single-point phenytoin dosage predictions in singapore chinese

Journal of Clinical Pharmacy and Therapeutics (1997) 22, 47–52

Single-point phenytoin dosage predictions in SingaporeChineseE. Chan PhD

Department of Pharmacy, National University of Singapore, Singapore

SUMMARY

Phenytoin dosing is often difficult in a clinicalsituation because of the non-linear nature ofphenytoin metabolism at therapeutic plasmaconcentrations. This study was performed toexamine retrospectively five pharmacokineticmethods of adjusting phenytoin dosage basedon a single steady-state plasma phenytoinconcentration–dose pair in 66 epileptic Chinesechildren and adults. The methods comparedincluded four fixed-parameter(s) methods (1=thefixed Km (Michaelis–Menten constant) method;2=the fixed Vm (maximum rate of elimination)method; 3=the fixed Vmax/Km method; 4=thefixed S (slope of logarithmic growth model)method) and a Bayesian feedback method (method5). Measures of bias or accuracy (mean error,percentage dose) and precision (root mean squarederror, percentage dose) were 20·1/88·0,"1·85/21·5, 2·14/21·9,"1·07/21·1 and "1·98/22·2,respectively. Method 1 was significantly inferiorto methods 2–5 with respect to accuracy andprecision. The correlation between the predictedand observed doses was higher with methods 2–5(r=0·862, 0·855, 0·866 and 0·841, respectively)when compared to method 1 (r=0·539). Allmethods had a sizeable number of poor predictions(range: 21·2% for method 4 to 37·9% for method1), i.e. predictions with an error of greater than20% of the dose. With respect to the frequency ofpoor versus good predictions, comparisons of allmethods showed no significant differences.

INTRODUCTION

Phenytoin is one of the most frequently used anti-convulsant drugs for the treatment of grand mal and

focal seizures. Difficulties often arise in attempting todetermine an appropriate phenytoin dosage regimenfor a particular patient because of the non-linear natureof phenytoin metabolism at the therapeutic concen-tration range 10–20 mg/litre (1). To aid clinicians inmaking adjustments to individualized doses, severalmethods have been proposed using one steady-statephenytoin concentration–dose pair in the individualpatient and prior information about the populationpharmacokinetic parameter(s) of the drug (2–6). Thesemethods have been applied to Caucasian and Japanesepatients, whereas their clinical utilization in Chinesepatients has not been investigated (7–8). Recentstudies have demonstrated ethnic differences inphenytoin pharmacokinetics (9). Thus, a method whichis proved useful in one ethnic patient population maybe less applicable in another ethnic patient population.It is desirable under such circumstances to select amethod that gives more accurate and precise dosageadjustment for the particular patient population. Theobjective of the present study was to compare theapplicability of five established pharmacokineticmethods using a single steady-state concentration–dose pair to predict subsequent phenytoin dosage inChinese epileptic patients in Singapore.

METHODS

Drug monitoring profiles were retrospectivelyreviewed from epileptic Chinese patients at theNeurology Clinic of the Paediatric Department andthe Outpatient Clinic of the hospital. Sixty-six patientswere selected on the basis that they had two reliablesteady-state plasma phenytoin concentration measure-ments at different daily doses on different occasions.They were also not suspected to be non-compliant,although strict tests of compliance were not per-formed. Patients who received any concurrent medi-cation known to displace phenytoin from plasmaprotein binding sites were excluded from the study.

Correspondence: Dr Eli Chan, Department of Pharmacy, NationalUniversity of Singapore, 10 Kent Ridge Crescent, Singapore119260, Republic of Singapore.

? 1997 Blackwell Science Ltd 47

Patients with concurrent medications (primarily otheranticonvulsants) were included in the study if thedosages of these medications remained unalteredduring the period of concentration measurements.Twenty-two patients (33%) were female and 44 (67%)male. Forty-three (65%) patients were over 15 years ofage. Age and body weight ranged from 2 to 76 yearsand 12 to 82 kg, respectively.

The following methods utilized the most recentsteady-state phenytoin concentration–dose pair topredict the subsequent dosage for a given steady-stateplasma concentration. The population pharmacokineticparameters of phenytoin used were derived from theChinese population instead of those derived fromthe other ethnic patient populations (Japanese andcaucasians). The mean population parameters and theirintra- and inter-individual variability, necessary for theBayesian feedback prediction method, were previouslyestimated, using the population error model (9).

Method 1

This method utilizes the procedure proposed byRichens and Dunlop (2), described by equation 1.

Dn=Do * (Co(ss)+Km) * Cd(ss)/[(Cd(ss)+Km)* Co(ss)] (1)

where Dn is the new daily dose, Do is the initial dailydose, Co(ss) is the initial steady-state plasma concen-tration, Cd(ss) is the desired steady-state plasma con-centration and Km is the Michaelis–Menten constant.This method assumes that Km is constant and that themaximum rate of elimination (Vm) varies within thepatient population. Km is set to the population meanvalue (2·18 mg/litre) (Table 1).

