Limited-Sampling Strategy Models for Itraconazole and Hydroxy-Itraconazole Based on Data from a Bioequivalence Study

Abstract

The extensive interindividual variability in oral bioavailability of itraconazole prompted an assessment of the bioequivalence of two formulations marketed in Brazil, namely, Sporanox (reference) and Traconal (test). Eighteen healthy volunteers received single 200-mg oral doses of each formulation at 2-week intervals in a randomized, crossover protocol. The concentrations of itraconazole and hydroxy-itraconazole in plasma were measured by high-performance liquid chromatography, and the datum points (n = 396) were subsequently used to develop limited-sampling strategy models for estimation of the areas under the curve (AUCs) for both compounds. The 90% confidence intervals for individual percent ratios (test/reference formulations) of the maximum concentration of drug in serum, the AUC from 0 to 48 h and the AUC from time zero to infinity (AUC_0–∞) for itraconazole and hydoxy-itraconazole were below the range of 80 to 125%, suggesting that these formulations are not bioequivalent. Linear regression analysis of the AUC_0–∞ against time and a “jackknife” validation procedure revealed that models based on three sampling times accurately predict (R², >0.98; bias, <3%; precision, 3 to 7%) the AUC_0–∞ for each of the four formulation-compound pairs tested. Increasing the number of sampling points to more than three adds little to the accuracy of the estimates of AUC_0–∞. The three-point models developed for the reference formulation were validated retrospectively and were found to predict within 2% the AUC_0–∞ reported in previous studies performed under similar protocols. In conclusion, the data in this study indicate (i) that the tested formulations are not bioequivalent when single doses are compared and (ii) that limited-sampling strategy models based on three points predict accurately the AUC_0–∞s for itraconazole and hydroxy-itraconazole and could be a valuable tool in pharmacokinetic and bioequivalence studies of single oral doses of itraconazole.

Itraconazole is a broad-spectrum triazole antifungal agent which acts primarily by inhibiting the biosynthesis of ergosterol, an essential component of fungal cell membranes. The pharmacokinetics of orally administered itraconazole in humans (7, 9) are characterized by considerable interindividual variation in drug absorption, extensive tissue distribution, with the concentrations in tissue being many times higher than those in plasma, and an elimination half-life of ca. 24 h. Itraconazole is extensively metabolized in humans, yielding over 30 metabolites, including the antifungally active metabolite hydroxy-itraconazole.

The pharmacokinetics of orally administered itraconazole in plasma are dose dependent, and absorption from the gastrointestinal tract is affected by various factors, such as food intake versus fasting state (20, 22), gastric pH (12, 13), drug interactions (12, 18), AIDS (18), and the pharmaceutical formulation of the drug (2, 19). Itraconazole is commonly marketed as gelatin capsules that contain drug-coated microspheres. Three such formulations (100 mg of itraconazole/capsule) are registered and available in Brazil. Two of these, Sporanox (SPOR) and Itranax, have the same manufacturer (Janssen-Cilag Farmacêutica Ltda.) and are distinct from the third formulation, Traconal (TRAC; Achê Laboratórios Farmacêuticos s.a.). The lack of bioequivalence data among these formulations provided the initial drive for the present comparative study of the bioavailability of SPOR versus that of TRAC. The data collected for the bioequivalence analysis were then used for the development of a limited-sampling strategy (LSS) for estimation of the areas under the curve (AUCs) for both itraconazole and hydroxy-itraconazole. Strategies that use a limited number of samples and that have proven to be sufficiently robust to allow accurate estimation of individual pharmacokinetic parameters are very valuable, especially if sampling at “unsociable” hours is avoided. In addition, the costs of sample acquisition and the assay are decreased by the reduction in the number of samples that are required.

MATERIALS AND METHODS

Clinical protocol.

The open-label, randomized study described here used a two-way, crossover design in which the two treatment phases were separated by a 14-day washout period. The study protocol was approved by the Ethics Committee of the Hospital Universitário Clementino Fraga Filho, Rio de Janeiro, Brazil, and all participants provided written, informed consent. Eighteen healthy volunteers (7 men and 11 women; age range, 19 to 48 years; mean ± standard error of the mean [SEM] age, 27.1 ± 1.7 years; weight range, 50 to 77 kg; mean ± SEM weight, 63.9 ± 1.9 kg) were enrolled in the study. They were nonsmokers and had no clinically significant abnormalities, as determined 2 weeks before the start of the study on the basis of a medical history, physical examination, electrocardiogram, and standard laboratory test results (i.e., blood cell count, biochemical profile, and urinalysis). The enrolled volunteers had not used any investigational drug in the 6 months preceding the present study. Prescription drugs other than oral contraceptives were not allowed during the study. Itraconazole, because of its affinity for mammalian cytochrome P-450, has the potential for clinically important interactions with oral contraceptives. Indeed, unwanted pregnancy and pill cycle disturbances, such as breakthrough bleedings and delayed or absent withdrawal bleedings, have been reported during concomitant use of itraconazole and oral contraceptives (15, 16). However, the six volunteers in this study who were taking oral contraceptives reported no such disturbances.

