Gender-dependent differences in cytochrome P450 activity, drug metabolism, drug elimination, and their clinical consequences are increasingly apparent. P450 3A4 is the most abundant P450 isoform in the human liver and is responsible for metabolizing a vast and diverse assortment of therapeutic agents, including opioids, benzodiazepines, and local anesthetics. P450, 3A4 activity is higher in women, influenced by steroid hormone levels, and is speculated to vary during the menstrual cycle. This investigation tested the hypothesis that P450 3A4 activity varies during the menstrual cycle. Alfentanil clearance was used as a metabolic probe for P450 3A4 activity.


Alfentanil (20 micrograms/kg bolus) was administered to nine nonsmoking, nonpregnant female volunteers (age, 26 +/- 5 yr) with normal menstrual cycles on three separate occasions during the same menstrual cycle: days 2 (menstrual phase), 13 (estrogen peak), and 21 (progesterone peak). Venous plasma alfentanil concentrations were determined by gas chromatography-mass spectrometry. Alfentanil clearance was determined by noncompartmental methods and by a three-compartment model with both pooled population and two-stage analysis.


There was no significant difference in any measure of alfentanil clearance. Noncompartmental clearances (mean +/- SD) were 3.62 +/- 0.76, 3.81 +/- 0.96, and 3.60 +/- 0.84 ml/kg/ min, respectively, on days 2, 13, and 21 of the menstrual cycle.


Alfentanil clearances were not different on menstrual cycle days 2, 13, and 21, strongly suggesting no change in P450 3A4 activity. Menstrual cycle differences in alfentanil clearances do not contribute to interindividual variability in alfentanil disposition in women. If other P450 3A4 substrates are comparable, then menstrual cycle variability in their metabolism may not be a consideration in dosing or in the design of pharmacokinetic investigations.

Cytochrome P450 3A4 is responsible for the biotransformation of myriad therapeutic drugs, toxins, and endogenous substrates, and it has the broadest substrate profile of any known P450 isoform. [1–3] P450 3A4 is the most abundantly expressed P450 isoform, comprising 20–60% of total P450. [4] P450 3A4 is considered responsible for metabolizing more than one half of all currently used therapeutic drugs. [5] These include several drugs commonly used in anesthesia and those with a narrow therapeutic index, such as opioids (alfentanil, sufentanil, fentanyl, methadone, dextromethorphan), benzodiazepines (midazolam, triazolam, diazepam), local anesthetics (lidocaine, ropivacaine), immunosuppressives (cyclosporine), and certain antihistamines (terfenadine). [3,6–8]

Gender-based differences in drug metabolism and pharmacokinetics and their attendant clinical consequences, particularly for those therapeutic agents for which biotransformation is mediated by P450 3A4, have been increasingly recognized. These differences were recently reviewed. [5,9] Systemic clearance of several P450 3A4 substrates, including alfentanil, midazolam, erythromycin, prednisolone, methylprednisolone, verapamil, and diazepam, is 20–40% higher in women than in men, suggesting greater P450 3A4 activity. Human P450 3A4 activity was higher in microsomes prepared from the livers of women than those from men, [10] although not all investigators agree. [4,11] Gender disparity in P450 3A4 activity has been attributed to differences in endogenous sex steroid hormone concentrations. [5] Exogenous steroids, such as oral contraceptives, are also thought to alter P450 3A4 activity and the metabolism of P450 3A4 substrates. [5] In addition, there may be a hormonally based age-related component to gender differences in P450 3A4 activity because alfentanil clearance was diminished in postmenopausal compared with younger women but not in older men. [12,13]

