Introduction

Digoxin is widely prescribed for the treatment of congestive heart failure in clinical practice. Because of its low therapeutic index, narrow safety range and strong side effects, toxicity may also be caused by routine dosage1, 2, 3, 4. Elderly patients with heart failure are more susceptible to toxicity because their impaired renal function may cause the clearance of digoxin to decrease. Therefore, individualized medication of digoxin is of great significance.

Approved by the US FDA in 1999, NONMEM1, 2, 3, 4, 5, 6, 7, 8 is the best model for clinical individualized medication. It was built on the basis of a combination of the classical pharmacokinetic model, the fixed-effect model and the statistical model. The principle of the extended non-linear least squares was applied to estimate the population pharmacokinetic parameters using the patients' sparse plasma concentration data, pathological factors, physiological factors and coadministration.

This paper aimed: 1) to build a population pharmacokinetic basic model of digoxin in 119 older Chinese patients; 2) to analyze the effects of fixed-effect factors such as weight, age, gender, hepatic and renal function, and concomitant medications on this model; 3) to establish the full regression model and the final model; and 4) to determine whether the final model is stable and reliable by intra-validation and clinical applications.

Materials and methods

Data sources

Routine clinical data were retrospectively collected from 119 older patients in the general hospital of the air force, PLA. 113 of the 119 patients (95%) were suffering from varying degrees of congestive heart failure (CHF). The data collected were the patient's age, gender, weight (WT), dosage regimen of digoxin, serum concentration (173 observations), hepatic and renal function including alanine aminotransferase (ALT), aspartate aminotransferase (AST), blood urea nitrogen (BUN), serum creatinine (Cr), and albumin(ALB), as well as concomitant medications including spironolactone (SPI), calcium channel blocker (CCB), nitrate, and propofenone. Patient information is given in Table 1.

Table 1 Summary of patient's information.
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Drug

Digoxin, 0.25 mg/pellet, was from Sine Pharmaceutical Co, Ltd, Shanghai, China.

Inclusion and exclusion criteria

Inclusion criteria

Older patients (over 60 years old) taking digoxin orally for more than 7 d were included in the study.

Exclusion criteria

Patients with serious hepatic and renal dysfunction and digoxin serum concentrations higher than the maximum detection limit or lower than the minimum detection limit were excluded from the study.

Instruments and software

The measurement of digoxin in serum was carried out by fluorescence polarization immunoassay (FPIA) using the TDx-FLx system (Abbott, USA). The minimum detectable concentration for digoxin was 0.2 μg/L4, 7. The population pharmacokinetics analysis of digoxin was performed using NONMEM software (Version V, Level 1.0, Globomax, USA).

Structural pharmacokinetic model

The structural pharmacokinetic model (eg, a one-, two-, or three-compartment model)5 was considered first. Previous studies1, 2, 7 reported that a one-compartment model and the first-order kinetics process could describe the time course of digoxin steady state concentrations in plasma. In this paper, a one-compartment open model was selected as a population structural PK model.

Equations of digoxin PPK basic model

Equations of the digoxin PPK basic model were as follows:

Cl/F=θ1×ExP(ETA(1))

Vd/F=θ2×ExP(ETA(2))

Ka =θ3×ExP(ETA(3))

Y=YPRED+YPRED×ERR(1)+ERR(2)

where Cl, Vd, and Ka represents clearance rate (L/h), apparent volume of distribution (L), and absorption rate constant (h-1), respectively. Since all doses in the present study were given orally and it was impossible to assess the absolute bioavailability (F), the parameters Cl and Vd were interpreted as Cl/F and Vd/F, respectively. The typical population value for Cl/F, Vd/F, and Ka is θ1, θ2, and θ3, respectively. The inter-individual random effect for Cl/F, Vd/F, and Ka is ETA(1), ETA(2), and ETA(3), respectively. They are independently distributed random variables with mean zero and variance ω2. Y, and YPRED represent observed concentrations and the corresponding predicted values, respectively. ERR(1) and ERR(2) are inter-individual random effect factors, representing independent, identically distributed statistical error with mean zero and variance σ2 for serum concentrations. The former is the proportional error and the latter is the additive error.

Framework of the full regression model

Before establishing a full regression model, we selected some initial parameters of Ka, Vd/F, and Cl/F in accordance with the relevant literature to estimate parameters of the basic model (ie, no covariates). Each candidate covariate such as gender, age, WT, ALT, AST, BUN, Cr, ALB, and coadministration was added, in turn, to the base model and the difference in the objective function values was noted. The difference of the objective function value (ΔOFV) obtained by comparing each model was analyzed by chi-square test (test level was set to 0.05). Any single covariate that made ΔOFV exceed 3.84 was considered significant (P<0.05, 1 degree of freedom) and added to the model; otherwise it was excluded. According to the ΔOFV, meaningful covariates were lined up in descending order; then the effect of covariates on the model was further investigated by stacking covariates stepwise according to the above order to screen the significant covariates. The full regression model was to be established by the covariates.