In each treatment phase, the volunteers were hospitalized at 7:00 a.m., after an overnight (>10-h) fast. A catheter was introduced in a superficial vein, and then the volunteers received a standard breakfast, consisting of 200 ml of homogenized milk, two slices of bread with ham and cheese, and one apple. After 30 min, each volunteer took two 100-mg itraconazole capsules with 200 ml of water. Nine volunters received the two formulations on one day in one sequence and on the other day in the opposite sequence in a balanced crossover design. Water intake was restricted for 2 h after drug administration. At 4 and 7 h after drug administration, the volunteers received a standard lunch and snack, respectively, and after 10 h they were discharged. The volunteers returned to the hospital 24 and 48 h after drug administration for blood sampling.

Eight-milliliter blood samples were drawn into heparinized tubes 5 min before (zero time) and 1, 2, 3, 4, 5, 6, 8, 10, 24, and 48 h after the administration of itraconazole. Each blood sample was centrifuged within 30 min after collection, and the plasma was separated and stored at −20°C. The plasma itraconazole and hydroxy-itraconazole concentrations were measured by high-performance liquid chromatography (21). The applied method has a quantification limit of 2.0 ng/ml for both itraconazole and hydroxy-itraconazole. Standard curves were linear in the evaluated concentration ranges, and the overall precision, as obtained from tests with independently prepared control plasma samples, ranges from 2.6 to 8.6% (12.7 to 1,979 ng/ml) for itraconazole and from 3.4 to 10.1% (12.5 to 1,961 ng/ml) for hydroxy-itraconazole.

Drugs.

The products used in the study were commercially available as SPOR (batches 602708 and 602798; date of manufacture, November 1996) and TRAC (batches 96EE078 and 96L04; dates of manufacture, May 1996 and November 1996, respectively).

Pharmacokinetic and statistical analysis.

The peak concentrations of itraconazole and hydroxy-itraconazole in plasma (C_max) and the time to reach C_max (T_max) were determined from the individual plasma drug concentration data. The terminal elimination rate constants (k_el) for each compound were estimated by linear regression analysis of the datum points describing a terminal log-linear decay phase. The terminal half-lives (t_1/2s) were calculated as ln 2/k_el. The AUCs from 0 to 48 h (AUC_0–48) were calculated by trapezoidal summation and from time zero to infinity (AUC_0–∞) by adding the value of the plasma drug concentrations at 48 h divided by k_el to the AUC_0–48 obtained by the trapezoidal method. The AUCs thus obtained are taken as the “best estimates” of parameter values.

Individual test/reference (SPOR/TRAC) ratios for C_max, AUC_0–48, and AUC_0–∞ and individual test − reference differences (SPOR − TRAC) for T_max were obtained for assessment of bioequivalence. The data were analyzed statistically by both parametric (one-way analysis of variance for natural log-transformed data) and nonparametric methods. The bioequivalence range for the individual percent ratios of natural log-transformed variables was defined as 80 to 125%.

LSS development.

All-subset linear regression analysis (11) of the AUC_0–∞ best estimates against the concentration at a particular time (C_time) (independent variables) was carried out in order to develop an LSS to estimate AUC_0–∞s for itraconazole and hydroxy-itraconazole following the administration of each itraconazole preparation. Thus, four preparation-compound pairs were analyzed, namely, SPOR-itraconazole (SPOR-ITR), SPOR–hydroxy-itraconazole (SPOR-HYD), TRAC-itraconazole (TRAC-ITR), and TRAC–hydroxy-itraconazole (TRAC-HYD). Computations were carried out by using function leaps (5) in Splus 4.0 (14). This analysis produced equations of the form AUC_0–∞ = A₀ + A₁ × C₁ + A₂ × C₂… A_n × C_n, where A_n is a coefficient, and n is the number of samples. Regression equations were then ranked according to the R² criterion in order to identify those that provided the best fit for 1 to 10 plasma samples obtained at various times. The LSS-derived AUC_0–∞ estimates were then compared with the best estimates of AUC_0–∞ for each of the 18 volunteers’ data sets. The bias of these LSS-derived estimates was assessed by calculating the mean difference (MD; in percent) from the best estimates, where MD = [(derived estimate − best estimate)/best estimate] × 100, and precision was assessed by calculating the mean absolute difference (MAD; in percent).

