Blood samples for PK analysis were collected within 0.5 hours before dosing, 0.5, 1, 2, 3, 4, 5, 6, 8, 12 and 24 h after dosing on day 1; within 0.5 hours before dosing on day 7 and day 10; within 0.5 h before dosing and 0.5, 1, 2, 3, 4, 5, 6, 8, 12, 24, 48, 72, 96 and 120 h after dosing (blood samples for sitagliptin group were not collected at 72 h, 96 h and 120 h) on day 14. At each blood sampling point, 3 mL of blood samples were collected into centrifuge tubes containing anticoagulant (K₂EDTA) and centrifuged at 1500 g, 2-8°C for 10 min, the plasma samples were separated and stored at -70 ± 10°C until analysis. Plasma concentrations of cetagliptin and sitagliptin were determined using validated liquid chromatography-tandem mass spectrometry methods. For cetagliptin and sitagliptin, the linear calibration ranges were 0.5-5000 ng/mL and 1-800 ng/mL, respectively (31).

PK parameters were calculated using non-compartmental analysis with Phoenix WinNonlin (version 8.1, Certara, Co., Princeton, NJ, United States). Peak plasma concentration after administration (C_max) and time to reach C_max (T_max) were obtained directly from the observed data, elimination half-life (t_1/2) was calculated as ln2/λz using the best fit mode, where λz was the terminal elimination rate constant. Area under the plasma concentration-time curve from zero to the last measurable concentration (AUC_0-t) was estimated using the linear trapezoidal method and AUC from zero to infinity (AUC_0-∞) was calculated as AUC_0-t+C_t/λ_z, where C_t was the last measured concentration. The average value of the steady-state concentration (C_{av, ss}) was calculated as AUC_0-τ/τ (τ=24h). Apparent total plasma clearance after non-intravenous (CL/F) and apparent volume of distribution in terminal phase after non-intravenous (V_z/F) were calculated as Dose/AUC_0-∞ and CL/λ_z, respectively. Accumulation ratios of C_max (R_Cmax) and AUC (R_AUC0-24h) were calculated as C_{max, day 14}/C_{max, day 1} and AUC_{0-τ, day 14}/AUC_{0-24 h, day 1}.

Blood samples for DPP-4 activity determination were collected at the same time points as for PK. 1 mL blood samples were collected into blood-collecting tubes containing K₂-EDTA. The tubes were placed on ice until centrifugation. The blood samples were centrifuged at 2-8°C, 1500 g for 10 min within 1 hour after blood collection. After centrifugation, the supernatant were evenly divided into two aliquots and stored at -80 ± 10°C. The plasma DPP-4 activity was determined using a fluorescent method with the substrate Gly-Pro-7-amide-4-methylcoumarin. A range of 3-400 µM was covered by the linear calibration. For the 80-120% range, the relative error of accuracy was met (31).

The degree of inhibition of DPP-4 enzyme activity relative to baseline (DPP-4 inhibition, %) after administration was calculated as the following equation:

The calculated PD parameters for evaluation of DPP-4 inhibition were as follows: maximum observed response (R_max), the time of maximum observed response (T_Rmax), area under the effect curve from the time of dosing to 24 h or the last measurable response (AUEC_{0-24 h}, AUEC_0-t), the duration for DPP-4 inhibition rate of >80% (DUR_80%), the observed effect at 24 h postdose (E_{24 h}) and minimum observed response (R_min) on day 14.

Furthermore, a maximum inhibitory efficacy (E_max) model was used to evaluate the relationship between plasma concentrations (cetagliptin or sitagliptin) and DPP-4 inhibition. E_max and the plasma concentration of cetagliptin or sitagliptin that produced half the maximum effect (EC₅₀) were provided using Phoenix WinNonlin software version 8.1.

Blood samples for GLP-1 activity evaluation were collected at the same time points as for PK. 2 mL blood samples were collected for GLP-1 activity detection (20 μL DPP-4i was added to blood-collecting tubes beforehand). The tubes were placed on ice until centrifugation. The blood samples were centrifuged at 2-8°C, 1500 g for 10 minutes within 1 hour after blood collection. After centrifugation, the blood samples were evenly divided into two aliquots and stored at -80 ± 10°C. Plasma active GLP-1 concentrations were determined using a validated ELISA method. Linear calibration curves were obtained in the concentration range of 0.017-276 pM (31).

The change of GLP-1 concentration from baseline (△GLP-1) was calculated as follows:

The calculated parameters for GLP-1 activity were as follows: the baseline GLP-1 value before dosing (Baseline), R_max, T_Rmax, AUEC_0-t, AUEC_0-24h, GLP-1 concentration change at 2 h after lunch (△GLP-1-6h), GLP-1 concentration change at 2 h after dinner (△GLP-1-12h), R_min on day 14, and the average response on day 14 (R_avg).