Establishing the final model

To check the role of each covariate in the full regression model, backward elimination was used5, 8 (test level was set to 0.01). A change of OFV was observed once one covariate was eliminated from the model. If the OFV increased by more than 6.63 (P<0.01, 1 degree of freedom), it indicated that the factor was significant and may be reserved in the final model.

Model validation

Intra-validation

The bootstrap method was used to verify the stability of this model in this research. All data were randomly divided into ten groups, one of which contained 10% of the raw data. The control file of the final model was used to calculate the OFV of each of 10 groups. The final model would be proved stable if the difference of OFV between each group and the final model was less than 3.84 (P>0.05).

Application in clinical practice or extra-validation

After fixing each θ value estimated by the final model, clinical information data of another 8 patients were input into the NONMEM program to estimate the individually predicted values of the digoxin steady-state serum concentration and compared them with the observed values. The percent difference between the predicted and observed concentrations was calculated using the formula [(observed value–individual predicted value)/observed value]×100%. The linear relation was also analyzed between the predicted and observed concentrations.

Results

Basic model

The collected data were analyzed by the subroutines ADVAN2 of the NONMEM software according to a one-compartment model. We got parameter estimates of 4.88 L/h for Cl/F, 514 L for Vd/F, and 1.63 h−1 for Ka (Table 2). Because the absorption phase in the data had been completed, Ka and inter-individual variation were fixed to 1.63 h-1 and 0, respectively, in the next calculation to avoid the effect of Ka fluctuation on the stability of model.

Table 2 Parameter estimates of digoxin basic model.
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Full regression model

The basic model of Cl/F was markedly affected by SPI, ALB, WT, Cr, and gender and the basic model of Vd/F was markedly affected by SPI, ALB, WT, Cr (Table 3). However, when these factors were stacked, Cl/F or Vd/F was significantly affected by the combination of SPI, WT, and Cr or the combination of SPI and WT (Table 4). We got parameter estimates of 5.63 L/h for Cl/F, 707 L for Vd/F and 1.63 h-1for Ka (Table 5).

Table 3 Fixed effect factors of significance when they existed individually.
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Table 4 Modeling process of full model of digoxin population pharmacokinetics.
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Table 5 Parameter estimates of digoxin full regression model by NONMEM.
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Final model

The combination of SPI, WT, and Cr significantly affected Cl/F using backward elimination (ΔOFV>6.63, P<0.01) (Table 6). All parameters of the final model are given in Table 7. The population estimates for Cl/F and Vd/F were 5.9 L/h and 550 L, respectively. The inter-individual variability (CV) was 49.0% for Cl/F and 94.3% for Vd/F. The residual variability (SD) between the observed and predicted concentrations was 0.365 μg/L. The final regression model formula is Cl/F=5.9×[1–0.412×SPI]×[1–0.0101×(WT–62.9)]×[1–0.0012×(Cr–126.8)] (L/h); Ka: 1.63 (h−1); Vd/F: 550 (L). The figure of the final model is presented in Figure 1.

Table 6 Backward elimination process of full regression model.
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Table 7 Parameter estimates of digoxin final model by NONMEM.
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Figure 1
figure 1

The distribution of data points were more concentrated and uniform in the lower graph (B) than those in the upper graph (A). Predicted values, individual predicted values vs observed concentrations. Predicted values (PRED); Individual predicted values (IPRE); Observed concentrations (DV).

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Model validation

We used the control file of the final model to calculate OFV of each of the 10 groups. The difference between OFV and the primitive function value was less than 3.84 (P>0.05), which showed that the model was stable.

Clinical information of another 8 elderly patients with heart failure taking digoxin orally for a long time was collected. The individual values of digoxin steady-state serum concentration from these 8 patients had been predicted by the established final model (Table 8). The results displayed that the percent difference between the predicted and the observed concentration was −4.3%–+25%. Correlation analysis showed that there was a linear correlation between observations and predicted values (y=1.35x+0.39, r=0.9639, P<0.0001), indicating that the model can be used in clinical practice to predict digoxin serum concentration.