“Jackknife” prediction and exchange of training sets (see below) were used to validate the procedures described above. Once the limited-sampling concentration times were chosen for each of the four preparation-compound data sets, a jackknife prediction of the AUC_0–∞ was made for each of the 18 volunteers. A jackknife prediction (10) is made when the regression equation for the prediction of the AUC_0–∞ is derived by using n (in our case n = 3) fixed concentrations of choice from 17 of the volunteers, and this equation is used to predict the AUC_0–∞ for the 18th volunteer. Thus, for each subset of sampling times, a slightly different regression equation is used to predict the AUC_0–∞ for each volunteer. By discarding one observation at a time and fitting a new model for the n − 1 remaining observations, the particular observation which is the object of study does not influence the estimation of the regression parameters.

As a second validation approach, the 18 observations comprising one data set for itraconazole (i.e., either SPOR-ITR or TRAC-ITR) were used to estimate the regression coefficients under a three-point LSS model. These coefficients and the concentrations observed at the same respective times, but after administration of the other drug preparation to each of the 18 study subjects, were then used to estimate the AUC_0–∞. The AUC_0–∞s thus obtained were then compared to the available best estimates available for each drug preparation. The first set of observations (used for the development of the LSS regression equations) is referred to as the training data set, and the expression “exchange of training sets” is coined to describe this validation procedure.

RESULTS

All subjects completed the study protocol, and both itraconazole preparations were well tolerated, with no adverse effects being reported.

Pharmacokinetic data and bioequivalence assessment.

The plasma drug concentration-time curves (Fig. 1) show that the mean concentrations of both unchanged itraconazole and the active metabolite hydroxy-itraconazole, at all sampling points, were higher for SPOR than for TRAC. The pharmacokinetic data summarized in Table 1 reveal large interindividual variability in C_max, AUC_0–48, and AUC_0–∞ for both itraconazole and hydroxy-itraconazole after the administration of either SPOR or TRAC. Nevertheless, the mean values of these parameters were consistently higher after SPOR administration than after TRAC administration. Table 2 shows that the 90% confidence intervals (CIs) for individual percent ratios (TRAC/SPOR) of C_max, AUC_0–48, and AUC_0–∞ for both itraconazole and hydroxy-itraconazole were outside the bioequivalence range of 80 to 125%. This is interpreted as indicating that the two formulations are not bioequivalent. T_maxs for both itraconazole and hydroxy-itraconazole, however, did not differ significantly between the two preparations. Also, the individual hydroxy-itraconazole/itraconazole AUC ratios calculated for SPOR (mean ± SEM AUC_0–48, 2.99 ± 0.11 ng · h/ml; mean ± SEM AUC_0–∞, 2.78 ± 0.09 ng · h/ml) or TRAC (mean ± SEM AUC_0–48, 3.02 ± 0.10 ng · h/ml; mean ± SEM AUC_0–∞, 2.80 ± 0.11 ng · h/ml) did not differ significantly, suggesting that the extent of hydroxy-itraconazole formation was similar for both preparations.

FIG. 1.

Mean ± SEM concentrations of unchanged itraconazole (A) and the active metabolite hydroxy-itraconazole (B) in the plasma of 18 volunteers after the oral administration of single doses (200 mg) of two different itraconazole preparations, namely, SPOR and TRAC.

TABLE 1.

Pharmacokinetic parameters of itraconazole and hydroxy-itraconazole in healthy volunteers^a

Parameter	Itraconazole		Hydroxy-itraconazole
	SPOR	TRAC	SPOR	TRAC
Cmax (ng · ml−1)
Mean ± SD	242.6 ± 149.2	155.9 ± 81.9	383.4 ± 151.4	281.8 ± 110.6
Geometric mean	201.5	135.0	347.5	260.2
AUC0–48 (ng · h · ml−1)
Mean ± SD	2,567 ± 1,809	1,538 ± 772	7,313 ± 4,092	4,661 ± 2,448
Geometric mean	2,091	1,369	6,202	4,093
AUC0–∞ (ng · h · ml−1)
Mean ± SD	3,194 ± 2411	1,811 ± 958	9,052 ± 7,629	5,171 ± 3,202
Geometric mean	2,546	1,590	7,014	4,398
kel (h−1)
Mean ± SD	0.039 ± 0.014	0.042 ± 0.012	0.057 ± 0.019	0.066 ± 0.016
Geometric mean	0.036	0.040	0.052	0.063
t1/2 (h)
Mean ± SD	20.8 ± 8.9	18.0 ± 6.6	14.8 ± 9.0	11.5 ± 4.2
Geometric mean	19.2	17.1	13.2	10.9
Tmax (h)
Median	3.5	4	4	4
Range	2–5	2–5	2–6	3–5

^aEach volunteer ingested 200-mg itraconazole capsules as SPOR or TRAC. 

