1. Применение различных методов математического моделирования для решения клинических задач на примере моделирования ингибиторов почечной реабсорбции глюкозы
Яковлева Татьяна
X конференция группы по математическим моделям и численным методам в биоматематике ИВМ РАН
6 ноября 2018 года

2. Type 2 Diabetes Mellitus treatment via SGLT2 inhibitors
Plasma glucose is filtered by the kidneys with the rate of glomerular filtration (GFR)
Glucose in kidney tubules is subsequently retrieved by the sodium-dependent glucose co-transporter 2 and 1 (SGLT2 and SGLT1) preventing it from disappearing from the body through the urine
If the amount of filtered glucose exceeds the maximum reabsorption capacity of transporters, it starts to appear in the urine
SGLT2 inhibitors (SGLT2i) represent a class of compounds for the treatment of type 2 diabetes mellitus (T2DM)
Inhibition of glucose reabsorption results in plasma glucose lowering, which is beneficent for diabetic subjects
Dapagliflozin, canagliflozin and empagliflozin are the SGLT2i, widely used as anti-T2DM therapy
Glomerular filtration (~180 g/day)

3. PopPKPD, quantitative systems pharmacology, meta-analysis
Challenges in SGLT2i development
Application of dapagliflozin in type 1 diabetes mellitus (T1DM) in Japanese population
Greater efficacy of canagliflozin in T2DM population compared to other SGLT2i
Increased frequency of adverse events (bone fractures and amputations) for canagliflozin
PopPKPD, quantitative systems pharmacology, meta-analysis

4. Exposure-response modeling comparison between T1DM Japanese and non-Japanese patients treated with dapagliflozin
Phase IIa study was performed to support the dapagliflozin approval in T1DM Japanese population.
No statistically significant differences were observed in 24-hours urinary glucose excretion (UGE) between 5 and 10 mg dapagliflozin doses.
Why 5 and 10 mg dapagliflozin cause the same 24h UGE in Japanese study, but not in previously performed non-Japanese study?
Should we adjust the optimal dose for Japanese population?
Population exposure response modeling using individual data from
non-Japanese and Japanese studies

5. Non-linear mixed effects model of urinary glucose excretion
A non-linear mixed effects (NLME) model was developed in NONMEM software to characterize the relationship between area under curve of dapagliflozin plasma concentration (AUC0-24h) on Day 7 and Day 7 24h UGE
Model structure: UGE= UGE 0 + Emax× AUC 0−24 EAUC 50 + AUC 0−24
UGE0 – regressor, taken directly from the data as the 24h UGE at Day 0
AUC0-24h – regressor, the observed dapagliflozin AUC0-24h at Day 7
Emax – parameter, the maximum treatment-induced 24h UGE change at Day 7
EAUC50 – parameter, AUC0-24h at which half maximal UGE change is achieved
typical (“mean”) value of parameter in the population
residual error ~N(0, σ2)
covariate value for ith subject
Covariates:
Age
Body weight
Race
Fasting plasma glucose
Mean plasma glucose
Insulin dose
etc.
𝜃 𝑖 = 𝜃 𝑝𝑜𝑝 + η 𝑖 + 𝜀 𝑖 + β 𝑐𝑜𝑣 ∗𝑐𝑜 𝑣 𝑖
parameter value for ith subject
random effect ~N(0, ω2)
covariate coefficient
constant
𝐲=𝐟+𝐚∗𝐞
proportional
𝒚=𝒇+𝒃∗𝒇∗𝒆
combined
𝐲=𝒇+(𝒂+𝒃∗𝒇)∗𝒆
Constant, proportional and combined residual error models were evaluated:

6. Day 7 mean plasma glucose Day 7 percent CFB in total insulin dose
Factors that affect UGE in 5 and 10 mg treatment cohorts
Dapagliflozin AUC0-24
Baseline eGFR
For a given dapagliflozin dose, the exposure was similar in each population (A)
No significant differences in baseline estimated GFR (eGFR) were observed for different cohorts (B)
Higher Day 7 mean plasma glucose (C) and a greater reduction in total insulin dose (D) were observed in the Japanese population compared with the non-Japanese population
Day 7 mean plasma glucose
Day 7 percent CFB in total insulin dose
Solid horizontal line is median (50th percentile)
Bars are IQR
Whiskers represent the range of values no greater than Q1 – 1.5*IQR and Q *IQR
Datapoints are outliers
Text within bars denotes median values
AUC0-24=area under the concentration curve over a 24-hour period; CFB=change from baseline; eGFR=estimated glomerular filtration rate; IQR=interquartile range; SMBG=self-monitored blood glucose; Q=Quartile

7. The model is able to explain observed discrepancy between Japanese and non-Japanese studies
Dose-response of dapagliflozin on Day 7 24h UGE
The apparent differences between glucosuria in Japanese and non-Japanese patients can be explained by differences in insulin titration behavior in the two studies
Japanese and non-Japanese patients with T1DM have similar dapagliflozin exposure–response relationships, and therefore no dose adjustment is recommended in Japanese patients with T1DM
Shaded area: simulated interquartile ranges
Grey text: simulated 24h UGE values for each dosing group in each study
Error bars: standard deviation of experimental data.
UGE = urinary glucose excretion

8. Quantitative systems pharmacology (QSP) model of renal glucose reabsorption
Despite SGLT2 contributing 80-90% to renal glucose reabsorption, clinical observations showed SGLT2i decrease reabsorption by only 30–50%.
Canagliflozin, a dapagliflozin competitor, possesses higher efficacy in T2DM patients at marketed doses.
Why SGLT2 inhibitors decrease reabsorption by 30–50% only?
Why canagliflozin shows greater UGE in subjects with T2DM?
Are there any differences in reabsorption processes between healthy and T2DM subjects?
A physiologically-based model of glucose filtration, reabsorption and excretion, that includes dapagliflozin, canagliflozin, empagliflozin

9. 𝑇𝑜𝑡𝑎𝑙 𝑅𝐺𝑅 = 𝑅𝐺 𝑅 𝑆𝐺𝐿𝑇1 +𝑅𝐺 𝑅 𝑆𝐺𝐿𝑇2
Structure of the renal glucose reabsorption model
A 4-compartment model of renal glucose filtration, reabsorption and excretion was developed using a system of ordinary differential equations
The total renal glucose reabsorption rate (RGR) is the sum of contributions from both cotransporters, each governed by Michaelis-Menten kinetics
Inhibition of SGLT-mediated renal glucose reabsorption is modeled as a simple competitive process characterized by compound-specific Ki values
𝑇𝑜𝑡𝑎𝑙 𝑅𝐺𝑅 = 𝑅𝐺 𝑅 𝑆𝐺𝐿𝑇1 +𝑅𝐺 𝑅 𝑆𝐺𝐿𝑇2
𝑅𝐺 𝑅 𝑆𝐺𝐿𝑇 = 𝑉 𝑚𝑎𝑥 𝑆𝐺𝐿𝑇 ∗𝐺𝑙𝑢𝑐𝑜𝑠 𝑒 𝑙𝑢𝑚𝑒𝑛 𝐾 𝑚 𝑆𝐺𝐿𝑇 ∗ 1+ 𝐷𝑟𝑢 𝑔 𝑙𝑢𝑚𝑒𝑛 𝐾𝑖 𝑆𝐺𝐿𝑇 +𝐺𝑙𝑢𝑐𝑜𝑠 𝑒 𝑙𝑢𝑚𝑒𝑛
𝑉 𝑚𝑎𝑥 𝑆𝐺𝐿𝑇 : maximal rates of reabsorption by SGLT2 and SGLT1
𝐾 𝑚 𝑆𝐺𝐿𝑇 : glucose affinity constants for SGLT2 and SGLT1
𝐺𝑙𝑢𝑐𝑜𝑠 𝑒 𝑙𝑢𝑚𝑒𝑛 : glucose concentrations in the proximal convoluted tubule and proximal straight tubule compartments
𝐷𝑟𝑢 𝑔 𝑙𝑢𝑚𝑒𝑛 : SGLT inhibitor concentration in corresponding lumen compartments
𝐾𝑖 𝑆𝐺𝐿𝑇 : the affinity of an inhibitor to a particular SGLT

