Modeling Diverse Anti-Diabetic Drug Effects Using Indirect Response Models: Review

Background: Diabetes is a major health risk in many countries and incidence rates are increasing. Diverse anti-diabetic agents act through various mechanisms on different organs. A large array of mathematical models has been proposed to describe anti-diabetic drug effects. Objectives: 1) To systematically compare structural models that were used to model anti-diabetic drug effects. 2) To provide a state-of-the-art review and future perspectives for modeling of drug effects in diabetes. 

Methods: Medline, Embase, the references of published papers, and various meeting websites were searched. We focused on mechanism-based models that describe drug effects, and on identification of major strengths, limitations and applications of the published models. 

Results: The well-established Minimal Model was used by some authors to model drug effects (n=4 studies), but its use is limited for applications other than diagnostic tests. Many investigators (n=8) have applied biophase distribution models for the description of anti-diabetic drug effects which do not always appropriately describe the physiology and pharmacology of the system and drug. More recently, effects of various agents on glucose and insulin were modeled with indirect response models (IDR, total: n=10, population models: n=4). Such models provided better curve fits and described the effects of anti-diabetic drugs on the glucose-insulin homeostasis more mechanistically than biophase models. The latter tended to require different parameter estimates for different dose groups which might be due to structural model misspecification. IDR could adequately describe various types of anti-diabetic drug action. Stimulation of insulin secretion by sulfonylurea drugs has been modeled successfully (n=2), as well as inhibition of glucose production or stimulation of glucose utilization by thiazolidinediones (n=3), metformin (n=3), and exogenous insulin (n=2). Average estimates for first-order removal of glucose from plasma (kout) range from 0.325 to 4.34 h-1 (median 1.38, n=6) for single dose studies. Average estimates for kout of glycosylated hemoglobin were 0.019 and 0.027 day-1 (n=2). By use of IDR, various doses of the same drug, as well as different drugs and mechanisms of action could be described simultaneously in one model. 

Conclusions: IDR models often described anti-diabetic effects more appropriately than effect compartment models. IDR models can describe several mechanisms of action, relative to production and loss of glucose and insulin. Such models may be used as the basis to address future needs in diabetes modeling, such as including the glucose-insulin feedback, develop mechanistic models for new drug groups, consider dual drug effects on complementary subsystems, and incorporate elements of disease progression. 

This work was supported by the UB – Pfizer Strategic Alliance.