TABLE 2.

Bioequivalence assessment of two itraconazole preparations

Parameter	% Ratios for TRAC/SPOR
	Itraconazole		Hydroxy-itraconazole
	Parametric	Nonparametrica	Parametric	Nonparametric
Cmax
Geometric mean	67.0	65.2	74.8	74.5
90% CI	55.6–80.8	52.8–81.4	65.4–85.6	65.4–86.9
AUC0–48
Geometric mean	65.5	67.5	66.0	64.2
90% CI	53.8–79.6	51.8–77.3	54.7–79.7	52.4–78.6
AUC0–∞
Geometric mean	62.5	60.3	62.7	60.3
90% CI	51.1–76.4	50.0–73.8	51.2–76.7	49.1–75.9
Tmax
Median	0.2b	0.0	−0.06	0.0
Range	0.0–0.5c	−1–3	−0.5–0.5	−2–2

^aNonparametric results are expressed as a point estimate and the CI for individual ratios; for T_max, however, results are expressed as a point estimate and the 90% CI of individual differences (4, 8). 

^bArithmetic mean of individual differences. 

^cThe 90% CI of individual differences. 

LSS.

The concentration-in-plasma data sets for the 18 volunteers and an all-subset regression approach were used to identify the most informative sampling times for 1 to 10 samples for each preparation-compound pair tested, namely, SPOR-ITR, SPOR-HYD, TRAC-ITR, and TRAC-HYD. The results of this analysis (Table 3) show that the most informative sampling strategies for the estimation of AUC_0–∞ depend on the preparation-compound pair. For example, for three samples, the most informative times were 1, 4, and 48 h for SPOR-ITR; 3, 8, and 48 h for SPOR-HYD; 1, 8, and 48 h for TRAC-ITR; and 3, 10, and 48 h for TRAC-HYD. Each of these triple concentrations in plasma correlated well (R² > 0.98) with the corresponding AUC_0–∞. Increasing the number of sampling points led to higher values of R² and consistently increased the precision (MD) and reduced the bias (MAD) of the estimates of AUC_0–∞ for regressions with three or fewer samples. Increasing the number of sampling points to more than three adds little to the precision and bias of the estimates of AUC for each preparation-compound pair tested. From this analysis we conclude that an LSS based on three samples is adequate for estimation of the AUC_0–∞ for each pair tested. Table 4 indicates the 10 most informative sampling times and the corresponding equations derived for estimation of the AUC_0–∞ by using three sample times for each pair tested.

TABLE 3.

R², bias, and precision of the best linear equations for n sample times derived by using the all-subset regression approach to estimate the AUC_0–∞ for each of the 18 subjects for the four preparation-compund pairs tested