10. Contribution of SGLT1 and 2 to renal glucose reabsorption
Summary reabsorption capacity for healthy (blue) and T2DM subjects (red) measured by stepwise hyperglycemic clamp procedure (A) and model-predicted maximal SGLT1/2 contribution to glucose reabsorption
Dots represent experimental data (mean ± SD), lines represent model predictions
Both SGLT1 and SGLT2 contribution to RGR is increased in T2DM patients compared to healthy subjects

11. Normalization to MPG and eGFR
QSP model of SGLT2i: Compound differentiation
Analysis of 24-hours UGE under SGLT2i treatment in healthy (A) and T2DM subjects (B, C) A B
Canagliflozin was shown to have higher affinity to SGLT1 transporter
Normalization of median glucose filtration fluxes resulted in similar potencies for dapagliflozin and empagliflozin.
Normalization to MPG and eGFR
(A), (B): Curves represent model predictions for subjects with median MPG and eGFR levels within the treatment group, including dapagliflozin (red), canagliflozin (blue), empagliflozin (green); Dots represent pooled sets of experimental 24-h UGE d
(C): Model predictions with median MPG and eGFR levels calculated based on the pooled dataset for all three drugs. C

12. Glucosuria-related adverse events for the SGLT2i dapagliflozin and canagliflozin: a  meta-analysis
Canagliflozin was shown to increase the incidence of bone fractures and amputations
Which adverse events are more frequent in canagliflozin-treated population compared to dapagliflozin?
Is it a class effect for all SGLT2i or is it only canagliflozin-related?
Is urinary glucose excretion a cause of these adverse events?
Model-based meta-analysis of adverse evens in dapagliflozin- and canagliflozin-treated populations

13. Incidence of genital mycotic infections in T2DM patients
Frequency of adverse events is increased for canagliflozin treatment, but not for dapagliflozin treatment
Incidence of genital mycotic infections in T2DM patients
Dapagliflozin
Canagliflozin
33 Phase IIb/III T2DM clinical trials of dapagliflozin and canagliflozin were analyzed (28,973 patients in total)
The occurrence of genital mycotic infections (GMI), urinary tract infections and volume depletion were quantified using a meta-analysis approach
Logistic regression models were used to assess the relationship between dose and the incidence of AEs
Significantly higher proportion of T2DM patients treated with canagliflozin experienced a incidence of GMI adverse events compared to dapagliflozin at approved doses
The higher incidence of GMIs for canagliflozin was not fully explained by differences in glucosuria

14. Acknowledgments Victor Sokolov Kirill Peskov Lulu Chu Weifeng Tang
Peter J. Greasley
Susanne Johansson
Gabriel Helmlinger
David W. Boulton
Robert C. Penland
Shinya Ueda
Joanna Parkinson
Sergey Aksenov
Peter Greasley

15. Thank you for your attention!
Спасибо за внимание!
Thank you for your attention!

16. Backup

17. Meta-analysis procedure
The Meta-analysis was performed using a random-effects model with the Maximum-Likelihood estimator.
Logit-transformed AEs were used. Certain AE subgroups of dapagliflozin, in all AE outcomes (male genital mycotic infections and volume depletion), were less than 5%, and are considered to be rare events. It has been shown that, for AE rates <5%, the normal distribution assumption for within-trial variability is no longer valid and leads to a bias in the estimation of the mean effect size [J Clin Epidemiol. 2008;61:41-51]
For rare events as well as other events, we therefore used the normal-binomial general linear mixed model (GLMM) approach [Stat Med. 2010;29: ], as implemented in using the metafor package in R software (Version 3.4.4)
A risk difference between the treatment and placebo was then calculated to reveal the treatment effect for low doses and high doses.