The menstrual cycle and attendant hormonal changes may also substantially affect drug metabolism. For example, methaqualone systemic clearance and C-oxidation (but not N-oxidation) were two times greater on day 15 compared with day 1 of the menstrual cycle, [14] whereas caffeine systemic clearance was less during the luteal phase (days 16–26) compared with the follicular phase (days 1–5). [15] P450 3A enzymes catalyze steroid metabolism and are inducible by certain steroids. [1] Uterine contents of P450 3A mRNA and immunoreactive P450 3A protein vary with changes in steroid hormone concentrations that occur during pregnancy and the menstrual cycle in humans. [16] The expression frequency and content of endometrial P450 3A7 mRNA during the uterine secretory phase (days 15–28) were significantly greater than that detected during the proliferative phase (days 6–14). [16] Similar menstrual cycle changes in hepatic P450 3A4 content, activity, or both could substantially affect the elimination of P450 3A4 substrates.

The influence of hormonal changes during the menstrual cycle on cytochrome P450 3A4 activity and P450 3A4-mediated drug disposition is unknown. The purpose of this investigation was to determine the influence of the menstrual cycle on P450 3A4 activity. Systemic alfentanil clearance was used as a noninvasive probe for P450 3A4 activity. [17–21] We tested the hypotheses that alfentanil clearance varies during the menstrual cycle, and that hormone-induced changes in P450 3A4 activity partly explain the interindividual variability in alfentanil clearance observed in women.

Participant Selection and Clinical Protocol 

Nine nonsmoking, nonpregnant female volunteers participated in the investigation after giving written informed consent. The investigational protocol was approved by the institutional human subjects committee. Volunteers were in good health with no remarkable medical problems, weighed within 20% of ideal body weight, had no history of hepatic or renal disease, and were taking no prescription medications. Women were excluded if they had used oral contraceptives or levonorgestrel implants within 3 months or medroxyprogesterone within 1 yr. All participants had regular menstrual cycles (26–32 days) and menstrual periods (3–7 days). Participants with a history of ovarian cystectomy, oophorectomy, infertility, irregular menstrual periods, spotting between menstrual periods, or irregular or abnormal menstrual cycles were excluded.

Alfentanil clearance was determined on three separate occasions during the same menstrual cycle: the proliferative phase (day 2 of the menstrual cycle), estrogen peak (day 13), and the progesterone peak (day 21). Participants abstained from use of alcohol, grapefruit, grapefruit juice, [22] and caffeine for 12 h before and during each study period (60 h total) and from food and liquids after midnight the day before each alfentanil administration. The protocol was similar to that described in our accompanying article, [21] with venous samples obtained for 480 min. Urine was not collected.

Analytical Methods 

Plasma alfentanil concentrations were determined by gas chromatography-mass spectrometry, as described previously, except that derivatization was omitted. [23] Calibration standards and curves were prepared daily (0.1–300 ng/ml). Quality control samples (1, 50, 100 ng/ml) were analyzed at the beginning, middle, and end of each batch. Interday coefficients of variation were 9.8%, 5.8%, and 2.5% at 1, 50, and 100 ng/ml, respectively.

Data Analysis 

Three methods were used to analyze plasma alfentanil concentration versus time data:(1) A mamillary approach, which included both two-stage modeling and naive-pooled data analysis, provided a full distribution of parameter estimates. [24](2) Noncompartmental analysis eliminated a potential for model misspecification. (3) A statistical approach minimized the possibility of missing a small but statistically significant difference caused by sample size. Details of the analysis methods are provided in the appendix. Results are expressed as means +/- SD.

(Table 1) provides participant demographic data. All participants had menstrual cycles of normal duration and menstrual periods of usual flow and duration. Mean plasma alfentanil concentration versus time data obtained on menstrual cycle days 2, 13, and 21 are shown in Figure 1, along with concentrations predicted using parameter averages obtained by two-stage analysis with a three-compartment model. The three disposition curves are virtually superimposed. Table 2summarizes parameters. There were no significant differences in the macroconstants, compartmental rate constants, or intercompartmental clearances at the three times studied. Specifically, the parameters most pertinent to systemic drug elimination (gamma, k10, Cl) were indifferent to the phase of the menstrual cycle. In addition, the rate constants were highly invariant compared with the parameter standard deviations, which represent interindividual differences of 20–40%.

