journal of applied biopharmaceutics and pharmacokinetics ... · 20 journal of applied...

Journal of Applied Biopharmaceutics and Pharmacokinetics, 2017, 5, 19-25 19

E-ISSN: 2309-4435/17 © 2017 Synchro Publisher

Phenomenological and Mathematical Evaluation of Aberrant Values (Outliers) in Bioequivalence Studies

M. Manolache1, C. Mircioiu1, I. Mircioiu2,*, I. Prasacu1 and R. Sandulovici2

1University of Medicine and Pharmacy “Carol Davila”, Bucharest, Romania, Faculty of Pharmacy, 6th Traian Vuia str 2Titu Maiorescu University, Faculty of Pharmacy, Bucharest, Romania

Abstract: Outliers in results concerning both tested and reference drugs induce a high risk of a false bioequivalence decision. Paper presents phenomenological aspects which have to be examined in analysis of possible outlier data and some mathematical methods applicable in case of non-normal distributed data.

Experimental part is represented by a bioequivalence study of two formulations containing omeprazole, which is characterized by a high variability due to chemical instability of the protection film and active substance, food effects in absorption, partition of subjects between poor and extensive metabolizers, effect of omeprazole on regulation of gastrointestinal pH etc.

Examined parameters included Cmax, AUC and their ratios. Comparison was made both intra and inter- subjects. Alternative mathematical methods were discussed in case of ratios, when applicability of tests starting from normal distribution of data are no more applicable.

The results indicated that outliers influencing decision concerning bioequivalence appeared at the ratio of maximum concentrations which was influenced concomitant by chemical instability, food, absorption and metabolism.

Keywords: Phenomenological and mathematical outliers, omeprazole pharmacokinetic.

1. INTRODUCTION

Outlier signifies “out of line”, i.e. values differing from the rest of data, having a very low probability of appearance and representing a possible infringement of distribution law of the population data. The term is used mainly by mathematicians In biological domain some other terms as “discordant values”, or “non-normal values” or “discrepant values” are more usual [1].

Elimination of outlier data or curves was until recently considered practically unacceptable by drug authorities the Food and Drug Administration on Statistical Approaches to Establishing Bioequivalence stating that “deletion of outlier values is generally discouraged” [2]

The problem of outliers is much more general, the debate concerning it being connected to all clinical trials. For example guidance ICH E9 “Statistical principles for clinical trials” [3] specifies:

“Clear identification of a particular value as an outlier is most convincing when justified medically as well as statistically, and the medical context will then often define the appropriate action. Any outlier

*Address correspondence to this author at the Titu Maiorescu University, Faculty of Pharmacy, Bucharest, Romania; E-mail: [email protected]

procedure set out in the protocol or the statistical analysis plan should be such as not to favour any treatment group a priori.”

Acceptable explanations to exclude pharmacokinetic data or to exclude a subject would be protocol violations like vomiting, diarrhoea, analytical failure etc.

Outliers in bioequivalence (BE) studies became a very hot subject after introducing of the scaled criteria. Outliers connected with reference drug increase the within-subjects variability

!

WR

2 and implies the enlargement of the acceptance interval for bioequivalence.

A “good outlier” can increase so much acceptance region so that all tested drugs become bioequivalent. In these conditions the risk of acceptance of bioequivalence in case of non-bioequivalent drugs is very high, an un-acceptable risk for patients,

Following these considerations, recently, FDA launched a contest for a research concerning “Evaluation of Aberrant Observations and Their Impact on Bioequivalence Assessment ” [4].

Usual problems to be solved in case of suspicion of outliers would be:

• Evaluation of the probability of concerned data in a given hypothesis regarding distribution law experimental data,

20 Journal of Applied Biopharmaceutics and Pharmacokinetics, 2017, Vol. 5 Manolache, et al.

• Analysis of the effect of rejection of data on the decision concerning BE,

• Final decision of declaring data as “outliers” and their elimination.