Preparation-compound	n	Sample time(s) (h)	R2	MD (% [mean ± SD])	MAD (% [mean ± SD])
SPOR-ITR	1	48	97.32	−5.88 ± 23.34	14,99 ± 18.53
	2	4, 48	99.06	−2.23 ± 12.85	7.99 ± 10.13
	3	1, 4, 48	99.50	−2.23 ± 13.24	7.05 ± 11.31
	4	1, 2, 4, 48	99.69	−1.50 ± 11.39	6.34 ± 9.46
	5	1, 2, 4, 10, 48	99.85	−0.61 ± 5.69	3.98 ± 4.00
	6	1, 2, 3, 4, 8, 48	99.92	−0.34 ± 3.95	2.94 ± 2.57
	7	1, 2, 3, 4, 8, 24, 48	99.95	−0.42 ± 3.73	2.53 ± 2.71
	8	1, 2, 3, 4, 8, 10, 24, 48	99.95	−0.39 ± 3.58	2.36 ± 2.66
	9	1, 2, 3, 4, 5, 6, 8, 24, 48	99.95	−0.38 ± 3.75	2.37 ± 2.88
	10	1, 2, 3, 4, 5, 6, 8, 10, 24, 48	99.95	−0.35 ± 3.61	2.22 ± 2.81
TRAC-ITR	1	24	95.50	−1.55 ± 13.50	10.74 ± 7.91
	2	8, 48	97.62	−1.52 ± 10.09	7.07 ± 7.17
	3	3, 8, 48	99.33	−0.83 ± 5.49	4.15 ± 3.55
	4	1, 2, 5, 48	99.59	−0.15 ± 4.93	3.44 ± 3.44
	5	2, 5, 8, 24, 48	99.74	−0.31 ± 3.67	2.70 ± 2.42
	6	2, 5, 8, 10, 24, 48	99.79	−0.14 ± 3.36	2.48 ± 2.20
	7	1, 2, 5, 8, 10, 24, 48	99.80	−0.07 ± 3.20	2.43 ± 2.00
	8	1, 2, 4, 5, 8, 10, 24, 48	99.80	−0.11 ± 2.99	2.38 ± 1.73
	9	1, 2, 4, 5, 6, 8, 10, 24, 48	99.81	−0.12 ± 2.97	2.37 ± 1.70
	10	1, 2, 3, 4, 5, 6, 8, 10, 24, 48	99.81	−0.12 ± 2.94	2.31 ± 1.73
SPOR-HYD	1	48	96.07	−11.20 ± 43.43	25.78 ± 36.27
	2	8, 48	98.53	−0.51 ± 11.17	8.31 ± 7.21
	3	1, 8, 48	98.68	−0.19 ± 9.25	7.12 ± 5.65
	4	1, 2, 8, 48	98.76	−0.35 ± 10.75	8.15 ± 6.74
	5	1, 4, 5, 8, 48	98.80	0.20 ± 10.58	7.69 ± 7.03
	6	1, 4, 5, 6, 8, 48	98.90	−0.34 ± 11.20	7.94 ± 7.66
	7	1, 3, 5, 6, 8, 24, 48	98.97	−0.81 ± 12.36	9.51 ± 7.60
	8	1, 2, 3, 5, 6, 8, 24, 48	99.03	−0.85 ± 12.01	9.05 ± 7.63
	9	1, 2, 3, 5, 6, 8, 10, 24, 48	99.07	−0.75 ± 11.51	8.33 ± 7.71
	10	1, 2, 3, 4, 5, 6, 8, 10, 24, 48	99.10	−0.48 ± 11.01	7.67 ± 7.69
TRAC-HYD	1	24	96.20	0.76 ± 14.33	11.52 ± 8.10
	2	5, 48	99.22	−0.21 ± 7.30	5.37 ± 4.77
	3	3, 10, 48	99.67	0.06 ± 5.30	3.59 ± 3.79
	4	3, 10, 24, 48	99.81	0.24 ± 2.69	2.14 ± 1.57
	5	2, 4, 10, 24, 48	99.88	0.04 ± 1.74	1.55 ± 0.70
	6	2, 4, 5, 10, 24, 48	99.89	0.12 ± 1.85	1.65 ± 0.75
	7	2, 4, 5, 8, 10, 24, 48	99.90	0.08 ± 2.02	1.69 ± 1.02
	8	1, 2, 4, 5, 6, 10, 24, 48	99.90	0.09 ± 2.09	1.77 ± 1.05
	9	1, 2, 3, 4, 5, 6, 10, 24, 48	99.90	0.11 ± 2.02	1.65 ± 1.10
	10	1, 2, 3, 4, 5, 6, 8, 10, 24, 48	99.90	0.11 ± 2.02	1.65 ± 1.10

TABLE 4.

R², bias, and precision of the ten best linear equations on three sample times derived by the all-subset regression approach to estimate the AUC_0–∞ for each of the 18 subjects for the four preparation-compund pairs tested

