Abstract
Aims
HMG-CoA reductase inhibitors are available for use in low density lipoprotein-cholesterol (LDL-C) lowering therapy. The purposes of this study were to develop a population pharmacodynamic (PPD) model to describe the time course for the LDL-C lowering effects of statins and assess the efficacy of combination therapy based on electronic medical records.
Methods
Patient backgrounds, laboratory tests and prescribed drugs were collected retrospectively from electronic medical records. Patients who received atorvastatin, pitavastatin or rosuvastatin were enrolled. A physiological indirect response model was used to describe the changes observed in LDL-C concentrations. The PPD analysis was performed using nonmem 7.2.0 with the first order conditional estimation method with interaction (FOCE-INTER).
Results
An indirect response Imax model, based on the 2863 LDL-C concentrations of 378 patients, successfully and quantitatively described the time course for the LDL-C lowering effects of three statins. The combination of ezetimibe, a cholesterol absorption inhibitor, decreased the LDL synthesis rate (Kin) by 10.9%. A simulation indicated that the combined treatment of ezetimibe with rosuvastatin (2.5 mg day−1) led to superior clinical responses than those with high doses of rosuvastatin (5.0 mg day−1) monotherapy, even in patients with higher baseline LDL-C concentrations prior to the treatment.
Conclusions
A newly constructed PPD model supported previous evidence for the beneficial effects of ezetimibe combined with rosuvastatin. In addition, the established framework is expected to be applicable to other drugs without pharmacokinetic data in clinical practice.
Keywords: electronic medical record, LDL cholesterol, population pharmacodynamics, statins
What is Already Known about this Subject
There is currently no population pharmacodynamic model to describe the time course for the low density lipoprotein-cholesterol (LDL-C) lowering effects of statins with regards to covariate factors (e.g. co-medicated drugs), which may enhance clinical efficacy, based on information obtained from electronic medical records in a general hospital.
What this Study Adds
The indirect response model successfully and quantitatively described the time course for the LDL-C lowering effects of statins (atorvastatin, pitavastatin and rosuvastatin) and the efficacy of ezetimibe.
Patients with higher baseline LDL-C concentrations are recommended to receive a combination with ezetimibe rather than an increased dose of rosuvastatin.
The established framework is expected to be applicable to other drugs without pharmacokinetic data in clinical practice and may detect influential factors for drug therapy.
Introduction
Hydroxy-methyl-glutaryl coenzyme A (HMG-CoA) reductase inhibitors (statins) are widely used to treat hypercholesterolaemia. Statins are available for use in intensive and aggressive low density lipoprotein-cholesterol (LDL-C) lowering therapy. They have also been shown to have beneficial effects by increasing high density lipoprotein-cholesterol (HDL-C) and decreasing triglyceride concentrations [1]. Statins are competitive inhibitors of the HMG-CoA reductase responsible for a rate-limiting step in cholesterol biosynthesis at the cellular level [2,3]. By inhibiting HMG-CoA reductase, statins promote the expression of LDL receptors on hepatocytes, which lowers both LDL and total serum cholesterol concentrations due to increased uptake from the circulation [3].
Lipid-modifying therapies have been shown to decrease the risk of coronary heart disease (CHD) in patients with hypercholesterolaemia and those with relatively normal concentrations of LDL-C. Expert panels have recommended lipid-modifying therapy to decrease elevated cholesterol concentrations, particularly LDL-C [4,5]. Guidelines in Japan have established target LDL-C concentrations according to different risk categories depending on the number of risk factors other than LDL-C [6]. However, large interindividual variability was previously observed in the LDL-C lowering response to statins [7]. Previous studies reported difficulties in achieving the target LDL-C concentrations recommended by the guidelines in an adequate number of patients treated with statin monotherapy [5,8–10]. These patients could receive an increased dose of a statin or a combination of other lipid lowering medicines [11]. However, information based on evidence to support appropriate individual treatments is currently insufficient. Therefore, information to individualize dose regimens and guide decisions regarding the initial dose, dose escalation schedule and combination therapy will be useful.
