMODEL00000121: Nathan_2008_HbA1c_prediction

Short description:
Linear regression model to describe the relationship between average plasma glucose and HbA1c
 Format: PharmML 0.8.x (0.8.1) Related Publication: .hiddenContent {display:none;} Translating the A1C assay into estimated average glucose values. Nathan DM, Kuenen J, Borg R, Zheng H, Schoenfeld D, Heine RJ Diabetes care, 8/2008, Volume 31, Issue 8, pages: 1473-1478 Affiliation: Diabetes Center, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA. dnathan@partners.org Abstract: OBJECTIVE: The A1C assay, expressed as the percent of hemoglobin that is glycated, measures chronic glycemia and is widely used to judge the adequacy of diabetes treatment and adjust therapy. Day-to-day management is guided by self-monitoring of capillary glucose concentrations (milligrams per deciliter or millimoles per liter). We sought to define the mathematical relationship between A1C and average glucose (AG) levels and determine whether A1C could be expressed and reported as AG in the same units as used in self-monitoring. RESEARCH DESIGN AND METHODS: A total of 507 subjects, including 268 patients with type 1 diabetes, 159 with type 2 diabetes, and 80 nondiabetic subjects from 10 international centers, was included in the analyses. A1C levels obtained at the end of 3 months and measured in a central laboratory were compared with the AG levels during the previous 3 months. AG was calculated by combining weighted results from at least 2 days of continuous glucose monitoring performed four times, with seven-point daily self-monitoring of capillary (fingerstick) glucose performed at least 3 days per week. RESULTS: Approximately 2,700 glucose values were obtained by each subject during 3 months. Linear regression analysis between the A1C and AG values provided the tightest correlations (AG(mg/dl) = 28.7 x A1C - 46.7, R(2) = 0.84, P < 0.0001), allowing calculation of an estimated average glucose (eAG) for A1C values. The linear regression equations did not differ significantly across subgroups based on age, sex, diabetes type, race/ethnicity, or smoking status. CONCLUSIONS: A1C levels can be expressed as eAG for most patients with type 1 and type 2 diabetes. Contributors: Paolo Magni
 Context of model development: Clinical end-point; Diagnostic model; Discrepancy between implemented model and original publication: The model is the same of the original publication, even if in the original publication the dependent variable was MPG, while the model here reported uses HbA1C as dependent variable to be compliant with other studies that use this model, e.g. Moller et al. CPT Pharmacometrics Syst Pharmacol. 2014 Jul;3(7):e122.; Model compliance with original publication: Yes; Model implementation requiring submitter’s additional knowledge: No; Modelling context description: OBJECTIVE—The A1C assay, expressed as the percent of hemoglobin that is glycated, measures chronic glycemia and is widely used to judge the adequacy of diabetes treatment and adjust therapy. Day-to-day management is guided by self-monitoring of capillary glucose concentrations (milligrams per deciliter or millimoles per liter). We sought to define the mathematical relationship between A1C and average glucose (AG) levels and determine whether A1C could be expressed and reported as AG in the same units as used in self-monitoring. RESEARCH DESIGN AND METHODS—A total of 507 subjects, including 268 patients with type 1 diabetes, 159 with type 2 diabetes, and 80 nondiabetic subjects from 10 international centers, was included in the analyses. A1C levels obtained at the end of 3 months and measured in a central laboratory were compared with the AG levels during the previous 3 months. AG was calculated by combining weighted results from at least 2 days of continuous glucose monitoring performed four times, with seven-point daily self-monitoring of capillary (fingerstick) glucose performed at least 3 days per week. RESULTS—Approximately 2,700 glucose values were obtained by each subject during 3 months. Linear regression analysis between the A1C and AG values provided the tightest correlations (AGmg/dl = 28.7 × A1C ? 46.7, R2 = 0.84, P < 0.0001), allowing calculation of an estimated average glucose (eAG) for A1C values. The linear regression equations did not differ significantly across subgroups based on age, sex, diabetes type, race/ethnicity, or smoking status. CONCLUSIONS—A1C levels can be expressed as eAG for most patients with type 1 and type 2 diabetes.; Modelling task in scope: estimation; Nature of research: Clinical research & Therapeutic use; Therapeutic/disease area: Endocrinology;
 Validation Status: Annotations are correct. Certification Comment: This model is not certified.
• Model owner: Paolo Magni
• Submitted: Dec 12, 2015 2:55:22 PM
##### Revisions
• Version: 8
• Submitted on: Oct 10, 2016 8:28:43 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 6
• Submitted on: Jun 2, 2016 7:56:27 PM
• Submitted by: Paolo Magni
• With comment: Model revised without commit message
• Version: 2
• Submitted on: Dec 12, 2015 2:55:22 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.

### Name

Generated from MDL. MOG ID: Method_2_Nathan_mog

 T

### Function Definitions

 $\mathrm{additiveError}:\mathrm{real}\left(\mathrm{additive}:\mathrm{real}\right)=\mathrm{additive}$

### Covariate Model: $\mathrm{cm}$

#### Continuous Covariates

$\mathrm{MPG}$

### Parameter Model: $\mathrm{pm}$

#### Random Variables

${\mathrm{EPS_1}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=1\right)$

#### Population Parameters

$\mathrm{BETA0_POP}$
$\mathrm{BETA1_POP}$
$\mathrm{RES}$

#### Individual Parameters

$\mathrm{BETA0}=\mathrm{pm.BETA0_POP}$
$\mathrm{BETA1}=\mathrm{pm.BETA1_POP}$

### Structural Model: $\mathrm{sm}$

#### Variables

$\mathrm{HBA1C}=\mathrm{pm.BETA0}+\mathrm{pm.BETA1}\cdot \mathrm{cm.MPG}$

### Observation Model: $\mathrm{om1}$

#### Continuous Observation

$Y=\mathrm{sm.HBA1C}+\mathrm{additiveError}\left(\mathrm{additive}=\mathrm{pm.RES}\right)+\mathrm{pm.EPS_1}$

## External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_Nathan_data.csv

### Column Definitions

Column ID Position Column Type Value Type
$\mathrm{ID}$
$1$
$\mathrm{id}$
$\mathrm{int}$
$\mathrm{TIME}$
$2$
$\mathrm{idv}$
$\mathrm{real}$
$\mathrm{DV}$
$3$
$\mathrm{dv}$
$\mathrm{real}$
$\mathrm{MPG}$
$4$
$\mathrm{covariate}$
$\mathrm{real}$
$\mathrm{EV}$
$5$
$\mathrm{undefined}$
$\mathrm{real}$

### Column Mappings

Column Ref Modelling Mapping
$TIME$
$T$
$DV$
$\mathrm{om1.Y}$
$MPG$
$\mathrm{cm.MPG}$

## Estimation Step

 OID $\mathrm{estimStep_1}$ Dataset Reference $\mathrm{nm_ds}$

### Parameters To Estimate

Parameter Initial Value Fixed? Limits
pm.BETA0_POP
$1.63$
false
$\left(,\right)$
pm.BETA1_POP
$0.035$
false
$\left(,\right)$
pm.RES
$1$
false
$\left(0,\right)$

### Operations

#### Operation: $1$

 Op Type generic
##### Operation Properties
Name Value
algo
$\text{foce}$

## Step Dependencies

Step OID Preceding Steps
$\mathrm{estimStep_1}$