Preparation compund	R2	Equation	MD (% [mean ± SD])	MAD (mean % ± SD)
SPOR-ITR	99.50	333.93 − 3.97 · C1 + 4.78 · C4 + 106.28 · C48	−2.23 ± 13.24	7.05 ± 11.31
	99.32	175.23 + 3.13 · C4 + 4.44 · C6 + 100.09 · C48	−1.17 ± 8.03	5.30 ± 6.02
	99.27	247.34 + 3.49 · C4 + 5.00 · C8 + 95.84 · C48	−2.04 ± 8.80	5.33 ± 7.19
	99.27	−74.92 + 2.41 · C2 + 9.72 · C6 + 100.82 · C48	0.39 ± 6.19	5.18 ± 3.16
	99.25	224.80 + 3.69 · C4 + 6.28 · C10 + 93.41 · C48	−1.86 ± 8.40	5.42 ± 6.57
	99.17	156.21 + 2.04 · C3 + 6.49 · C6 + 103.10 · C48	−1.27 ± 7.86	5.56 ± 5.54
	99.16	268.14 + 3.32 · C4 + 1.73 · C5 + 103.08 · C48	−1.87 ± 10.61	6.72 ± 8.27
	99.10	207.41 + 2.70 · C3 + 10.85 · C10 + 90.32 · C48	−2.20 ± 8.67	5.61 ± 6.86
	99.10	55.61 + 2.80 · C2 + 12.86 · C8 + 90.39 · C48	−1.56 ± 6.74	5.24 ± 4.35
	99.09	301.27 + 3.99 · C4 + 5.91 · C24 + 98.20 · C48	−2.20 ± 11.85	7.20 ± 9.51
TRAC-ITR	99.33	117.69 + 2.56 · C3 + 11.16 · C8 + 79.89 · C48	−0.83 ± 5.49	4.15 ± 3.55
	99.14	111.52 + 4.34 · C1 + 6.67 · C5 + 95.52 · C48	−0.13 ± 7.08	4.84 ± 5.02
	98.92	92.87 + 2.59 · C4 + 11.15 · C8 + 77.45 · C48	−0.92 ± 6.51	4.94 ± 4.17
	98.76	148.01 + 1.62 · C2 + 12.23 · C8 + 90.49 · C48	−1.32 ± 7.70	5.05 ± 5.84
	98.72	177.75 + 1.83 · C2 + 42.37 · C24 + 60.99 · C48	−1.30 ± 9.39	6.37 ± 6.86
	98.69	169.68 + 2.53 · C3 + 36.01 · C24 + 59.89 · C48	−1.06 ± 8.68	6.31 ± 5.86
	98.62	107.79 + 1.97 · C2 + 5.56 · C5 + 98.34 · C48	−0.50 ± 5.59	4.66 ± 2.92
	98.50	4.09 + 3.82 · C5 + 10.96 · C8 + 83.21 · C48	−0.44 ± 7.53	5.57 ± 4.89
	98.30	77.04 + 10.04 · C8 + 28.59 · C24 + 61.84 · C48	−1.15 ± 8.54	6.01 ± 6.00
	98.20	75.83 + 2.36 · C2 + 8.10 · C6 + 98.52 · C48	−0.56 ± 6.88	5.38 ± 4.13
SPOR-HYD	98.68	218.84 + 5.58 · C1 + 15.14 · C8 + 98.23 · C48	−0.19 ± 9.25	7.12 ± 5.65
	98.56	274.81 ± 1.07 · C2 + 14.87 · C8 + 99.40 · C48	−0.35 ± 9.99	7.40 ± 6.47
	98.56	321.88 + 3.25 · C5 + 11.20 · C8 + 100.61 · C48	−0.36 ± 11.10	8.35 ± 7.04
	98.55	351.45 ± 1.18 · C4 + 13.75 · C8 + 99.84 · C48	−0.46 ± 10.77	7.93 ± 7.04
	98.54	428.49 + 13.53 · C8 + 4.57 · C24 +94.90 · C48	−0.47 ± 11.43	8.62 ± 7.23
	98.54	342.17 + 0.44 · C3 + 14.95 · C8 + 99.20 · C48	−0.47 ± 10.85	8.08 ± 6.99
	98.53	358.86 + 16.60 · C8 − 1.29 · C10 + 99.15 · C48	−0.57 ± 11.34	8.43 ± 7.33
	98.53	342.01 + 0.51 · C6 + 14.89 · C8 + 99.19 · C48	−0.48 ± 11.14	8.28 ± 7.19
	98.53	136.35 + 4.79 · C1 + 13.56 · C6 + 104.09 · C48	−0.13 ± 10.49	7.95 ± 6.56
	98.52	419.84 + 4.74 · C1 + 10.61 · C5 + 105.38 · C48	−0.72 ± 12.40	9.52 ± 7.64
TRAC-HYD	99.67	−325.60 + 4.32 · C3 + 19.95 · C10 + 54.10 · C48	0.06 ± 5.30	3.59 ± 3.79
	99.62	−95.49 + 10.37 · C5 + 17.03 · C24 + 61.66 · C48	0.20 ± 5.18	4.10 ± 3.02
	99.61	−291.70 + 5.04 · C4 + 16.76 · C10 + 58.37 · C48	−0.27 ± 4.66	3.53 ± 2.93
	99.50	−86.96 + 5.60 · C1 + 13.39 · C5 + 82.56 · C48	−0.42 ± 6.77	4.32 ± 5.12
	99.49	−278.72 + 10.30 · C5 + 6.28 · C8 + 76.42 · C48	−0.20 ± 7.00	5.06 ± 4.67
	99.47	−278.81 + 3.38 · C2 + 23.11 · C10 + 51.83 · C48	−0.34 ± 6.46	4.84 ± 4.13
	99.46	−282.93 + 1.98 · C2 + 13.70 · C5 + 80.83 · C48	−0.20 ± 6.28	4.77 ± 3.91
	99.37	−290.92 + 2.08 · C3 + 12.94 · C5 + 80.27 · C48	−0.13 ± 6.34	4.80 ± 3.97
	99.33	−87.01 + 10.76 · C6 + 23.53 · C24 + 51.14 · C48	0.38 ± 6.54	5.13 ± 3.89
	99.33	137.54 + 5.09 · C4 + 10.56 · C8 + 75.26 · C48	−0.87 ± 6.71	5.12 ± 4.24