Particularly, the “problem” is acute when omission of outliers lead to a bias in the decision of bioequivalence from rejection to acceptance. In this case appears naturally the suspicion of subjective analysis and torture of data.

Recent European guidance [5] for BE rules specify it concerns elimination of outliers:

“Exclusion of data cannot be accepted on the basis of statistical analysis or for pharmacokinetic reason alone because it is impossible to distinguish the formulation effects from other effects influencing the pharmacokinetics”.

As indirect rule, we could understand that correlated pharmacokinetics and statistical arguments would be the only acceptable approach.

The first part of this paper present some critical phenomena in the biopharmaceutical phase which can lead to suspected outlier data in BE studies which, by far, are much more numerous than that specified in guidance, implying an in depth analysis, previous to all mathematical hypothesis and statistical inferences.

Additionally, some of the “out of guidance phenomena” will be illustrated in case of a BE study comparing two omeprazole formulations.

2. METHODS

2.1. EXPERIMENTAL METHODS

2.1.1. Clinical Method

A two periods, cross-over study, with two sequences was undertaken in order to compare LOSEC® 20 mg (gastrorezistant capsules containing 20 mg omeprazole).

2.1.2. Astra Zeneca

Astra Zeneca with a generic formulation. One week of wash-out period separated consecutive treatments. Blood samples were collected before dosing (0.0 hours) and 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 10.0 and 12.0 after drug administration.

The study was approved by National Ethics Committee and National Medicines Agency.

2.1.3. Analytical Method

Plasma levels of omeprazole were determined using a liquid chromatographic validated method.

2.1.4. Computerized Methods for Estimation of Parameters

Pharmacokinetic analysis was performed using the subroutines of the software KINETICA 3.1 and TOPFIT 2.0 [6].

3. CRITICAL PHENOMENA INDUCING OUTLIER DATA IN BE STUDIES

Pharmacokinetics of omeprazole was highly variable it concerns time-lag, maximum concentration, time of maximum, area under curve as can be seen in figure 1.

!

"!!

#!!!

#"!!

$!!!

$"!!

! $ % & ' #! #$()*+,-./

!

Figure 1: Plasma levels of omeprazole, reference (R) and tested (T) formulation.

Phenomenological and Mathematical Evaluation of Aberrant Values Journal of Applied Biopharmaceutics and Pharmacokinetics, 2017, Vol. 5 21

This variability was observed also by other authors [7-10] being determined by a series of phenomena and parameters in both biopharmaceutic and pharma-cokinetic phase.

3.1. Potentially Critical Phenomena in Biopharmaceutical Phase

After administration of a dosage form, occurs the release of active substance which is called usually biopharmaceutical phase. In vivo release is not accessible to experiments, so that, estimations regarding phenomena in this phase are obtained from in vitro experiments and for further correlations between these results and in vivo measured pharmacockinetics.

Rate and extent of the in vivo release kinetics are function of: dose, excipients, solubility, micelar solubility, administered form of active substance (base or salt), interconversions, stability, supersaturation, physiological of different GI segments conditions, blood preprandial and postprandial conditions during the trial, liver preprandial and postprandial, food and fasting conditions. Practically all these factors could become a source of outlier data.

In case of omeprazole we have to take into consideration first of all its stability. Which is strongly dependent on pH. It is decomposed in acidic conditions, and is stable in alkaline conditions, this being the reason of its formulation as enterosoluble pellets. Since the enterosoluble film is not completely resistant to gastric secretion, a smaller or greater part of pellets being destroyed, with an effect on both Cmax and area under curve (AUC).

An in vitro dissolution experiment reported wide different properties for two given products. Less than 10% of the drug content was recovered from the tested formulation following a pre-exposure to pH 3 or 4, compared with over 90% recovered from the Losec® formulation [11].