Table 1. Demographic Data 

Table 1. Demographic Data 
Table 1. Demographic Data 

Figure 1. Average (+/- SE, for clarity) alfentanil plasma concentrations determined on day 2, day 13, and day 21 of the menstrual cycle. Symbols depict measured concentrations and lines represent predicted concentrations using macroconstant parameters derived from a three-compartment model using the two-stage approach (Table 2).

Figure 1. Average (+/- SE, for clarity) alfentanil plasma concentrations determined on day 2, day 13, and day 21 of the menstrual cycle. Symbols depict measured concentrations and lines represent predicted concentrations using macroconstant parameters derived from a three-compartment model using the two-stage approach (Table 2).

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Table 2. Alfentanil Pharmacokinetic Parameters 

Table 2. Alfentanil Pharmacokinetic Parameters 
Table 2. Alfentanil Pharmacokinetic Parameters 

Alfentanil concentrations in individual participants on menstrual cycle days 2, 13, and 21 are shown in Figure 2, along with concentrations predicted using parameters obtained by pooled population analysis with a three-compartment model (Table 2). Similar to Figure 1, the three disposition curves are nearly identical. Because population parameters are derived from the complete data set, standard deviations are not obtained. Regardless of the model, parameters were relatively invariant throughout the menstrual cycle.

Figure 2. Individual alfentanil plasma concentrations determined on menstrual cycle days 2, 13, and 21. Solid lines are predicted concentrations using kinetic parameters derived from a three-compartment model using a pooled population approach.

Figure 2. Individual alfentanil plasma concentrations determined on menstrual cycle days 2, 13, and 21. Solid lines are predicted concentrations using kinetic parameters derived from a three-compartment model using a pooled population approach.

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Alfentanil elimination clearance and volume of distribution for each volunteer on days 2, 13, and 21 of the menstrual cycle, as determined by noncompartmental analysis, are shown in Figure 3, and the two-stage averages and standard deviations are provided in Table 2. We observed no significant or consistent change in alfentanil clearance during the menstrual cycle.

Figure 3. Alfentanil steady-state volume of distribution and systemic clearance on days 2, 13, and 21 of the menstrual cycle determined by noncompartmental analysis. Individual results for the nine participants are shown.

Figure 3. Alfentanil steady-state volume of distribution and systemic clearance on days 2, 13, and 21 of the menstrual cycle determined by noncompartmental analysis. Individual results for the nine participants are shown.

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The final method of data analysis was a comparison of interday variance in alfentanil concentrations with the interparticipant and the statistical variances in alfentanil concentrations (Figure 4). Initial comparisons were between intra- and interindividual variances using Equation 11and Equation 12and non-normalized data. The result (not shown) was that interindividual variance was an order of magnitude larger than the intraindividual variance. This is not surprising based on the model of Equation 8. Although it is expected that the epsilonijk, which contain both measurement and statistical errors, should be similar in the two comparisons, the structural models g(Vij, Deltaij, t sub k) are expected to vary among individuals. Specifically, the concentration terms (Vij) are probably responsible for more of the interparticipant variance than are the rate terms (Deltaij). Because most of the concentration variance can be eliminated by normalizing the data, the interindividual and intraindividual variances were again compared using normalized data. Figure 4shows the back-transformed data and variances, calculated as described in Equation 7, Equation 8, Equation 9, Equation 10. Even with the effect of the interindividual Vijdifferences removed, the variance between individuals still exceeds the variance of a given volunteer throughout the menstrual cycle.

Figure 4. Comparison of interindividual (squares), intraindividual (circles), and estimated statistical (triangles) variances for alfentanil plasma concentration data.

Figure 4. Comparison of interindividual (squares), intraindividual (circles), and estimated statistical (triangles) variances for alfentanil plasma concentration data.

