A pharmacokinetics‐based approach to the monitoring of patient adherence to atorvastatin therapy

Abstract The inadequate adherence of patients whose hyperlipidemia is treated with atorvastatin (ATR) to medical instructions presents a serious health risk. Our aim was to develop a flexible approach based on therapeutic drug monitoring (TDM), nonparametric population pharmacokinetic modeling, and Monte Carlo simulation to differentiate adherent patients from partially and nonadherent individuals in a nonrandomized, unicentric, observational study. Sixty‐five subjects were enrolled. Nonparametric, mixed‐effect population pharmacokinetic models of the sums of atorvastatin and atorvastatin lactone concentrations (ATR+ATRL) and of the concentrations of the acid and lactone forms of ATR and its 2‐ and 4‐hydroxylated pharmacologically active metabolites (ATR+MET) were elaborated by including the TDM results obtained in 128 samples collected from thirty‐nine subjects. Monte Carlo simulation was performed based on the elaborated models to establish the probabilities of attaining a specific ATR+ATRL or ATR+MET concentration in the range of 0.002–10 nmol (mg dose)−1 L−1 at 1–24 h postdose by adherent, partially adherent, and nonadherent patients. The results of the simulations were processed to allow the estimation of the adherence of further 26 subjects who were phlebotomized at sampling times of 2–20 h postdose by calculating the probabilities of attaining the ATR+ATRL and ATR+MET concentrations measured in these subjects in adherent, partially adherent, and nonadherent individuals. The best predictive values of the estimates of adherence could be obtained with sampling at early sampling times. 61.54% and 38.46% of subjects in the adherence testing set were estimated to be fully and partially adherent, respectively, while in all cases the probability of nonadherence was extremely low. The evaluation of patient adherence to ATR therapy based on pharmacokinetic modeling and Monte Carlo simulation has important advantages over the collection of trough samples and the use of therapeutic ranges.

A recent meta-analysis has shown that, in patients who had pathological serum lipid levels, statin-based therapy resulted in a 24% reduction in the occurrence of major coronary events for each 1.0 mmol/L decrease in low-density lipoprotein cholesterol (LDL-C) levels, regardless of age. [3][4][5] The primary advantage of administering atorvastatin {(3R,5R)-

7-[2-(4-fluorophenyl)-3-phenyl-4-(phenylcarbamoyl)-5-propan-2-
ylpyrrol-1-yl]-3,5-dihydroxyheptanoic acid, ATR} over other statins is the negligible extent of its renal excretion which eliminates the need of dose adjustment due to renal impairment. However, the cytochrome 450 3A4-mediated hepatic metabolism of ATR is extensive, resulting in the formation of 2-hydroxy-(2OATR) and 4-hydroxy atorvastatin (4OATR), as well as of the lactonized forms (ATRL, 2OATRL, and 4OATRL, Figure 1) which causes its pharmacokinetics to be complex. [6][7][8][9][10] According to the American Heart Association, the incidence of statin-associated muscular symptoms and statin-induced diabetes mellitus, conditions prompting the discontinuation of statin therapy, is approximately <0.1% and 0.2% per year of therapy, respectively. 11 However, a considerably larger proportion of patients discontinues ATR therapy beyond the first year of treatment, presenting a very serious health risk on the long term. [12][13][14] The underlying reasons for abandoning the otherwise safe and comfortable measures are currently unknown. Consequently, establishing an evidence-based procedure for the verification of adherence would be an important first step in identifying these reasons and, ultimately, in improving the clinical outcome of ATR therapy.
Therapeutic drug monitoring (TDM) is a tool for the clinical verification of patient adherence to medical instructions with relatively small ambiguity in its performance as compared to other approaches. Recently, a small-scale study conducted with 24 participants has proposed a cut-off concentration of 0.05 nmol (mg dose) −1 L −1 regarding the sum of ATR+ATRL concentrations assayed 24 h post dose to identify individuals who missed at least the last dose (referred to as "partial adherence") with 100% sensitivity and 83% specificity, and those who missed the last three doses or more (referred to as "nonadherent patient") with 100% sensitivity and 100% specificity. Due to the interindividual variability of metabolism, it was nevertheless proposed that the sums of ATR, ATRL, 2OATR, 2OATRL, 4OATR, and 4OATRL (ATR+MET) concentrations, taken as a single entity, should also be evaluated with a 0.1 nmol (mg dose) −1 L −1 cut-off concentration indicating partial adherence. 15 These cut-off concentrations were not based on pharmacokinetic evaluation.
The uncertainties associated with accurate dose times in the outpatient setting confound comparison of a measured concentration to a range or threshold that depends on a specific elapsed time between dose and sample, especially if the target timing is inconvenient for the patient, for example, very early in the morning or late at night. In contrast, population pharmacokinetic modeling based on flexibly timed sampling, combined with Monte Carlo simulation to assess the probability of obtaining such a concentration, allows a more robust estimate than the assessment of trough or other specifically timed concentrations by transforming adherence into a continuous probability rather than a categorical variable. Earlier, Neely has used this approach successfully for verifying the adherence of modeling and Monte Carlo simulation has important advantages over the collection of trough samples and the use of therapeutic ranges.