To assess the impact of investigational products on glucose, insulin, C-peptide, and glucagon, OGTT tests were conducted on day -1 and day 15 following a fasting period of more than 8 hours. Subjects received a 75 g oral glucose dose and blood samples (1.5 mL for glucose, 3.5 mL for insulin and C-peptide, 2 mL for glucagon) were collected at 0, 0.167, 0.5, 1, 1.5, 2, and 3 h after ingestion of glucose. The PD parameters (AUEC_0-t) for glucose, insulin, C-peptide, and glucagon were calculated by using drug effect module of non-compartmental method with Phoenix WinNonlin.

A total of 560 plasma concentrations of cetagliptin from 32 patients with T2DM were used for PopPK analysis. The structural model was tested using either one- or two-compartment PK models. Individual variation was modeled using an exponential form (Equation 1):

P_j represents the typical value of the jth parameter in population and Pij represents the true value of a parameter for the ith subject on the jth parameter. The inter-individual variability ( η ) of PK parameters was assumed to follow a log-normal distribution with a mean of 0 and a variance in ω 2 .

The additive error model (Equation 2), proportional error model (Equation 3), and additive and proportional error model (Equation 4) were evaluated to describe the residual variability:

Where C_ij is the observation concentration of the ith subject at the jth sampling point and IPRED_ij is the subject’s prediction value. The residual variability ( ε ) is normally distributed with a mean of 0 and a variance in σ 2 .

The stepwise forward inclusion/backward elimination approach was used to investigate the covariate effects on PopPK parameters.

As a result of data with an absolute value of CWRES greater than 5 being excluded, only 554 blood concentrations of cetagliptin were included in development of the PopPK/PD model. A direct-effect model was used to build the PK/PD model; and the model formula was as follows:

Where E m a x = maximum DPP-4 inhibition (%); C = plasma concentration; E C 50 = plasma concentration of cetagliptin that achieves 50% of the maximum drug effect; and γ = hill coefficient, which describes the steepness of the concentration-response curve.

Interindividual variation and residual variability were considered the same as the PopPK model.

Goodness-of-fit plots were assessed to describe the adequacy of the final PopPK/PD model, including observations vs. population predictions, observations vs. individual predictions, conditional weighted residuals (CWRES) vs. population predictions, and CWRES vs. time., A bootstrap resampling procedure was performed to assess the stability of the final PopPK/PD model. A total of 1000 bootstrap datasets were generated by random sampling with replacement, and the PK parameters were re-estimated using the final population model. The median parameter value and their 95% confidence intervals (95% CIs) from bootstrap estimates were compared using the estimates of the final model. In addition, a visual predictive check (VPC) was used to assess the predictive ability of the final model. A total of 1000 simulations of the final population PK model were performed. The VPC graphically showed the observations and different percentiles of simulated concentrations (5th, median, and 95th percentiles).

Mean plasma DPP-4 inhibition-time profiles of cetagliptin, sitagliptin, and placebo are shown in Figure 2 , and the PD parameters are summarized in Table 3 .

As shown in Figure 2 , compared with the placebo group, plasma DPP-4 activity was significantly inhibited following administration of cetagliptin or sitagliptin. After single administration, the R_max values for 50 mg cetagliptin, 100 mg cetagliptin, and sitagliptin were 86.39, 88.78, and 90.10%, respectively. The corresponding DUR_80% values were 8.39, 21.1, and 16.3 h, respectively. The results showed that the intensity of DPP-4 inhibition induced by 100 mg cetagliptin was comparable with that induced by sitagliptin, while the duration of inhibition was longer than that of sitagliptin. The DPP-4 inhibition reached a steady state ( Figure 2 ) after 1 week of daily dosing. After multiple administration, the R_max values for 50 mg cetagliptin, 100 mg cetagliptin, and sitagliptin were 89.47, 89.99, and 90.43%, respectively. The corresponding DUR_80% values were 21.9, 32.3, and 18.6 h, respectively. And the E_24h were 78.43, 83.91, and 77.72%, respectively, suggesting that the intensity and duration of DPP-4 inhibition induced by 50 mg cetagliptin was comparable with that induced by sitagliptin, and 100 mg cetagliptin showed a much longer sustained DPP-4 inhibition (≥80%) than sitagliptin. Meanwhile, the accumulation ratios of AUEC_0-24h for 50 mg cetagliptin, 100 mg cetagliptin, and sitagliptin were close to 1.

The relationship between plasma concentrations of cetagliptin or sitagliptin and DPP-4 inhibition was evaluated by an E_max model ( Figure 3 ). The DPP-4 inhibitory intensity increased with the drug concentration and reached a plateau. The E_max values for cetagliptin and sitagliptin were 92.47% and 91.68%, respectively. And EC₅₀ values were 5.37 and 6.73 ng/mL, respectively.