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Another variance comparison is possible if the extended least-squares fits are used to estimate the statistical variances, as in Equation 11and Equation 12. The assumption is that although the population estimates of the true data g(Vj, Deltaj, tk) may be imperfect, the g(Vij, Deltaij, tk) estimates obtained by fitting to triexponentials should be accurate to within the statistical variances. These comparisons are done for the raw data dijk(Figure 4). The intraindividual variances derived from raw, non-normalized data (dijk) corresponded well with those derived from normalized data (dijk). Thus only one curve is shown for the intraindividual variances, which were less than or equal to the estimated statistical variances, again showing that there was no demonstrable effect of the menstrual cycle on alfentanil pharmacokinetics.

Progesterone concentrations in plasma obtained on days 2 and 21 were determined after conclusion of the investigation to assess participants' ovulatory status. Five women had clearly ovulated, based on progesterone concentrations exceeding 3 ng/ml, whereas the ovulatory status of the other women was uncertain. Alfentanil clearances on days 2, 13, and 21 in the former group (3.56 +/- 1.03, 3.41 +/- 1.00, and 3.47 +/- 0.96 ml/kg/min) were not significantly different from each other, nor were they different from those in the latter group (3.86 +/- 0.60, 4.43 +/- 1.01, and 4.19 +/- 1.12 ml/kg/min). Thus results from participants who had clearly ovulated were not different from those of all participants with normal menstrual cycles.

The hypothesis we tested was that P450 3A4 activity would vary significantly during the menstrual cycle, with a greater drug clearance expected during the luteal phase of the cycle. Alfentanil clearance was used as the noninvasive probe of P450 3A4 activity. Alfentanil is a low-extraction drug cleared almost exclusively by hepatic biotransformation, with less than 1% eliminated unchanged in urine. [25] Such clearance is independent of hepatic blood flow [26] and unaffected by variability in protein binding. [27,28] Thus alfentanil systemic clearance is equivalent to hepatic intrinsic clearance. [29] P450 3A4 is the predominant isoform responsible for alfentanil hepatic intrinsic clearance. Both pathways of alfentanil hepatic metabolism in humans, [25,30] piperidine N-dealkylation to noralfentanil [17,19] and amide N-dealkylation to N-phenylpropionamide, [19] are catalyzed predominantly by P450 3A4 in human liver microsomes in vitro. P450 3A4 activity is also the primary determinant of human alfentanil metabolism and clearance in vivo. Alfentanil systemic clearance in humans was significantly diminished by the P4503A inhibitors troleandomycin [20,21] and ketoconazole, [31] and increased after P450 3A induction by rifampin. [20,21] Furthermore, there was an excellent correlation between alfentanil clearance and P450 3A4 activity, [21] measured as the clearance of midazolam, a validated in vivo probe for P450 3A4 activity. [32]

Our results show that alfentanil clearance was not different during the three major phases of the menstrual cycle. Using either two-stage, pooled population, or noncompartmental analysis, no measure of alfentanil clearance, including elimination clearance (both absolute and weight adjusted), k10, or Cl1, was significantly different on days 13 (ovulatory phase) and 21 (luteal phase) compared with day 2. Day 13 corresponds approximately to peak plasma estrogen concentrations and the day before ovulation, and day 21 is approximately 1 day after peak plasma progesterone concentrations. Thus the similarity in alfentanil disposition on days 2, 13 (estrogen surge), and 21 (progesterone surge) suggest that hepatic cytochrome P450 3A4 activity does not vary significantly with hormonal changes during the menstrual cycle, at least on days 2, 13, and 21. Menstrual cycle changes in uterine P450 3A4 content [16] apparently do not influence systemic alfentanil clearance. Because uterine P450 3A4 content is small compared with that in the liver, [16] the latter is the prime organ of alfentanil metabolism and systemic clearance.