Method 2

The second method utilizes the procedure proposedby Chiba et al. (4), described by equation 2.

Dn=Vm * Cd(ss)/[Co(ss) * (Vm/Do"1)+Cd(ss)] (2)

This method assumes that Vm is constant and Km

varies within the patient population. Vm is set to anage-adjusted population mean value (10·9 mg/kg/dayfor <15 years, 8·05 mg/kg/day for >15 years) (Table1).

Method 3

This method utilizes the procedure proposed byMartin et al. (3), described by equation 3.

Dn=Vm/Km/(R/Cd(ss)+1/Km) (3)

where R is the ratio of the observed initial steady-state plasma concentration (Co(ss)) to the expectedinitial steady-state plasma concentration (Ce(ss)),and Ce(ss)=Do * Km/(Vm"Do). Km is set to thepopulation mean value while Vm is set to anage-adjusted population mean value (Table 1).

Method 4

The fourth method utilizes the procedure proposedby Wagner (6), described by equation 4.

Dn=Do+ ln(Cd(ss)/Co(ss))/S (4)

where S is the slope parameter of the logarithmicgrowth model. The slope of the least squares regres-sion line from a plot of ln Css versus daily dose givesan estimate of S. S is set to the population mean valueof 0·648 days#mg/kg. The S-values were derivedfrom the current study population. No statisticallysignificant difference in S was found betweenchildren (0·593&0·389 days#mg/kg) and adults(0·676&0·478 days#mg/kg) when the S-valueswere estimated from the plots of ln Css versusweight-adjusted daily dose (mg/kg/day).

Method 5

The fifth method utilizes the general Bayesian feed-back method proposed for dosage prediction bySheiner and Beal (5). This method minimizes thefollowing objective function (OBJ) in the case of onefeedback prediction.

Table 1. Values for population pharmacokinetic parametersof phenytoin in Chinese epileptic patients

Parameter

Age group (years)

<15 >15

Km (mg/l) 2·18 2·18Vm (mg/kg/day) 10·9 8·05óKm (% CV ) 53·9 53·9óVm (% CV ) 48·2 26·9óE (mg/kg/day) 1·57 (CV 24·3%) 1·57 (CV 24·3%)

CV=coefficient of variation, E=residual error.

48 E. Chan

? 1997 Blackwell Science Ltd, Journal of Clinical Pharmacy and Therapeutics, 22, 47–52

OBJ= [(Vm"Vm(i))/óVm ]2+[(Km"Km(i))/óKm ]2 + [(Do"D)/óE]2 (5)

where Vm and Km are the population mean values,Vm(i) and Km(i) are the individual parameter estimateswith respect to which the function is to be minimized,óVm, óKm are the inter-individual standard deviationsfor Vm and Km, respectively, óE is the residual errorstandard deviation (between predicted and observeddosage) which accounts for all uncertainties causedby intra-individual time variation in Vm and Km, assayand sampling errors, and model misspecification;and D=Vm(i)*Co(ss)/(Km(i)+Co(ss)), where Co(ss) is theobserved steady-state plasma concentration associatedwith Do. With the current estimates of Vm(i) and Km(i),the individual new daily dose required to achieve adesired steady-state plasma concentration (Cd(ss)) canthen be predicted using equation 6.

Dn=Vm(i)*Cd(ss)/(Km(i)+Cd(ss)) (6)

Table 1 lists the population mean values and theintra- and inter-individual standard deviation valuesused. The non-linear multiple regression program2(), based on Bayesian algorithm formicrocomputer, was employed in this feedbackprediction (10).

The predictive performance of each method wasmeasured in terms of mean prediction error (ME) andsquare root of mean squared prediction error (RMSE)(11). The former is a measure of bias (or accuracy)whereas the latter is a measure of precision. Poorpredictions, those that yielded absolute errors greaterthan 20% of observed doses, were also tabulated forcomparison between methods—the chi-squared testfor a contingency table was performed on thetabulated data of poor versus good predictions. Theassessment of bias for each method was performedusing the one-sample t-test. The strength of associ-ation between the predicted and observed dailydoses was measured using Pearson’s correlation coef-ficient (r). Direct comparison between methods forME and RMSE was performed using the Friedmantest, a non-parametric one-factor repeated measuresanalysis of variance. Statistical significance was definedas P<0·05.