Another source of outlier behaviour issues from the partition coefficient of omeprazole, logP=2.24 [12]. Its higher solubility in lipids lead to an interaction with food during absorption and to intensive first pass metabolism after absorption.

Dramatic effect of foods on variability of pharmacokinetics can be seen in figure 2.

Figure 2: Plasma levels of omeprazole in feed conditions.

An increased resistance of the film covering omeprazole pellets can lead to apparition of a lag-time in absorption and increase of the time of maximum concentration (Figure 3).

Figure 3: Delayed absorption of omeprazole in one patient.

3.2. Critical Phenomena in Pharmacokinetic Phase

In pharmacokinetic phase outlier candidates could be individual plasma concentrations, entire curves, pairs of curves subsets of curves etc.),

Following the chemical decomposition of omeprazole after release in gastric acidic secretion it is possible to appear very low maximum concentrations and areas under curves. As can be seen in figure 1 there is a very high inter-subject variability in plasma levels but outliers seem to appear mainly as very large AUCs rather than very small ones.


At gastric level there is another factor influencing stability of omeprazole, but in opposite direction. It should be retained that Omeprazole inhibit acid secretion. Consequently, omeprazole is more stable after several administrations, due to the inhibition of gastric acid secretion and this results to the increase of its bioavailability (higher Cmax and AUC values), than after first administration [13]. From here, it is possible to appear, at some subjects, high ratios between the values of pharmacokinetic parameters in first and in second period. One example is given in the figure 3.

!"!

!"#

!"$

!"%

!"&

'"!

'"#

! '! #! (!

)*+,-.-/0

123456-4

123456-44

Figure 3: Outliers it concerns the ratio between parameters in the two periods of the study ( a. volunteer 3, b. volunteer 27).

The problem is that, as can be seen in figure 3b, it happened also appearance of lower concentrations in the second phase. Or, possible, the maximum concentration in the phase I in figure 3a is an outlier.

Omeprazole undergoes rapid and extensive metabolism in the liver, the oxidative processes being predominant [14, 15].

Direct sequencing of the CYP2C19 gene was performed in 50 randomly selected Korean subjects. Some individuals exhibited an outlier phenotype response in the omeprazole study, presenting a significant decrease in omeprazole metabolism in vivo. [16]. Metabolism of omeprazole was proposed as a method for identification and selection of outliers in a population [17].

In this case, outlier higher plasma levels could be explained as consequence of reduced metabolism.

In fact inter-subjects variability does not influence the decision concerning bioequivalence. But a part of characteristics of subjects can change from first period to the second one. For example is reported that chronic administration of 40 mg doses of omeprazole shifts the metabolic ratio in extensive metabolizers toward that in poor metabolizers (PMs), apparently because of the nonlinear metabolic clearance of the drug [18].

Finally, the factors implicated in bioavailability and pharmacokinetics of active substances administered in different formulations are much more numerous than usually considered, acting in different directions. In fact their evaluation have to start from final, naked eye and statistical suspicion concerning existing of outliers. As it was discussed, outliers considered until recent time were considered only in the yard of tested drugs. The outliers in pharmacokinetics of reference drugs were considered as inoffensive and treated with unpardonable indulgence. From this reason the problem was not analyzed in depth and have farther to integrate physicochemical, physiological and mathematical aspects.

3.3. Mathematical and Statistical Approach

From the mathematical point of view, the central method of rejecting some values as outliers is based on the structure of errors in a “normal” distributed population [19-22].

If values are normal distributed, the most probable is the mean value, and probability of other values decreases exponentially with their distance from mean.

Probability of finding a value in a given interval (a, b) is given by the formula:

P(a < X < b) =1

! 2"e

#(x#µ)2

2! 2

$

%

& dx (1)


Where, σ2 is the variance and µ is the mean of population.

Even in the case of values which are not normal distributed, the probability of the values in the interval (µ-3σ, µ+3σ) remains very high.