An explanation for apparent differences in uterine P450 3A7 and hepatic P450 3A4 response to the menstrual cycle cannot be delineated from the present and previous investigations. Schuetz et al. [16] proposed that changes in endogenous substrates and hormones, which are known to influence hepatic P450 3A expression, [33] also underlie P450 3A7 regulation. Specifically, steroid hormones and glucocorticoids and their respective receptors were implicated. Human P450 3A activity can be induced by dexamethasone, prednisone, and prednisolone (but not by progesterone), [34–36] and rat P450 3A is induced by myriad glucocorticoids and a pregnenolone derivative. [37] Hepatic P450 3A4 and uterine P450 3A7 may respond differently to a hormonal stimulus or may be regulated in a completely different manner.

Menstrual cycle effects on pharmacokinetics have been reported for a few drugs and were recently reviewed. [5] During the midphase, compared with the beginning of the menstrual cycle, methaqualone systemic clearance and C-oxidation were two times greater. [14] In contrast, systemic clearance of caffeine [15] and theophylline [38] were greater during the follicular phase (days 1–5) compared with the luteal phase (days 16–26), and phenytoin clearance was 50% greater during the menstrual period compared with the midcycle. [39] Paracetamol clearance was somewhat higher on day 12 compared with day 21. [40] The metabolism of phenobarbital, ethylmorphine, alprazolam, nitrazepam, and phenazone were apparently not affected by the menstrual cycle. [5] The present results indicate that alfentanil clearance, and thus P450 3A4 activity, are similarly unaffected by the menstrual cycle. If clearance of other P450 3A4 substrates mirrors that of alfentanil, then menstrual cycle variability in P450 3A4 activity would not appear to be a consideration in the metabolism of P450 3A4 substrates (alfentanil, sufentanil, fentanyl, methadone, dextromethorphan, midazolam, triazolam, diazepam, lidocaine, or ropivacaine) used in anesthesia, although these have not been tested individually and some other menstrual cycle factor might influence their disposition. Similarly, it appears that pharmacokinetic investigations of P450 3A4 substrates in female participants may not need to consider menstrual cycle synchronization.

There is considerable interpersonal variability in alfentanil pharmacokinetics, [41,42] specifically a tenfold variability in systemic clearance. [43–45] Variability in alfentanil clearance is greater in women than in men, and there is an age-dependent decline in alfentanil clearance in women but not men that may represent postmenopausal change. [12,13] Dose requirements of alfentanil appeared to be significantly higher during the ovulatory and luteal phases (days 12–24) of the menstrual cycle compared with menses and were 50% higher on day 14 of the menstrual cycle compared with day 2.* The mechanisms for these observed differences are unknown. The present investigation suggests that menstrual cycle kinetic variability does not contribute to interindividual variability in alfentanil disposition in females. Furthermore, higher alfentanil dose requirements on days 12–24 of the menstrual cycle are also not explained by menstrual cycle differences in pharmacokinetics.

Although a relatively small number of women were studied in this investigation, the possibility of a type-two statistical error seems small. That is, the inability to detect a significant menstrual cycle effect on alfentanil kinetics when a true effect did occur was unlikely. Power analysis using the standard deviations obtained from the two-stage analysis suggested the ability to detect a 20% difference in elimination clearance at the 0.05 level of significance with a power of 80%. The data were well described by the three-compartment pharmacokinetic model, and the parameters obtained are similar to those reported previously after bolus administration. [27,28,41,46,47] In addition, the goodness-of-fit is also indicated by the reduced chi-squared statistic, chi squaredr. These results are provided in Table 3. Because chi squaredris the ratio of the variance of the fit to the variance of the data, a chi squaredrless than or equal to 1 represents an excellent fit. The small values of chi aquaredrfor the individual fits reflects the adequacy of three compartments to describe the data. As the model is generalized, the chi squaredrwill increase. Nevertheless, the chi squaredrfor the population fits still approximated one. The values from the two-stage approach indicated less-adequate model fitting, most likely due to variance in the two-stage averages for V1. When V1was allowed to vary as a parameter in the two-stage approach, the chi squaredrresults approach those obtained by population estimates.** The intraindividual variance in alfentanil plasma concentrations was less than the interindividual variance and the statistical variance in the assay measurements.