RESULTS

Figure 1 presents the scatter diagrams of predictedversus observed daily dose for each method. Only 63

of the 66 cases are shown for method 1, because thethree extreme cases excluded (predicted doses of 1353,1635 and 1862 mg/day were at least four times theobserved doses) were far from the cluster of themajority of data. The correlation between the pre-dicted and observed values was found to be higherwith methods 2–5 (r=0·862, 0·855, 0·866 and 0·841,respectively) when compared to method 1 (r=0·539for all cases or 0·632 for 63 cases).

The measures of bias and precision for all theprediction methods are summarized in Table 2.Method 4 appeared to be the least biased(ME=–1·07% of the dose) and the most precise(RMSE=21·1% of the dose), whereas method 1 wasthe most biased (ME=20·1% of the dose for all casesor 3·01% of the dose for 63 cases) and the least precise(RMSE=88·0% of the dose for all cases or 74·4% ofthe dose for 63 cases). When all cases were taken intoaccount, method 1 was significantly different frommethods 2–5 with respect to predictive performance interms of bias and precision. Methods 2–5 tended tohave similar precision and accuracy (see Table 2) andto have no bias—the 95% confidence intervals con-tained zero and the ME values were not significantlydifferent from zero.

Table 3 summarizes the number of poor predictionsfor each method. Method 4 had fewer poor predic-tions (21·2%) when compared to other methods.Method 1 had the highest number of poor predictions(37·9%), most of which were over-predictions. Method5 had the next highest number of poor predictions(33·3%), most of which were under-predictions.Methods 2–4 tended to be unbiased for poor predic-tions; the number of over-predictions was equal to thatof under-predictions. With respect to the frequency ofpoor versus good predictions, comparisons of allmethods showed no significant differences.

DISCUSSION

The wide inter-individual variability in both Vm andKm for phenytoin and its narrow therapeutic indexhave created a demand for its routine use in thera-peutic drug monitoring during antiepileptic treatment.It is important to do this in the most cost-effectivemanner possible. With the limited number of plasmadata normally available in therapeutic monitoring,considerable efforts have been devoted to devisingand testing methods to individualize phenytoin dose

Phenytoin dosage predictions 49


Fig. 1. Predicted versus observed phenytoin dosage for each method.

50 E. Chan


based on a single-point phenytoin plasma concen-tration determined at steady-state. Such a dosingmethod (dosage optimization) should be without bias,have good precision and be as simple as possible toapply.

The present study examined five dosing methodsusing a single steady-state plasma concentration–dosepair to predict subsequent phenytoin dosage inSingapore Chinese patients with epilepsy. The predic-tive performance of method 1 (the fixed Km method)appeared to be inferior to the other four methods withrespect to bias (or accuracy) and precision. Previousstudies have demonstrated that variability in Km is themain factor causing inter-individual differences in thedosage and steady-state plasma concentration relation-ship (9). Substantial deviations of individual Km(i) fromthe population mean value might at least in part, ifnot completely, account for the three cases ofextremely large over-predictions and the relativelypoor predictive performance of the fixed Km method.

The correlation coefficients (0·866 and 0·841 formethods 4 and 5, respectively) obtained in this studyare similar to those (0·878 and 0·871, respectively)reported by Yukawa et al. (7) who demonstrated thecomparable predictive performance between methods4 and 5 in Japanese patients. The predictive perform-ance of methods 2–5 appeared to be similar in terms of

bias and precision. However, when the frequency ofpoor predictions were also taken into account, method4 (the fixed S method) tended to be more robust thanthe other methods, method 2 (the fixed Vm method)tended to outmatch both method 3 (the fixed Vm/Km

method) and method 5 (the Bayesian feedbackmethod), while method 1 (the fixed Km method)appeared to be the least promising prediction method.A trend was also demonstrated between method 2 andmethod 5 when Yuen et al. (8) examined the predictiveperformance between these two methods in USpaediatric patients, although they found the lattertended to have less poor predictions than the former.It is worthwhile to note that method 4 tended to havethe same number of under-predictions and over-predictions, whereas for method 5 most of the poorpredictions were under-predictions. A similar findingwas reported in Japanese patients by Yukawa et al. (7).Under-predictions may minimize the risk of potentiallytoxic dosages. This view may put method 5 in somesort of advantageous position over method 4. How-ever, subtherapeutic doses may leave epileptic patientswithout adequate control of fits, which may in turnincrease the risk of permanent brain damage. Method4 offers additional advantage over method 5, becausefor the application of the latter, software on Bayesianalgorithm for microcomputer is required, whereas thesimplicity of the former allows dosage predictionsusing a pocket calculator. As previously noted (9),there are differences in both Vm and Km (based on thetraditional Michaelis–Menten model) among differentethnic patient population groups. On the basis of thelogarithmic growth model, the S estimates (fromthe plots of ln Css versus daily dose) obtained in thepresent Chinese population (0·0216&0·0134 days/mgand 0·0127&0·0108 days/mg for 31·0&15·8 kgchildren and 57·1&12·3 kg adults, respectively) werehigher than those reported in Japanese patients