In such case, it seems that it is possible to solve problem of outliers is the frame of mathematics. Unfortunately, this is not true.

Bioequivalence of the two formulations was tested using two-sided Schuirmann test [23]. Pharmacokinetic parameters Cmax and AUC obtained in the experiment were considered, after logaritmation as normally distributed random variables with the structure [24]:

Yijk = µ + Sik + Pj + F(j,k) + C(j-1,k) + eijk

where;

‐ µ = the overall mean

‐ i = index for subject, i = 1, nk

‐ j = index for period

‐ k = index for sequence

‐ F(j,k) = the direct fix effect of the formulation in the kth sequence which is administered at the jth period k

‐ C(j-1,k = the fixed first-order carry - over effect of the formulation in the kth sequence which is administered at the (j-1)th period, where C(0,k) = 0 and ΣC(j-1,k)=0

‐ eijk = the (within subject) random error in observing Yijk .

The Sik is the random variable corresponding to subject i in the sequence k and is considered to be normally distributed with the same mean and the same variance for all subjects. This happens in almost but not in all cases. For example if subject population is partitioned in two subpopulations, poor and extensive metabolizers, the decision concerning bioequivalence is not directly influenced, but usual rules for defining mathematically the outliers are seriously affected.

Sharing into subclasses of the population of plasma level curves can appear even in cases not connected with metabolism, like for example in a study concerning meloxicam suppositories [25]. Partition into two separated subsets appeared only in case of reference drug, being connected with the biopharmaceutical phase of release of meloxicam from suppositories. The

formulations appeared clear as being bioequivalent, but the application of usual parametric rules failed to prove this.

0,0

0,5

1,0

1,5

2,0

0

1

2

3

3

,

4

4

,

5

67

8

9

1

0

1

2

2

4

4

8

7

2

Figure 4: Plasma levels of meloxicam after administration of suppositories.

!

"!

#!!

#"!

$!!

$"!

! $! %!

Figure 5: Ratio of maximum concentrations

C

max

T / Cmax

R (%) a. As function of number of patient, b. ordered values (the numbers of subjects were assigned randomly).


The mathematical problem of deciding on the outlier character of a result becomes much more difficult for example in the case of ratios of parameters but these ratios determine bioequivalence. In our study, two ratios were found approximately 200% (figure 5). Naked eye examination put in evidence that these two values are isolated, are “outlier values”. Cmax or more exactly log Cmax populations are normally distributed, but the distribution of their ratios is unknown and usual methods are no more applicable.

For ratios presented in Table 1, it was applied the classical Dixon test for extreme values [26] in our case the highest data.

r =Xk! X

k!2( )Xk! X

3( )

where, X k is the highest value,

Table 1:

R T T/R Order T/R

352 271 77 65

1397 1066 76 66

2321 2390 103 67

418 278 66 70

487 600 123 73

1173 855 73 74

302 380 126 76

1404 935 67 77

661 565 85 79

590 476 81 81

511 542 106 82

330 214 65 84

365 305 84 85

431 403 93 89

916 1026 112 91

554 758 137 93

1146 800 70 93

1413 1451 103 94

450 932 207 101

563 462 82 103

595 719 121 103

358 325 91 106

680 501 74 107

454 691 152 112

1195 1204 101 112

1345 1203 89 114

521 797 153 121

955 883 93 121

726 876 121 123

1657 1889 114 126

603 646 107 134

455 361 79 137

328 368 112 152

775 1495 193 153

1747 1646 94 193

322 431 134 207

mean T/R= 105

stdev 33

It was obtained the value r=0.39 and, since the result is not greater than 0.40, the 5% level of significance, 207 cannot be considered outlier in contradiction with what suggests the naked eye examination of figure 5.

Another highly recommended test for outliers, the T method, is also calculated as a ratio, designated Tn, as follow [27]:

Tn=

Xn! X

S,

where, X n is the highest/extreme value, X is the mean and S is the standard deviation.