Table 3. Reduced Chi-squared Values (chi squaredr) for Nonlinear Analysis* 

Table 3. Reduced Chi-squared Values (chi squaredr) for Nonlinear Analysis* 
Table 3. Reduced Chi-squared Values (chi squaredr) for Nonlinear Analysis* 

The ideal noninvasive metabolic probe for P450 3A4 activity is still undefined. The erythromycin breath test (elimination of radioactive carbon dioxide after P450 3A4-catalyzed demethylation of intravenous radiolabeled erythromycin) has been used widely, [48,49] but there is a lack of correlation with other P450 3A4 probes, including alfentanil, dapsone, and cortisol. [50–53] Intravenous midazolam is a validated 3A4 probe, with midazolam systemic clearances having been correlated with actual liver (biopsy) content of P450 3A4 [32] and profoundly affected by hepatic P450 3A4 activity. [20,54] Intravenous alfentanil is another alternative P450 3A4 probe because P450 3A4 is the predominant if not sole isoform catalyzing alfentanil metabolism, alfentanil clearance is exquisitely dependent on P450 3A4 activity, and there is an excellent correlation between alfentanil and midazolam systemic clearances. Alfentanil was used as the P450 3A4 probe in our investigation because it is more extensively metabolized than midazolam, the metabolites do not undergo phase 2 conjugation, alfentanil clearance is more independent of hepatic blood flow, and most importantly, the clinical consequences of potential menstrual cycle variability in clearance were far greater for alfentanil than for midazolam.

In summary, cytochrome P450 3A4 activity assessed by alfentanil clearance did not vary among days 2, 13, and 21 of the menstrual cycle. Menstrual cycle variability in alfentanil clearance does not contribute to interindividual variability in alfentanil disposition and may not affect the metabolism or disposition of the various P450 3A4 drugs used in anesthesia.

The authors thank Eunice Reyla, R.N., Marilyn Burchett, R.N., and Judith Mattila, R.N., for their clinical assistance.

Compartmental Analysis 

Two-stage modeling and the naive-pooled data approach were used. For both compartmental methods, data were analyzed three times by nonlinear extended least-squares regression analysis (MKMODEL; Biosoft, Cambridge, UK) using different equations to estimate directly the macroconstants, microconstants, and intercompartmental clearances and volumes. Initially, both two- and three-compartment models were used, but the latter was selected based on the F ratio. In the two-stage approach, each of three alfentanil injections for each participant were analyzed to yield three parameter sets for each of nine women, and the mean and standard deviation were then calculated for each parameter on the three menstrual cycle days. In the naive-pooled approach, all nine participants were analyzed simultaneously to obtain a population estimate and standard error of the estimate for each parameter at each of three times during the menstrual cycle.

To determine the macroconstants, data were fit to the model shown in Equation 1, which represents the alfentanil concentration for the ithpatient during the jthday of the menstrual cycle at the kthtime. Equation 1

The preexponential terms are normalized such that their sum is unity, and all of the concentration information is contained in the term for the initial concentration; that is, dose divided by the central compartment volume. Omission of the j subscript from the concentration term implies that V1is independent of cycle time and that the same alfentanil dose was used for a given patient. Parameter standard deviations were calculated for the two-stage results, and the chi squared sub r were calculated for both two-stage and naive-pooled approaches to gauge the quality of the fits. The Vssand Cl were calculated using Equation 2, Equation 3.

Data were also analyzed directly to obtain the microconstants as described previously. [21] Finally, data were also analyzed to obtain the compartmental volumes and intercompartmental clearances directly, where the model parameters are V1, V2, V3, Cl1, Cl2, and Cl3(Equation 4).