Population pharmacodynamic (PPD) analysis with non-linear mixed-effect modelling is a method used to describe the relationship between the dosing regimen and effect (or response) data, and permits an assessment of the influence of covariates (e.g. age, gender and co-administered drugs) [12]. Since the concentrations of most drugs are not routinely measured in general hospitals, PPD analysis without pharmacokinetic (PK) data represents a practical method to assess the above mentioned information.
The aims of this study were to (i) develop a PPD model to describe the LDL-C lowering process in Japanese adult patients treated with atorvastatin, pitavastatin or rosuvastatin based on electronic medical records, (ii) assess the PPD model, developed for its predictability of the efficacy of rosuvastatin monotherapy and in combination with ezetimibe, thereby supporting the improved efficacy of the combination therapy through model-based analysis and (iii) suggest an established framework as a tool that is applicable to the assessment of the effects of other drugs without pharmacokinetic data in clinical practice.
Methods
Study design and patients
Patient backgrounds (e.g. gender and age), laboratory tests and prescribed drugs were collected retrospectively from electronic medical records available at the Fukuoka Tokushukai Medical Center (Fukuoka, Japan). Monitoring LDL-C concentrations was set as a routine laboratory test in Japan. Therefore, these concentrations could also be obtained prior to the statin treatment. All data including LDL-C concentrations were collected at the time of each visit, and how often LDL-C was measured and the time between visits was not standardized (but followed the physician's directions). All medical staff (e.g. physicians, nurses and pharmacists) asked patients about drug compliance to confirm drug exposure at each visit. The physician increased the dose of a statin or prescribed co-medication(s) when LDL-C concentrations had not sufficiently decreased. We were able to obtain all concomitant medication information (including daily dose and the duration), which was prescribed in this hospital (the Fukuoka Tokushukai Medical Center) during the study periods, from electronic medical records. If a patient visited doctors in other hospitals, we confirmed information about the concomitant medications by medical referral letters. Therefore, the concomitant medical information was available with temporal data by electronic medical records and medical referral letters. The study protocol was approved by the Fukuoka Tokushukai Ethics Committee (ethics approval number 250404). Patients who received atorvastatin (Lipitor), pitavastatin (Livalo), or rosuvastatin (Crestor) were enrolled between November 2009 and October 2011. In the present study, we focused on more potent statins. The usual initial dose for atorvastatin was 5–20 mg once daily (pre- or post-food) and that for pitavastatin was 1–2 mg once daily in the evening. However, 4 mg could be administered to patients requiring a marked reduction in LDL-C concentrations. Rosuvastatin was administered at 2.5–5 mg once daily (pre- or post-food) as a typical initial dose. This could be increased, if necessary, at intervals of 4 weeks up to 10 mg. Patients had no history of statin treatment prior to the study. Patients who had serum LDL-C concentrations <60 mg dl−1 before the study or were treated with multiple statins were excluded.
Data analysis
The PPD analysis was performed using nonmem 7.2.0 (Icon Development Solutions, Ellicott City, MD) with the first order conditional estimation method with interaction (FOCE-INTER). Graphic processing of the nonmem output was performed with Xpose (version 4.3.2) for the statistical package R (version 2.13.1) and S-PLUS (version 8.1; Mathematical Systems, Inc., Tokyo, Japan) [13].
Population pharmacodynamic analysis
A physiological indirect response model [14] was used to describe changes in LDL-C levels as follows (Figure 1):
Figure 1.
The final population pharmacodynamic model describing the time course for the low density lipoprotein-cholesterol (LDL-C) lowering effects of statins. Kin, LDL-C synthesis rate constant; Kout, LDL-C elimination rate constant; Baseline, baseline LDL-C concentration before the statin treatment; Dose, daily dose of statins; Imax, maximum drug effect; ID50, daily dose resulting in 50% of Imax
 |
where Kin, Kout, and INH are the LDL-C synthesis rate constant, LDL-C elimination rate constant and drug inhibition, respectively. Baseline represents LDL-C concentrations before the statin treatments, and the relationships between Kin, Kout and baseline are defined by Kin = Baseline × Kout. The inhibition effect (INH) was related to the dose as follows:
 |
where Imax, ID50, and Dose are the maximum value of the inhibitory effect ranging from 0 and 1, daily dose resulting in 50% of Imax, and daily dose, respectively.