Diagnostic plots of the best estimate of AUC_0–∞ versus the LSS-derived AUC_0–∞ are shown in Fig. 2A to D for the various data sets. Jackknife plots (see Materials and Methods) show good agreement between the observed and the predicted quantities for each of the four preparation-compound pairs tested. Residual plots (data not shown) indicate that there is no need to search for either additional variable transformations or nonlinear relationships.

FIG. 2.

Scatter plots showing the relationship between the best estimated AUC_0–∞ and the AUC_0–∞ derived from the LSS models for each of the preparation-compound pairs: SPOR-ITR (A; datum at points 1, 4, and 48 h), TRAC-ITR (B; datum points at 3, 8, and 48 h), SPOR-HYD (C; datum points at 1, 8, and 48 h), and TRAC-HYD (D; datum points at 3, 10, and 48 h). The LSS regression equations for each pair were those described in the first line for each preparation-compound pair in Table 3.

Figure 3 shows validation plots for the exchange of the training sets approach applied to the SPOR-ITR and TRAC-ITR pairs (see Materials and Methods). Although the two drug preparations were not bioequivalent, the three-point LSS-derived regression functions for one pair proved to be robust enough for the adequate prediction of the AUC_0–∞ for the other pair. Thus, when the SPOR-ITRA data are used as the training set (the first equation for SPOR-ITR in Table 4), the predicted AUC_0–∞ for TRAC-ITRA correlates closely with the best estimate of the parameter value (R² = 0.96; MD = −13.40% ± 16.46%; MAD = 16.67% ± 12.91%). The converse (R² = 0.99; MD = 3.44% ± 5.76%; MAD = 5.11% ± 4.25%) is also true when TRAC-ITRA is used as the training set (the first equation for TRAC-ITR in Table 4).

FIG. 3.

(A) Scatter plot showing the relationship between the best estimated AUC_0–∞ for SPOR-ITR (abcissa) and the AUC_0–∞ derived from the LSS model by using the TRAC-ITR data as the training set (ordinate). The plasma itraconazole concentrations measured 3, 8, and 48 h after the administration of SPOR to each of the 18 volunteers were plugged in the first equation for the TRAC-ITR preparation-compound pair in Table 4. (B) Scatter plot showing the relationship between the best estimated AUC_0–∞ for TRAC-ITR (abcissa) and the AUC_0–∞ derived from the LSS model by using the SPOR-ITR data as the training set (ordinate). The plasma itraconazole concentrations measured 1, 4, and 48 h after the administration of TRAC to each of the 18 volunteers were plugged in the first equation for the SPOR-ITR preparation-compound pair in Table 4.

As a final test of the validity of the LSS developed in the current study, the two most informative equations derived for the SPOR-ITR pair (Table 4) were used to estimate the AUC_0–∞ from published data obtained under similar experimental conditions (1, 17). Table 5 shows that the LSS-estimated AUC_0–∞s are within 5% of the average AUC_0–∞s reported in the previous studies, even though these values differ substantially from 3,415 ng · h · ml⁻¹ (1) to 5,757 ng · h · ml⁻¹ (17). For data from both of the previous studies, the second equation displayed in Table 4 performed better than the first equation. This might be related to the use of the plasma drug concentrations at 1 h (C₁), the values of which are small and subject to large variability in the first equation but not in the second equation in Table 3.

TABLE 5.

Validation of the LSS models for SPOR-ITR

Reference	AUC0–∞ [ng · h · ml−1] (%) for SPOR-ITR
	Best estimatea	LSS derivedb
		First equation	Second equation
Barrone et al. (1)	3,415	3,298 (95.6)	3,524 (102.1)
Schäfer-Korting et al. (17)	5,757	5,158 (89.6)	5,788 (100.5)

^aAUC_0–∞ reported by the previous investigators. 

^bAUC_0–∞ estimated by using the first two equations in Table 4 and the published datum points. 