Noncompartmental Analysis 

Data for each participant at each of three times during the menstrual cycle were analyzed by noncompartmental analysis using the trapezoidal rule (PCNONLIN 4.2; SCI Software, Apex, NC), with subsequent two-stage calculations of means and standard deviations, to obtain the estimates for elimination clearance and volume of distribution.

Statistical Analysis 

Population statistical variances in alfentanil concentrations were calculated and used as a metric to compare both intra- and interparticipant variances. The data are represented by a three-dimensional array where dijkis the measured alfentanil concentration for the ithpatient during the jthday of the menstrual cycle at the kthtime. The general model for dijkis constructed such that Equation 5where g(Pijis the functional form of the structural model, Pijare the model parameters, tkare the independent variables, and epsilonijkare the random errors (due in part to assay variability) associated with the dijk, which have means of zero and variances that are unknown. Although the variance sigma sup 2 (epsilonijk) could be estimated by repetitive laboratory measurements of the same patient sample, this is not practical. As described before, the true data dijkare described by Equation 1, and these true data will differ from the observed data by the epsiijkof Equation 5.

To examine menstrual cycle effects on alfentanil kinetics, we can analyze the variance in plasma alfentanil concentrations throughout the cycle. However, this approach is problematic. The ultimate metric sigma2(epsilonijk) is unknown. Experimental data should fit no better than the statistical variances of the data. The hypothesis is that the intraindividual variance throughout the menstrual cycle is less than or equal to the unknown statistical variance in the data. As a first approximation, the intraparticipant and interparticipant variances of the concentration data at a given time point can be compared. To illustrate this, a more explicit form of Equation 5based on Equation 1is used:Equation 6. This form of the structural model emphasizes that there are terms that depend on concentration, Vij, and terms that depend on the rates, Deltaij. For example, in Equation 6, the Vijrepresent volume information and the Deltaijrepresent clearance information. In comparing the intraindividual and interindividual variances, the latter will be greater because of differences in Viand Deltaiamong individuals. Contributions to the variance due to differences in Vican be eliminated by using concentration-normalized data, calculated using the normalization constants, Nij, to back-transform from the normalized dijkto the raw data dijkusing Equation 7and Equation 8.

However, the excess variance due to any differences in Delta sub i will remain. The variance associated with the kthtime point for intra-versus interindividual comparisons are given by Equation 9and Equation 10, respectively.

Another approach is to compare the intraindividual variances of Equation 9with the statistical variances sigma2(epsilonijk). Although the statistical variances are unknown, they can be estimated from the data and appropriate multiexponential fits. As noted previously, models with three exponential terms have been shown to describe accurately alfentanil disposition. Let Equation 11represent such a fit. If epsilon sub ijkfare small relative to the epsilonijkof Equation 6, then Equation 12.

This analysis was conducted for non-normalized alfentanil concentration data, and the epsilonijkwas then used to determine whether the intraindividual variances throughout the menstrual cycle were significant.

Finally, the variances were used to determine the degree to which the obtained fits were appropriate for individuals and for populations. If dkand dKrepresent the observed and fit alfentanil concentrations at the kthtime, then chi-squared represents a sum of weighted residuals of the fit. Each term in the sum should approximate one if the fit is adequate. Dividing chi-squared in Equation 13by the degrees of freedom yields the reduced chi-squared (chi squaredr), which should approximate 1 for an ideal fit. Similar expressions can be used to determine goodness of fit for population models. In the previous calculations, dkwas used as an estimate of the variance of the dk, (sigma2dk). Although this will overestimate sigma2(dk) and thus underestimate chi squaredr, this provided a consistent metric for comparing fits throughout the analyses.

*Beattie WS, Buckley DM, Beattie AE, Forrest JB: Intraoperative alfentanil requirements vary during menstrual cycle. Anesthesiology 1991; 75:A403.

**The V1data in Table 1represent means, where V1was independent of menstrual cycle date, rather than having V1vary as a parameter.

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