The exponential error model was used to describe interindividual and residual variabilities. Various covariance structures with different variabilities were modelled and tested by applying the $OMEGA block option in nonmem. A basic population model was selected based on Akaike's information criterion (AIC). Age, gender, and co-administered drugs (ezetimibe, fenofibrate, bezafibrate and tocopherol nicotinate) were selected as candidates for the covariate. Covariate selection was performed based on differences in the objective function value (OFV) estimated by nonmem between hierarchical models. Forward inclusion and backward elimination were used to develop the covariate model. The significance levels for forward inclusion and backward elimination were set at 0.01 and 0.001, respectively. The adequacy of the constructed PPD model was assessed by goodness of fit (GOF) plots at each step during development of the model. GOF was investigated using the plots of observations vs. population predictions (PRED) and individual prediction (IPRED), conditional weighted residuals (CWRES) vs. time after administration [15], CWRES vs. PRED and absolute individual weighted residuals (IWRES) vs. IPRED. The robustness of the final PPD model was confirmed using bootstrap analysis, a prediction-corrected visual predictive check (pcVPC) and normalized prediction distribution errors (NPDE). The median values and 95% confidence intervals (CI) for the parameter estimates obtained from 1000 bootstrap replicates of the original data set were compared with the original population parameters. A 90% prediction interval was determined for the pcVPC from the 5th and 95th percentiles of the simulated dependent data at each time point and was compared with the original data. A total of 1000 simulations were performed for the pcVPC. Bootstrap analysis and the pcVPC were performed with the software package Perl-speaks-nonmem [16].
Simulation for the dose−response relationship of statins
Using the final PPD model, LDL-C concentrations arising from dosages of 5, 10, 15, and 20 mg of atorvastatin, 1, 2, 3, and 4 mg of pitavastatin and 2.5, 5, 7.5, and 10 mg of rosuvastatin once a day for 12 weeks were simulated (5000 individuals in each dose level in each drug), and the maximum LDL-C reduction (%) and time to the maximum LDL-C reduction (weeks) were then calculated for the three statins.
Simulation to assess the impact of ezetimibe
We performed simulations to assess the impact of ezetimibe. LDL-C concentrations were initially simulated using the final PPD model 5 weeks after starting rosuvastatin monotherapy or a combination with ezetimibe. The percentage of patients who achieved the target LDL-C level (< 100 mg dl−1) was then calculated for each group. The Adult Treatment Panel III of the National Cholesterol Education Program set the goal for LDL-C lowering in high risk patients, who were established CHD and CHD risk equivalents, to <100 mg dl−1 [5]. The initial LDL-C concentrations of patients were assumed to be 140, 160, 180, 200, 220, or 240 mg dl−1. The dosing schedules were set to 2.5 mg rosuvastatin, 5 mg rosuvastatin, or 2.5 mg rosuvastatin plus ezetimibe once a day. Each Monte Carlo simulation generated LDL-C concentrations for 5000 individuals per dose level and baseline level. The effects of drug exposure/LDL-C window on the simulation and the percentages of patients who achieved the target LDL-C concentrations (in addition to <100 mg dl−1, we calculated <90 and <150 mg dl−1 as targets) were also calculated for each group. Monte Carlo simulations and data processing were performed by nonmem and R, respectively.
Results
Data description
A total of 2863 LDL-C concentrations from 378 patients treated with atorvastatin (n = 149), pitavastatin (n = 45), and rosuvastatin (n = 184) were available. The time courses of the LDL-C profiles before and after the statin treatments are shown in Figure 2. Median changes in LDL-C concentrations at 5 weeks (time required for the maximum response) after the atorvastatin, pitavastatin and rosuvastatin treatments were from 151 mg dl−1 at the baseline level to 86, 145 to 103, and 157 to 95 mg dl−1, respectively. Patient demographics and characteristics are summarized in Table 1. The median age of the three statin groups was 62 years. The median of the dosing periods for the atorvastatin, pitavastatin and rosuvastatin therapy were 362, 437 and 304 days, respectively.