The value obtained using T method was 3.1, so the data is greater than 2.9, the 5% level of significance. We can consider, either in this situation, the subject as outlier, i.e. the two tests are in contradiction, the highest ratio being, statistically, at the frontier between outlier or not outlier. Final decision could be taken in correlation with phenomenological considerations, in this case maybe the behavior of some subjects as poor metabolizers.

CONCLUSIONS

1. Outliers in bioequivalence studies have to be considered both connected with tested and reference drugs. Their elimination is no more banned since their neglecting could increase unacceptable the risk of patients.

2. Extreme results came from physico-chemical properties of drugs and their performance, from physiology of individual patients and from drug – living body interactions.


3. In case of omeprazole processes with variable rate and extent leading to possible outliers are in the biopharmaceutical phase, connected with stability of protective film and active substance, release kinetics, absorption and metabolism. Extreme values appeared in maximum concentrations, time of maximum concentrations and areas under plasma levels curves, but an influence of the decision concerning bioequivalence had only the maximum concentrations.

4. Usual mathematical methods for deciding the outlier character are applicable when data are normally distributed. In case of data splitted in different classes or ratios of data, have to apply less discriminative, but distribution free tests.

5. Considering the above results and other additional experience of authors, it is to propose the following rule in analyses of outliers data and subjects in BE studies: first to evaluate the data from the point of view of physiological pharmacokinetics, then apply the statistic tests and finally to evaluate the implications of decision concerning outliers on the decision concerning bioequivalence.

REFERENCES

[1] Barnett V and Lewis T. Outliers in Statistical Data 1994; 3-rd Edition, John Wiley.

[2] FDA. Guidance for Industry - Statistical Approaches to Establishing Bioequivalence 2001. Available at: https://www.fda.gov/downloads/ drugs/ guidances/ ucm070244.pdf

[3] http://www.ich.org/fileadmin/Public_Web_Site/ ICH_Products/Guidelines /Efficacy /E9/Step4/ E9_Guideline. pdf

[4] https://grants.nih.gov/grants/guide/rfa-files/RFA-FD-16-018.html

[5] Revised guideline on the conduct of bioequivalence studies for veterinary medicinal products. [http://www.ema. europa.eu/docs/en_GB/document_library/Scientific_ guideline]

[6] Heinzel G, Woloszczak R and Thomann P. Pharmacokinetic and Pharmacodynamic Data Analysis System for PC, Gustav Fisher Verlag, New York 1993.

[7] Regardh CG, Andersson T, Lagerstrom P, et al. The pharmacokinetics of omeprazole in humans. A study of single intravenous and oral doses. Ther Drug Monit 1990; 12:163-72. https://doi.org/10.1097/00007691-199003000-00010

[8] Regardh CG, Gabrielsson M, Hoffman KJ, et al. Pharmacokinetics and metabolism of omeprazole in animals and man. Scan J Gastroenterol Suppl 1985; 108: 79-94. https://doi.org/10.3109/00365528509095821

[9] Regardh CG. Pharmacokinetics and metabolism of omeprazole in man. Scan J Gastroenterol Suppl 1986; 118:

99-104. https://doi.org/10.3109/00365528609090907

[10] Cederberg C, Andersson T and Skanberg I. Omeprazole pharmacokinetics and metabolism in man. Scan J Gastroenterol Suppl 1989; 166: 33-40. https://doi.org/10.3109/00365528909091241

[11] Elkoshi Z, Behr D, Mirimsky A, Tsvetkov I and Danon A. Multiple-Dose Studies can be a More Sensitive Assessment for Bioequivalence than Single-Dose Studies: The Case with Omeprazole. Clin Drug Invest 2002; 22(9): 585-592. https://doi.org/10.2165/00044011-200222090-00003

[12] CDER NDA. 22-056 Prilosec (Magnezium omeprazole Delayed release oral suspension) Application, https://www.accessdata.fda.gov/drugsatfda .../022056s000EA.pdf