Method* Patients nBias, percentage dose(ME, 95% CI)

Precision, percentage dose(RMSE, 95% CI)

1 63† 3·01 ("5·95, 12·0) 74·4 (38·0, 53·3)‡2 66 "1·85 ("7·11, 3·41) 21·5 (13·3, 27·2)3 66 2·14 ("0·07, 3·35) 21·9 (15·5, 26·8)4 66 "1·079 ("6·27, 4·12) 21·1 (14·4, 26·2)5 66 "1·98 ("7·69, 3·73) 22·2 (11·6, 29·3)

Table 2. Comparison of single-pointdosage prediction methods

ME=mean error, RMSE=root meansquared error, CI=confidence interval.*Sources of methods: 1=Richens andDunlop, 2=Chiba et al., 3=Martin et al.,4=Wagner, 5=Bayesian feedback.†Three extreme cases excluded.‡Significantly different from methods2–5 (P<0·0001).

Table 3. Percentage of predictions with errors >20% ofobserved daily doses

Method 1 2 3 4 5

Over-prediction 22·7 13·6 15·2 10·6 10·6Under-prediction 15·2 13·6 15·2 10·6 21·7Total 37·9 27·2 30·4 21·2 33·3

Phenytoin dosage predictions 51


(0·0124&0·0049 days/mg and 0·0121&0·0070days/mg for 35·4&15·4 kg children and 54·5&7·9 kgadults, respectively), indicating that toxic plasma levelscould be achieved at lower phenytoin doses in ourethnic population group. Clearly, method 4 fulfilledthe criteria for a dosing method and the selection ofappropriate population parameter value is importantfor the success of its application.

The overall results obtained in the present studypoint to the usefulness of a single-point approach tophenytoin dosage prediction. The Bayesian methodwith one feedback (method 5) fails to display anyadvantage when compared to other methods, in par-ticular methods 2, 3 and 4, that require only part ofprior information about the population pharmaco-kinetic parameters of phenytoin. In view of the largenumber of predictions with an error of greater than20% of a dose, whichever method is employed to aidphenytoin dosage adjustments in epileptic patients,some individuals may still receive an inappropriatedosage regimen. It is therefore important that patientsreceive both phenytoin concentration monitoring andclinical status examination at appropriate intervalsafter dosage adjustments.

REFERENCES

1. Lund L. (1974) Anticonvulsant effect of diphenyl-hydantoin relative to plasma levels. Archives ofNeurology, 31, 289–294.

2. Richens A, Dunlop A. (1975) Phenytoin dosagenomogram. Lancet, 2, 1305–1306.

3. Martin E, Tozer TN, Sheiner LB, Riegelman S. (1977)The clinical pharmacokinetrics of phenytoin. Journal ofPharmacokinetics and Biopharmaceutics, 5, 579–596.

4. Chiba K, Ishizaki T, Miura H, Minagawa K. (1980)Michaelis–Menten pharmacokinetics of diphenylhydan-toin and application in the pediatric age patient. Journalof Pediatrics, 96, 479–484.

5. Sheiner LB, Beal SL. (1982) Bayesian individualizationof pharmacokinetics. Journal of Pharmaceutical Sciences,71, 1344–1348.

6. Wagner JG. (1985) New and simple method to predictdosage of drugs obeying simple Michaelis–Mentenelimination kinetics and to distinguish such kineticsfrom simple first order and from parallel Michaelis–Menten and first order kinetics. Therapeutic DrugMonitoring, 7, 377–386.

7. Yukawa E, Higuchi S, Aoyama T. (1988) Evaluation ofsingle-point phenytoin dosage prediction methods inpediatric patients. Journal of Pharmacobio-Dynamics, 11,736–743.

8. Yuen GJ, Latimer PT, Littlefield LC, Mackey RW.(1989) Phenytoin dosage predictions in paediatricpatients. Clinical Pharmacokinetics, 16, 254–260.

9. Chan E, Ti TY, Lee HS. (1990) Population pharmaco-kinetics of phenytoin in Singapore Chinese. EuropeanJournal of Clinical Pharmacology, 39, 177–181.

10. Yamaoka K, Nakagawa T, Tanaka H, Yasuhara M,Okumura K, Hori R. (1985) A nonlinear multipleregression program, 2(), based onBayesian algorithm for microcomputers. Journal ofPharmacobio-Dynamics, 8, 246–256.

11. Sheiner LB, Beal SL. (1981) Some suggestions formeasuring predictive performance. Journal of Pharmaco-kinetics and Biopharmaceutics, 9, 503–512.

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single-point phenytoin dosage predictions in singapore chinese

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