Figure 2.
Low density lipoprotein-cholesterol (LDL-C) profiles of the three statins (A), atorvastatin (B), pitavastatin (C) and rosuvastatin (D). The grey lines represent spline curves
Table 1.
Patient characteristics (n = 378)
| Characteristics | Atorvastatin | Pitavastatin | Rosuvastatin |
|---|---|---|---|
| Number of patients (male/female) | 149 (106/43) | 45 (27/18) | 184 (119/65) |
| Age (years) | 62 (31–89) | 64 (42–84) | 61 (27–91) |
| Number of patients per dose (daily dose, mg day−1)* | 106/55/2/2 (5/10/15/20) | 28/23/2/2 (1/2/3/4) | 151/40/2/1 (2.5/5/7.5/10) |
| Percentage frequency of patients per dose (daily dose, mg day−1) | 64.2/33.3/1.2/1.2 (5/10/15/20) | 50.9/41.8/3.6/3.6 (1/2/3/4) | 77.8/20.6/1.0/0.5 (2.5/5/7.5/10) |
| Number of LDL-C samples per patient | 7 (1–25) | 5 (2–21) | 7 (1–26) |
| Dosing period (days) | 362 (28–854) | 437 (10–744) | 304 (1–766) |
| Laboratory test | |||
| LDL-C (mg dl−1) | 151 (71–359) | 145 (81–232) | 157 (78–310) |
| HDL-C (mg dl−1) | 49 (28–126) | 52 (28–106) | 49 (19–93) |
| Total-C (mg dl−1) | 232 (144–473) | 222 (154–326) | 236 (112–392) |
| TG (mg dl−1) | 153 (42–542) | 138 (64–575) | 153 (40–807) |
| CPK (IU l−1) | 104 (26–2420) | 101 (35–513) | 88 (21–4200) |
| Number of patients who received the combination therapy | |||
| Fenofibrate | 1 | 0 | 2 |
| Bezafibrate | 0 | 0 | 1 |
| Ezetimibe | 0 | 0 | 12 |
| Tocopherol nicotinate | 1 | 0 | 6 |
HDL-C, high density lipoprotein-cholesterol; LDL-C, low density lipoprotein-cholesterol; Total-C, total cholesterol; TG, triglycerides; CPK, creatine phosphokinase. Data are shown as medians (minimum–maximum) unless otherwise specified.
Data may include multiple responses from the same individuals because of dosage changes.
Population pharmacodynamic model
The time course for the LDL-C lowering effects of statins was described by the physiological indirect response model (Figure 1). Statins show a delay in the occurrence of LDL-C lowering effects relative to plasma concentrations [17]. Therefore, the indirect response model describing this delay was selected. Statins inhibited the LDL-C synthesis rate constant (Kin) according to an Imax model with a common Imax (0.567) and different ID50 for each statin (Table 2). No significant difference was observed in the Imax and baseline values between the statins. The addition of a covariance structure did not significantly decrease the OFV. Ezetimibe for INH (P < 0.001) and age for baseline (P < 0.001) were significant covariates for the pharmacodynamics of statins based on nonmem analysis. The regression equations for each parameter in the final PPD model were INH = Imax × Dose/(ID50 + Dose) + 0.109 × ezetimibe (for ezetimibe, where 0 indicates the statin monotherapy and 1 indicates the addition of ezetimibe to the statin therapy), Baseline (mg dl−1) = 152 × (age/62)−0.240 and Kin (mg dl−1 day−1) = 32.8. The co-administration of ezetimibe inhibited Kin by 10.9%. GOF plots revealed the high predictive performance of the final PPD model (Figure 3A and B), and systematic deviations were not observed (Figure 3C, D and E). GOF plots also showed good predictive performance in patients receiving the combination with ezetimibe (Figure 3F and G), and no systematic deviations were observed (Figure 3H, I, and J). The estimated