[13] Larson C, Cavuto NJ, Flochhart DA, et al. Bioavailability and efficacy of omeprazole given orally and by nasogastric tube. Dig Dis Sci 1996; 41(3): 475-9 https://doi.org/10.1007/BF02282321

[14] Ishizaki T, Sohn DR, Kobayashi K, et al. Interethnic differences in omeprazole metabolism in the two S-mephenytoin hydroxylation phenotypes studied in caucasians and orientals. Ther Drug Monit 1994; 16: 214-5 https://doi.org/10.1097/00007691-199404000-00018

[15] Andersson T, Regardh CG, Dahl-Puustinen ML, et al. Slow omeprazole metabolizers are also poor S-mephenytoin hydroxylators. Ther Drug Monit 1990; 12: 415-6 https://doi.org/10.1097/00007691-199007000-00020

[16] Su-Jun Lee, Woo-Young Kim, Hyunmi Kim, Ji-Hong Shon, Sang Seop Lee and Jae-Gook Shin, Identification of New CYP2C19 Variants Exhibiting Decreased Enzyme Activity in the Metabolism of S-Mephenytoin and Omeprazole, Drug Metab Dispos, Epub 2009; 37(11): 2262-9.

[17] Arthur J. Atkinson, Principles of Clinical Pharmacology, Academic Press 2012.

[18] Kovacs, Peter*, Edwards, David J+, Lalka, David++ and Scheiwe Werner M. [S]; Stoeckel, Klaus [P] [High-Dose Omeprazole: Use of a Multiple-Dose Study Design to Assess Bioequivalence and Accuracy of CYP2C19 Phenotyping. Therapeutic Drug Monitoring 1999; 21(5): 526. https://doi.org/10.1097/00007691-199910000-00006

[19] Liao JJ. A new approach for outliers in a bioavailability/bioequivalence study. J Biopharm Stat. 2007; 17(3): 393-405. https://doi.org/10.1080/10543400701199528

[20] Ramsay T and Elkum N. A comparison of four different methods for outlier detection in bioequivalence studies. J Biopharm Stat 2005; 15(1): 43-52. https://doi.org/10.1081/BIP-200040815

[21] Examining outlying subjects and outlying records in bioequivalence trials. Wang W, Chow SC, J Biopharm Stat 2003; 13(1): 43-56. https://doi.org/10.1081/BIP-120017725

[22] Chow SC and Tse SK. Outlier detection in bioavailability/bioequivalence studies. Stat Med. 1990; 9(5): 549-58. Erratum in: Stat Med 1992; 11(3): 425. https://doi.org/10.1002/sim.4780090508

[23] Schuirmann DJ. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability J. Pharmacokin. Biopharm 1987; 15: 657-680. https://doi.org/10.1007/BF01068419

[24] Chow SC and Liu JP. Design and Analysis of Bioavailability and Bioequivalence Studies, cap. III, cap. IV; S. Bolton. Pharmaceutical Statistics, M. Dekker 1997.

[25] Vătăşescu A, Enache F, Mircioiu C, Miron DS and Sandulovici R. Failure of statistical methods to prove bioequivalence of meloxicam drug products. I. parametric methods, Farmacia 2011; 59(2): 161-169.


[26] Dixon WJ. Analysis of extreme values. Annals of Math Stat 1950; 21: 488-506. https://doi.org/10.1214/aoms/1177729747

[27] Bolton S and Bon C. Pharmaceutical Statistics, Informa Healthcare, Ney York, 2004.

Received on 19-12-2017 Accepted on 30-12-2017 Published on 31-12-2017 DOI: http://dx.doi.org/10.20941/2309-4435.2017.05.4

© 2017 Manolache, et al.; Licensee Synchro Publisher. This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

journal of applied biopharmaceutics and pharmacokinetics ... · 20 journal of applied...

Documents