As shown in Figure 4 , the T_Rmax of plasma active GLP-1 in cetagliptin, sitagliptin and placebo groups were similar. Plasma active GLP-1 concentrations were influenced by diet and increased after meals at 4 h and 10 h post dose. While compared with the placebo group, plasma active GLP-1 concentrations were much higher in cetagliptin and sitagliptin groups.

Table 4 shows the PD parameters of active GLP-1 following administration of cetagliptin, sitagliptin, and placebo in patients with T2DM. After single administration, the main parameters such as R_max, AUEC_0-24h, △GLP-1-6h and △GLP-1-12h in 100 mg cetagliptin group were higher than those in 50 mg cetagliptin group and comparable with those in 100 mg sitagliptin group (except for △GLP-1-6h, the former group was higher).

After multiple administration for 14 days, steady-state conditions were achieved. The baseline plasma active GLP-1 concentrations (R_0h) on day 14 in 50 mg cetagliptin, 100 mg cetagliptin, and sitagliptin groups were similar (1.787 vs 1.858 vs 1.700 pM). And the comparison results of the main parameters (such as R_max, AUEC_0-24h, △GLP-1-6h and △GLP-1-12h) in each group after multiple administration were consistent with those after single administration.

Compared with baseline, after administration of cetagliptin or sitagliptin, plasma glucose and glucagon levels showed an obvious decrease, while insulin and C-peptide showed an obvious increase ( Supplementary Figure 1 ).

Meanwhile, the changes of AUEC_{0-3 h} relative to baseline for plasma glucose in 50 mg cetagliptin, 100 mg cetagliptin, sitagliptin, and placebo were -4.97, -2.76, -0.66, and 1.61 h*mmol/L, respectively. The corresponding changes for insulin were 219.90, 292.18, 115.99, and 82.68 h*mmol/L, respectively. Changes for C-peptide were 1851.30, 1761.48, 1046.88, and 334.33 h*mmol/L, respectively. Changes for glucagon were -72.70, -7.21, -26.29, and 32.17 h*mmol/L, respectively ( Table 5 ). These results indicated that a trend of decline in plasma glucose and a trend of improvement of pancreatic β-cell function were observed after administration of cetagliptin.

The two-compartmental model was chosen as the structural model. An exponential variability error model was used to describe inter-individual variability, and a proportional error model was selected to account for residual variability. Covariate searches with the stepwise method identified TBIL as significant effect on V2, and covariate TBIL was included in the final population PK model. After including the covariates, the -2LL value of the model decreased from 4335 to 4326. (Δ-2LL=9). The final model parameters are summarized in Supplementary Table 1 . The Goodness-of-Fit (GOF) plots of the final model are shown in Supplementary Figures 2B, C . The GOF plots showed that the final model fitted most of the observed data well, but there were individual data deviations. The plots for CWRES vs. Time or population predictions are shown in Supplementary Figure 2A . Most CWRES were symmetrically distributed on both sides of the line (y=0) without significant deviation.

The resampling process was repeated 500 times by bootstrapping, and the median parameter values and 95% confidence interval (95% CI) results are summarized in Supplementary Table 1 . The median values were similar to those estimated by the final model, and the parameter estimates from the original data were all within 95% CI. Therefore, the final model has good stability.

The VPC results are shown in Figure 5 . In the VPC plots, the 90% prediction interval (90% PI) is the region between the predicted 5th and 95th percentiles. Most of the observations fell within 90% PI. The 5th, 50th and 95th quantiles of the observed values showed a similar trend to the 5th, 50th and 95th quantiles of the predicted values. The figure indicates that the final model has sufficient predictive power.

The population PK/PD model of cetagliptin was established using the Sigmoid-E_max model. The mixed error model illustrated the residual variability. The stepwise method was used for covariate screening, and no covariates were found to significantly affect PK/PD parameters. The estimates, relative standard errors (RSE), and inter-individual variation of the final model parameters are summarized in Supplementary Table 1 . The GOF plots of the final population PK/PD model are shown in Supplementary Figures 3B, C . The results showed that the final model fitted the observed data well without significant deviation. The plots for CWRES vs. Time or population predictions are shown in Supplementary Figure 3A . Most of the CWRES were distributed between ±4, but the CWRES showed obvious trend changes, suggesting that the model needs further optimization.

The resampling process was repeated 500 times by bootstrapping, and the median parameter values and 95% confidence interval (95% CI) results are summarized in Supplementary Table 1 .The median values were similar to the parameter values estimated by the final model, and those estimated by the model were all within 95% CI. As a result, the final model has good stability.

The Visual Predictive Check (VPC) results are shown in Figure 6 . In the VPC plots, the 90% prediction interval (90% PI) is the region between the predicted 5th and 95th percentiles. Most of the observations fell within 90% PI. The 5th, 50th and 95th quantiles of the observed values showed a similar trend to the 5th, 50th and 95th quantiles of the predicted values. The figure shows that the final model has adequate predictive capability.