parameters are summarized in Table 2, with the median and 95% CIs estimated from 1000 bootstrap resamplings. The median values of the estimates from bootstrapping were very similar to the population estimates in the final PPD model, and the significance of covariates was further verified by the finding that the 95% CIs of all parameters did not include 0. The pcVPCs in 149 atorvastatin-treated, 45 pitavastatin-treated, 172 rosuvastatin-treated, and 12 rosuvastatin plus ezetimibe-treated patients are shown in Figure 4. These results suggested that the final PPD model described the time course for the LDL-C lowering effects of statins well because 10.4%, 11.7%, and 9.9% of the observed LDL-C concentrations were outside the 90% prediction interval in patients receiving atorvastatin, pitavastatin, and rosuvastatin monotherapy, respectively. The QQ plot of the distribution of the NPDE vs. the theoretical N(0, 1) distribution and histogram of the NPDE are presented in Figure 5. The NPDE was expected to follow the N(0, 1) distribution. The mean and variance of NPDE were −0.0113 and 0.972, respectively. Individual plots of the observed and predicted LDL-C concentrations are shown in Figure 6. Individual changes in the time course of LDL-C concentrations after the treatment with statins was described well by IPRED.
Table 2.
Parameter estimates and results of 1000 bootstrap replicates from the final model
| Parameter | Estimate (RSE, %) | Shrinkage (%) | 1000 bootstrap samples | ||
|---|---|---|---|---|---|
| Median | 95% LLCI | 95% ULCI | |||
| Fixed effects | |||||
| Baseline (mg dl−1) | 152 (1.06) | − | 152 | 148 | 155 |
| Kin (mg dl−1 day−1) | 32.8 (8.81) | − | 32.7 | 28.0 | 39.2 |
| Imax | 0.567 (7.72) | − | 0.568 | 0.497 | 0.690 |
| ID50, Atorvastatin (mg) | 2.22 (32.3) | − | 2.24 | 1.16 | 4.27 |
| ID50, Pitavastatin (mg) | 0.860 (25.6) | − | 0.872 | 0.521 | 1.47 |
| ID50, Rosuvastatin (mg) | 1.04 (29.5) | − | 1.05 | 0.548 | 1.90 |
| PWage for Baseline | −0.240 (29.8) | − | −0.242 | −0.380 | −0.106 |
| INHEZT | 0.109 (18.9) | − | 0.110 | 0.0647 | 0.149 |
| Interindividual variability | |||||
| Baseline (%) | 15.0 (12.8) | 18.3 | 14.9 | 13.0 | 16.6 |
| Imax (%) | 41.4 (27.9) | 40.3 | 41.3 | 30.4 | 58.3 |
| ID50 (%) | 55.4 (41.7) | 49.2 | 53.4 | 29.7 | 80.3 |
| Residual variability | |||||
| σ2 (%) | 15.2 (2.94) | 8.4 | 15.1 | 14.2 | 16.0 |
RSE, relative standard error; 95% LLCI, lower limit of the 95% confidence interval; 95% ULCI, upper limit of the 95% confidence interval; Baseline, baseline LDL-C concentration before the statin treatment; Kin, LDL-C synthesis rate constant; Imax, maximum drug effect; ID50, daily dose resulting in 50% of Imax; PWage for baseline, power exponent of age for baseline; INHEZT, inhibition ratio of Kin in ezetimibe plus statin therapy; σ2, proportional residual variance.
Figure 3.
Goodness of fit plots of the final pharmacodynamic model in patients receiving statin monotherapy (A–E) and in combination with ezetimibe (F–J). Population predictions were made using population mean parameters. Individual predictions were obtained using individual empirical Bayesian estimated parameters. The solid lines represent the line of identify (A, B, F and G) and y = 0 (D, E, I and J). The dashed grey lines represent spline curves
Figure 4.