K E Y W O R D S
adherence, atorvastatin, metabolism, nonparametric pharmacokinetic model, pharmacokinetics, therapeutic drug monitoring F I G U R E 1 Overview of atorvastatin metabolism. CYP3A, Cytochrome P 450 3A a pediatric patient to her voriconazole dosing regimen. 16 We set forth a pharmacokinetics-based clinical laboratory procedure and decision-making algorithm for the TDM of ATR at any time that has passed from drug intake to sample collection.

| Study design and demographics
This research was a nonrandomized, unicentric, observational clinical study approved by the Regional and Institutional Committee of Demographic information on the recruited subjects is summarized in Table 1 (detailed information is provided in Supporting Information 1). Interaction with patients was made on a single occasion for the purposes of the study. Following physical examination and obtaining the written informed consent of the subjects, anthropometric data, habits related to drug intake, physical status, and posology were recorded.
Thirty-nine subjects comprised the model training set. Twentynine subjects took their first dose of ATR (n = 24 and n = 5 receiving 20 mg and 40 mg, respectively) under the supervision of the recruiting clinical team. Ten subjects had a history of treatment with ATR (n = 4 and n = 6 receiving 20 mg and 40 mg, respectively). These subjects were patients well known to the recruiting clinicians, and had been cooperative regarding their treatment. They had previously been requested to omit the last dose of ATR before the visit, were interrogated on the time of the last intake, and took their dose in front of the recruiting clinical team. A single subject disobeyed the instruction and took 20 mg ATR the evening before the visit.

| Laboratory procedures
Laboratory assays were conducted at the Department of Laboratory Medicine, Semmelweis University. A blood sample without any additive was drawn into a 6-mL collection tube immediately before drug intake ( Figure 2, c ini ). Three further blood samples, 6 ml each, were collected from subjects of the model training set at 2, 4, and 6 h post dose (c 2 , c 4 , and c 6 , respectively, Figure 2). Subjects in the adherence testing set donated a single 2-mL native blood sample.
All samples were centrifuged at 4000 g for 10 min immediately following their collection. 200 µL serum separated from c ini , c 2 , c 4 , and c 6 samples, as well as of those collected from subjects of the adherence testing set, was transferred to a 2-mL cryo vial, was frozen, and was allocated for the analysis of ATR and its metabolites.
Sera not analyzed immediately were frozen to −75°C until analysis.

| Data evaluation
Microsoft Excel 2013 and R were used for data evaluation. The results of anti-HMGCR measurements were calculated using Visual predictive checks and functions integrated into Pmetrics TM and the "stats" package of R were employed for the evaluation and optimization of the constructed population pharmacokinetic models.
Linear regression was performed on observed versus predicted concentrations. The mean weighted squared prediction error obtained for alternative models was compared. Student's t test was conducted to display the statistical difference of the mean weighted prediction error (bias) from zero. Kruskal-Wallis test was employed for establishing the deviation of the residuals from normal distribution. The distribution of the probabilities of random effects was checked visually with an accepted shrinkage range of 0%-30%. 24 The comparison was based on the number of support points, −2 × log likelihoods, the Akaike and the Bayesian information criteria. The models were considered to be statistically different from each other at p < .05.

| Pharmacokinetic modeling
The main characteristics of the constructed population pharmacokinetic models are displayed in Figure 3 and Table 2

| Evaluation of the adherence of individual subjects
The probabilities of full, partial, and nonadherence calculated for the subjects of the adherence testing set are displayed in Table 3. Three (1) TPR = number of subjects with dose − normalized concentrations lower than the cut − off in the less adherent group 50000 (2) FPR = number of subjects with dose − normalized concentrations lower than the cut − off in the more adherent group 50000 (3) optimal difference = min( | specificity i − sensitivity i | ) subjects reported taking ATR on the morning of visit. Twenty-three subjects reported to have ingested their last dose the day before.

Based on individual ATR+ATRL and ATR+MET concentrations which
were compared the results of the Monte Carlo simulations, partial adherence was suspected in 10 subjects (38.5%) of the adherence testing set. The individual concentrations provided no ground for assuming nonadherence for any of the subjects (Table 3).

| DISCUSS ION
The verification of patient adherence is a prerequisite for the efficient guidance of pharmacotherapy. Kristiansen and his coworkers have recently made an effort to discriminate between adherent, partially adherent, and nonadherent patients to whom ATR had been prescribed by assaying ATR and its hydroxylated metabolites. 15  Figure 4). Nevertheless, the evaluation both ATR+ATRL and ATR+MET seems to be of benefit in many cases due to the slower turnover of the hydroxylated metabolites.

F I G U R E 3
Patients who undergo adherence testing will, assumably, have taken multiple doses of ATR. To avoid the exclusion of potentially important sources of interindividual variability associated with prolonged ATR use, such as comedication or gut microbial differences, a mixed population of subjects who had a history of treatment, and who received the first dose during the visit, was formed.
Importantly, this decision could be made as the Pmetrics TM package could handle repeat dosing for population modeling and simulation.
The decision to not limit the administered dose of ATR to a single quantity was based on its linear pharmacokinetics. ATR+ATRL and ATR+MET were handled as a single chemical entity for modeling.   Table 2).
Several demographic, physiological, and laboratory parameters were tested as candidate covariates, including anti-HMGCR, the presence of which has been associated with statin myopathy. 26,27 No strong relationship of any of the tested candidates with random-effect pharmacokinetic parameters, or clinical status was identified.
Few data have been published on the absorption kinetics of ATR in human adults. The K a 's of ATR and ATR+ATRL were fixed at 2.59 h −1 and at 3.5 h −1 , respectively, in two earlier studies. 28,29 In

| CON CLUS IONS
The developed methodology allows the complex, probability-based evaluation of adherence to ATR therapy by using tools of bioinformatics currently available at no cost. This approach is considerably more realistic and efficient considering the complexity of the phar-

CO N FLI C T O F I NTE R E S T
The authors have no conflict of interest to declare. Zsáry coordinated the recruitment of subjects, the collection and evaluation of the clinical data, and revised the manuscript.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data obtained after the de-identification of subjects are available from the corresponding author upon a reasonable request.