Table 8 Individual predicted values vs observed concentrations.
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Discussion

The treatment of heart failure in the elderly often involves many kinds of medicines such as cardiac glycosides (digoxin, cedilanid D), ACEI, CCB, β2-receptor antagonists, organic nitrates, and diuretics (furosemide, spironolactone). The serum concentration of digoxin may be affected by various covariates such as gender, WT, Cr, or other medicines.

This study showed that covariates such as SPI, WT, and Cr markedly affected the total clearance of digoxin (Cl/F). The total clearance of digoxin was modeled as the sum of renal and non-renal clearance. According to the view reported by Yukawa4, the non-renal clearance of digoxin in our study was related to body weight, and the renal clearance was related to serum creatinine level. When the covariates were not considered, the population estimate for clearance was 4.88 L/h with a coefficient of variation (CV) of 61.2%. After Cr, WT and SPI were considered as covariates of Cl/F, the population estimate of Cl/F was 5.9 L/h with a CV of 49%, which fell within 4.4–7.7 L/h9 and 5.2–6.3 L/h10 in American patients (reported by Cheng et al and Bauer et al, respectively). However, Cl/F (5.9 L/h) was slightly higher than that in Korean patients (4.38 L/h)11 (Nagaraja et al) and American patients (4.87 L/h)12 (Sheiner et al) and lower than that in Japanese patients (10.3 L/h)13 (Yukawa et al) and American patients (8.25 L/h)14 (Williams et al). These differences may be related to case characteristics, different populations, population size, the length of disease course, the extent of myocardial damage and peripheral vascular tension, and/or the method of population analysis. In addition, P-glycoprotein (P-gp), the expression product of the human multidrug resistance 1 (MDR1) gene, is an important factor in the disposition of many drugs (such as digoxin, amiodarone, and quinidine)15, 16, 17, 18. There are 50 SNPs (single nucleotide polymorphism) in the MDR1 gene19 and exon 26 C3435T SNP is associated with a change in digoxin's oral absorption20, 21. The distribution of C3435T polymorphism is significantly influenced by ethnicity19. The interindividual variation in Chinese patients compared with American patients in our study may also be related to the different expression amounts of P-gp. A silent mutation in exon 26 of human MDR1 is associated with the impaired oral bioavailability of digoxin in humans; however, the causative molecular genetic mechanism of this observation is unknown20. In short, the exact causes of the above Cl/F differences remain to be further explored.

Spironolactone, a aldosterone receptor antagonist, or a diuretic, which could reserve potassium, is usually combined with digoxin to treat CHF. The main reason that SPI increases the serum concentration of digoxin is its inhibition of digoxin renal tubular excretion22.

Some literatures4, 22have shown that when digoxin is taken orally with CCBs, such as verapamil and diltiazem, serum concentration of digoxin is raised, potentially resulting in an increased risk of digitalis poisoning. Among the 119 patients in our study, 53 patients took nifedipine with digoxin and only one person took diltiazem. Our research revealed that nifedipine, one of the CCBs, had no effect on the final model, a finding similar to the results reported by Schwartz JB et al23.

In the validation group of 8 patients, predictions of the digoxin serum concentrations were made with the final regression model. The performance was interpreted as good because there was a good linear correlation between observations and the predicted values (y=1.35x+0.39, r=0.9639, P<0.0001). However, the use of this model in routine monitoring requires that certain conditions be met that are consistent with the conditions of the sub-population in the present study (for details see Table 1).

NONMEM can make full use of the sparse data of serum drug concentration to estimate PPK, and this might decrease sampling times. Therefore, it will be easily accepted by patients, especially older people22, 24 and neonates1, 2, 3, 7, 25, and is suitable for clinical individual administration of special populations5, 6. Although NONMEM demands few sampling times, it requires more cases from various phases — for example, the absorption phase, distribution phase, and elimination phase. The accuracy of the sampling time and the determination of the results should also be stressed to reduce the error. In short, the NONMEM method may be widely applied today and in the future in the study of population pharmacokinetics and individualized medication.

In conclusion, a population pharmacokinetic model for digoxin in a population of older Chinese patients was developed by NONMEM. The final PPK model that described digoxin clearance in a population of older Chinese patients is as follows: Cl/F=5.9×[1–0.412×SPI]×[1–0.0101×(WT–62.9)]×[1–0.0012×(Cr–126.8)] (L/h). This model can be used to predict digoxin serum concentration in clinical practice.

Author contribution

Zhong-dong LI and Jun LI designed the research; Yan GAO collected clinical information; Xiao-dan ZHOU performed the research; Xiao-dan ZHOU and Zheng GUAN analyzed data; Xiao-dan ZHOU and Zhong-dong LI wrote the paper.