Prediction-corrected visual predictive check plots for low density lipoprotein-cholesterol (LDL-C) after the start of the atorvastatin (A), pitavastatin (B), rosuvastatin (C and D) monotherapy, and in combination with ezetimibe (E). The grey open circles represent the observed LDL-C. The solid lines and dashed lines represent the predicted median and 90% prediction intervals, respectively. C and D show all treatments (−5 to 120 weeks) and (−5 to 10 weeks) treatment periods, respectively
Figure 5.
Normalized prediction distribution error (NPDE) analysis for the final model. The QQ-plot of the distribution of the NPDE vs. the theoretical N(0, 1) distribution (A). The histogram of the distribution of the NPDE with the density of the standard Gaussian distribution overlaid (B)
Figure 6.
Observed and predicted low density lipoprotein-cholesterol (LDL-C) concentrations in typical individuals. The open circles represent observed LDL-C concentrations. The solid lines and dashed lines represent individual Bayesian predicted LDL-C concentrations and population predicted LDL-C concentrations, respectively. The top, middle, and bottom plots show typical individuals treated with atorvastatin, pitavastatin and rosuvastatin, respectively
Simulation for the dose–response relationship of statins
The maximum LDL-C reduction (%) and time to the maximum LDL-C reduction (weeks) at different dosage schedules were simulated for the three statins (Table 3). Simulations were performed based on the final PPD model for the treatment duration of 12 weeks. The median of the maximum LDL-C reduction increased according to increases in the daily dose of statins. Meanwhile, the median of time to the maximum reduction was approximately the same irrespective of the daily dose of statins. The maximum effect was expected after 4 to 5 weeks of treatment.
Table 3.
Simulated maximum LDL-C reduction and time to the maximum effect (n = 5000)
| Daily dose (mg day−1) | Maximum LDL-C reduction (%)* | Time to the maximum effect (weeks)† | ||
|---|---|---|---|---|
| Median | 95% PIs | Median | 95% PIs | |
| Atorvastatin | ||||
| 5 | 38.4 | 20.5–57.2 | 4.3 | 3.0–6.0 |
| 10 | 45.3 | 27.0–63.2 | 4.4 | 3.1–6.1 |
| 15 | 48.4 | 30.7–66.2 | 4.4 | 3.1–6.3 |
| 20 | 50.6 | 32.5–68.0 | 4.4 | 3.1–6.1 |
| Pitavastatin | ||||
| 1 | 29.5 | 14.6–48.8 | 4.1 | 2.9-5.7 |
| 2 | 38.8 | 21.2–57.8 | 4.3 | 3.0–6.0 |
| 3 | 43.1 | 25.1–61.6 | 4.3 | 3.1–6.1 |
| 4 | 45.6 | 28.0–64.5 | 4.4 | 3.1–6.1 |
| Rosuvastatin | ||||
| 2.5 | 38.9 | 21.7–57.7 | 4.3 | 3.0–6.0 |
| 5 | 46.0 | 28.1–64.0 | 4.4 | 3.1–6.1 |
| 7.5 | 49.0 | 30.4–67.1 | 4.4 | 3.1–6.1 |
| 10 | 50.6 | 32.3–68.1 | 4.4 | 3.1–6.3 |
Percentage changes from baseline after 12 weeks of treatment.
Time to achieve the maximum LDL-C reduction. PIs, 2.5th–97.5th percentiles.
Simulation to assess the impact of ezetimibe
The impact of ezetimibe was assessed by Monte Carlo simulations because the effects of ezetimibe were only detected as a covariate of co-administered drugs in the final PPD model, and all patients who were co-administered ezetimibe received rosuvastatin (Table 1). Therefore, we focused on combination therapy with rosuvastatin and ezetimibe. As a result of Monte Carlo simulations based on the final PPD model, the probability of achieving an LDL-C concentration of <100 mg dl−1 after 5 weeks of treatment with regard to baseline levels of LDL-C was simulated (Figure 7). The effects of the daily dose of rosuvastatin and combination with ezetimibe on this probability were simulated. The baseline concentration before the statin treatment was an important determinant for the success rate, and the rate was lower in patients with high baseline concentrations. Higher probability was expected at 5 mg day−1 of rosuvastatin than at 2.5 mg day−1 at any baseline concentration of LDL-C. On the other hand, ezetimibe plus 2.5 mg day−1 of rosuvastatin showed a superior probability than that with 5 mg day−1 of rosuvastatin monotherapy in any baseline LDL-C concentration. When the target LDL-C concentration was set at two different conditions (<90 and 150 mg dl−1), ezetimibe plus 2.5 mg day−1 of rosuvastatin also showed a superior probability than that with 5 mg day−1 of rosuvastatin monotherapy in higher baseline LDL-C concentrations.