DISCUSSION

This paper describes for the first time the development of an LSS for the antifungal agent itraconazole and its active metabolite hydroxy-itraconazole. These strategies were developed with data from a bioequivalence study of two preparations of itraconazole in which a relatively large number of plasma samples were collected from 18 closely monitored healthy volunteers. The pharmacokinetics data reported here for SPOR, the reference itraconazole preparation, confirm the large interindividual variability in the C_maxs and of the AUCs for both the unchanged drug and the active metabolite hydroxy-itraconazole in healthy subjects (1, 9, 12, 17, 22). Nevertheless, the values reported here for the principal pharmacokinetic parameters obtained after the administration of single doses (200 mg) of itraconazole, given as SPOR, are within the range of previously reported data for itraconazole capsules manufactured for international distribution by the same pharmaceutical company (Table 6). This consistency adds strength to our conclusion, based on the individual test/reference ratios for C_max, AUC_0–48, and AUC_0–∞, that the test preparation TRAC is not bioequivalent to SPOR when the data obtained after the administration of single doses are compared. Since itraconazole is frequently used in prolonged (months) treatment courses, it would be important to assess the bioequivalence of these two preparations under conditions in which the plasma drug levels are at steady state. Because itraconazole exhibits nonlinear, saturable pharmacokinetics in the range of therapeutically effective doses (1, 6), it might be anticipated that differences in the bioavailability of SPOR versus that of TRAC will affect the bioequivalence parameters C_max and AUC for itraconazole and hydroxy-itraconazole to a larger extent under conditions in which plasma drug levels are at steady state than after the administration of single doses.

TABLE 6.

Pharmacokinetic parameters of itraconazole in healthy volunteers^a

Authors	Cmax (ng · ml−1)	AUC0–∞ (ng · h · ml−1)	Tmax (h)	t1/2 (h)
Hardin et al. (6)	272 (81)	4.16 (1.95)	3.0 (0.7)	21.0 (9.0)
van Peer et al. (20)	289 (100)	5.21 (2.12)	4.7 (1.4)	18.0 (4.0)
Schäfer-Korting et al. (17)	319 (132)	5.75 (2.24)	4.0 (1.4)	22.5 (7.8)
Barone et al. (1)	239 (85)	3.41 (1.15)	4.5 )1.1)	20.6 (5.4)
Present study	242 (149)	3.19 (2.41)	3.6 (1.1)	20.8 (8.9)

^aItraconazole capsules (200 mg) were taken after breakfast. Data are presented as means (standard deviations). 

The present study shows that the plasma AUC_0–∞ of itraconazole and hydroxy-itraconazole following the oral administration of 200 mg to healthy volunteers can be determined accurately by using only three plasma samples. The gain in accuracy and precision of the estimates achieved by choosing four or more sample times is marginal, at best (Table 3). The statistical principle of parsimony advises in favor of the use of models with fewer parameters, and we thus settle for three-sample regressions. Ten LSS models in this class were developed for each of the four preparation-compound pairs tested (Table 4) by using an all-subset regression approach. In general, the first three or four models in Table 4 for each pair are statistically indistinguishable, and one could consider additional criteria to be used to choose among them, as to avoid “unsociable” sampling times or to shorten the duration of the study. In particular, the best model for the SPOR-ITR pair involves samples taken 1 h after drug administration. The concentrations measured in plasma at this time are low and subject to greater variability than those measured at later times in the absorption phase of the plasma concentration-time curve. Because of this, the second-best model in Table 4 might be preferred, especially because the difference in the precision and bias of the two models for estimating the AUC_0–∞ of itraconazole after the administration of SPOR are minimal. Indeed, model 2 performed slightly better when both models were used to estimate the AUC_0–∞ from previously published data (Table 5).

The three-point LSS was chosen on the basis of a least-squares linear regression fitting procedure. Alternatively, the SAMPLE module of ADAPT II provides a strategy based on optimal sampling theory (3). LSSs based on the d-optimality criterion implemented in ADAPT II were also produced for the mean curve for the 18 study participants obtained by calculating the mean concentration of itraconazole in plasma after the administration of SPOR, the reference formulation, at each observation time. It was reassuring to observe (data not shown) that the sampling time allocation design for three samples given by the d-optimality criterion (1.43, 4, and 48 h) for the SPOR-ITR pair is essentially the same as that found by the regression method that we used (1, 4, and 48 h).

In conclusion, we describe the development of LSS methods for estimating the AUC_0–∞s of itraconazole and hydroxy-itraconazole with a large set of concentration-in-plasma datum points (n = 396) obtained in a bioequivalence assessment study. The LSS-derived three-point models accurately predicted the AUC_0–∞s for both compounds following the oral administration of either the reference (SPOR) or the test (TRAC) itraconazole formulation. The LSS developed for SPOR-ITR, when applied to data from previously published studies (1, 17) performed under experimental conditions similar to those used in the present study, accurately predicted the AUC_0–∞ for itraconazole. Thus, we suggest that the LSS models described here may be useful for future pharmacokinetic studies of itraconazole.