Figure 7.
Simulation of the success rates of rosuvastatin and rosuvastatin plus ezetimibe at various baseline concentrations of low density lipoprotein-cholesterol (LDL-C) based upon the final population pharmacodynamic model (5000 individuals in each baseline LDL-C concentration). Success rates represent the percentages of patients who achieved the target LDL-C concentration (A: <90 mg dl−1, B: <100 mg dl−1, and C: <150 mg dl−1) after 5 weeks of treatment. 
, rosuvastatin (2.5 mg day−1); 
, rosuvastatin (5 mg day−1); ▀, rosuvastatin (2.5 mg day−1) + ezetimibe
Discussion
In the present study, we developed a PPD model to describe the time course for LDL-C lowering effects after treatment with statins (atorvastatin, pitavastatin and rosuvastatin) using data from electronic medical records in a general hospital. In addition, based on the final PPD model, the effects of ezetimibe and baseline LDL-C concentrations on the success rate of the statin therapy were also simulated quantitatively. Furthermore, the individual time course of LDL-C concentrations was successfully described.
Besides the Imax model, we attempted to use a linear model in the model-building steps (AIC = 20912.58). A PPD model assuming that stains stimulated the elimination of LDL-C was also tested (AIC = 19520.45). However, the physiological indirect response model that considered the inhibition of LDL-C production gave the best description (AIC = 19491.15). Statins inhibit the activity of HMG-CoA reductase, which catalyzes the synthesis of mevalonate, a rate-limiting step in cholesterol biosynthesis [2,3]. Considering the mechanism of action of statins, it was reasonable that the rate of change in LDL-C concentrations over time was described by the indirect response model with inhibition of the LDL-C synthesis rate constant, Kin. To model the residual variability, several types of models [i.e. an additive error model (AIC = 19790.92), proportional error model (19441.79), and combined additive and proportional error model (19443.80)] were tested, and residual variability was best described with a proportional error model.
Faltaos et al. described the time course for the LDL-C lowering effects using a two compartment indirect response pharmacodynamic (PD) model without PK data [17]. Although we attempted to introduce their two compartment model to our PD data, the OFV was similar to that from our present model (data not shown). Kim et al. recently investigated the population PK–PD of simvastatin and simvastatin acid in healthy Korean volunteers using the indirect response PD model that considered the inhibition of LDL-C production [18]. Their estimated LDL-C synthesis rate constant (Kin, 1.14 mg dl−1 h−1) was similar to our value (1.37 mg dl−1 h−1). The Kin value has not yet been determined in humans. However, two PPD modelling studies reported the same value even in different data sets.
In the present study, the Kin value was estimated to be 10.9% lower in patients administered ezetimibe plus rosuvastatin than in patients receiving rosuvastatin monotherapy (Table 2). Ezetimibe is a strong inhibitor of cholesterol and phytosterol absorption, which has been shown to lead to a 15–20% decrease in plasma LDL-C concentrations [19,20]. It binds to a Niemann-Pick C1-Like 1 transporter, located in the small intestine, and blocks the absorption of both food-derived cholesterol and bile acid-derived reabsorbed cholesterol [21]. Ezetimibe has also been used as a potential additive lipid lowering agent in patients already receiving statins. Previous clinical trials reported that ezetimibe plus ongoing statin therapy lowered LDL-C concentrations by an additional 25.1%, while a reduction of 3.7% was observed in the placebo-statin group [22]. When ezetimibe was added to either atorvastatin 10 mg day−1 or rosuvastatin 2.5 mg day−1, a further 24.7% reduction in LDL-C was reported as opposed to only a further 16.4% reduction when the statin dose was doubled [23]. Taken together, our final PPD model supported previous evidence of the beneficial effects of ezetimibe combined with rosuvastatin therapy. We also attempted co-medication as a predictor for other parameters such as Kout and Imax. However, no significant effect was observed for all candidate co-medications, except for ezetimibe. Considering the mechanism of action of ezetimibe, we incorporated ezetimibe as a covariate for Kin.
LDL-C concentrations are known to increase slightly with age in young or middle-aged adults; however, total and LDL-C concentrations have been shown to decrease in the elderly (≥ 65 years of age) [24–28]. As shown in Table 2, a reduction in baseline LDL-C concentrations was observed with an increase in age. Because the median age in our population was 68 years old, the present results are consistent with previous findings.
The maximum LDL-C reduction (%) and time to reach the maximum effect of statins were simulated using the final PPD model (Table 3). Saku et al. investigated the safety and efficacy of atorvastatin, rosuvastatin and pitavastatin in Japanese patients with hypercholesterolaemia. The mean LDL-C reductions observed in their study were 44% at 10 mg day−1 atorvastatin, 42% at 2.5 mg day−1 rosuvastatin and 41% at 2 mg day−1 pitavastatin, which were consistent with our simulation results [29]. In addition to the reduction rate, previous studies reported that the time to reach the maximum effect of statins was 4 to 6 weeks, which was similar to our results (median period 4.1–4.4 weeks) [30–32].
As shown in Figure 6, we predicted the time course of LDL-C concentrations after the statin treatment individually. The LDL-C concentrations of the population prediction were elevated stepwise after the statin treatment in some individuals (e.g. A2 and R3 subjects) because their daily doses of statins were reduced during treatments. Although individual age, the daily dose of the statin, actual LDL-C measurements and ezetimibe were prerequisite information for this prediction, these visual plots may be useful to instruct patients of their own medication plan. However, external validation is necessary to verify the applicability of the final PPD model. Here, as for the potency of each statin, it should be focused on the relative potency rather than the absolute potency due to the high η-shrinkage for ID50 of about 40% and resultant possibility of inaccurately estimating the latter.
The results of this study must be considered within the context of several limitations because this was a retrospective study based on electronic medical records. First, the number of patients who received rosuvastatin therapy in combination with ezetimibe appeared to be too small for a reliable assessment. Patients who received the combination therapy with ezetimibe were not identical to those who received rosuvastatin monotherapy (i.e. not a crossover design). The median (range) value of baseline LDL-C concentrations for the combination therapy group was 145 mg dl−1 (117–310 mg dl−1). Because the range of baseline LDL-C concentrations for the combination therapy group included 140–240 mg dl−1, which was chosen for the simulation, the simulation result comparing the two groups for this selected range of baseline LDL-C concentrations was considered to be appropriate. Second, it could not be confirmed whether individual electronic medical records covered all medication information completely. However, we believe that almost all medication information was covered by the electronic medical records because the medical staff asked about all medicines (including not only previously used medicines, but also healthy foods) individually and recorded almost all their findings on the electronic medical records. Finally, this study lacked information regarding adherence to statins, diet and exercise. Therefore, these factors could not be incorporated into the model.
In summary, the PPD analysis successfully and quantitatively described the time course for the LDL-C lowering effects of atorvastatin, pitavastatin and rosuvastatin using data from electronic medical records. A newly constructed PPD model supported previous evidence of the beneficial effects of ezetimibe combined with rosuvastatin therapy. In addition, the established framework is expected to be applicable to other drugs without PK data in clinical practice.
Competing Interests
All authors have completed the Unified Competing Interest form at http://www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare no support from any organization for the submitted work, no financial relationships with any organizations that might have an interest in the submitted work in the previous 3 years and no other relationships or activities that could appear to have influenced the submitted work.
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