Statistične metode v Statistične metode v raziskavahraziskavah bioekvivalence bioekvivalence zdravilzdravil

Iztok GrabnarIztok Grabnar

Fakulteta za farmacijoFakulteta za farmacijo

Raziskave biološke Raziskave biološke uporabnosti in uporabnosti in bioekvivalencebioekvivalence

““The cutting edge of biomedical The cutting edge of biomedical sciences”sciences”

Znanstveni pogled:Interdisciplinaren značaj - Klinične discipline, kemijska in biokemijska analitika, farmacevtske znanosti (farmacevtska tehnologija, biofarmacija, farmakokinetika, farmakometrika)

Družbeni pogled:Udeleženi so - pacient, zdravnik (predpisovanje zdravil), farmacevt (izdaja zdravil), farmacevtska industrija, raziskovalne in regulatorne ustanove)

Vloga raziskav Vloga raziskav bioekvivalencebioekvivalence

• IND/NDAIND/NDA• ANDAANDA• Razvoj zdravila po registraciji Razvoj zdravila po registraciji

(SUPAC)(SUPAC)

DokumentiDokumenti

• FDAFDA– Code of Federal Regulations Title 21 Part 320Code of Federal Regulations Title 21 Part 320– Guidance for industry - Bioavailability and Guidance for industry - Bioavailability and

bioequivalence for orally administered drug bioequivalence for orally administered drug products- General considerationsproducts- General considerations

– Guidance for industry - Statistical approaches to Guidance for industry - Statistical approaches to establishing bioequivalenceestablishing bioequivalence

• EMEAEMEA– Note for guidance on the investigation of Note for guidance on the investigation of

bioavailability and bioequivalencebioavailability and bioequivalence

DefinicijeDefinicije

• Biološka uporabnostBiološka uporabnostBiovailability means the rate and extent to which the active Biovailability means the rate and extent to which the active ingredient or active moiety is absorbed from a drug product ingredient or active moiety is absorbed from a drug product and becomes available at the site of action.and becomes available at the site of action.

• BioekvivalencaBioekvivalencaAbsence of Absence of significant differencesignificant difference in the rate and extent to in the rate and extent to which the active ingredient or active moiety in which the active ingredient or active moiety in pharmaceutical equivalents or pharmaceutical alternatives pharmaceutical equivalents or pharmaceutical alternatives becomes available at the site of drug action when becomes available at the site of drug action when administered at the same molar dose under similar administered at the same molar dose under similar conditions in an conditions in an appropriately designed studyappropriately designed study..

• Terapevtska ekvivalencaTerapevtska ekvivalencaA medicinal product is therapeutically equivalent with A medicinal product is therapeutically equivalent with another product if it contains the same active substance or another product if it contains the same active substance or therapeutic moiety and, clinically, shows the same efficacy therapeutic moiety and, clinically, shows the same efficacy and safety as that product, whose efficacy and safety has and safety as that product, whose efficacy and safety has been established.been established.

Terapevtska ekvivalencaTerapevtska ekvivalenca

• EMEAEMEA– A medicinal product is therapeutically equivalent A medicinal product is therapeutically equivalent

with another product if it contains the same active with another product if it contains the same active substance or therapeutic moiety and, clinically, substance or therapeutic moiety and, clinically, shows the same efficacy and safety as that product, shows the same efficacy and safety as that product, whose efficacy and safety has been established.whose efficacy and safety has been established.

• FDAFDA– Drug products are considered to be therapeutic Drug products are considered to be therapeutic

equivalents only if they are pharmaceutical equivalents only if they are pharmaceutical equivalents and if they can be expected to have the equivalents and if they can be expected to have the same clinical effect and safety profile when same clinical effect and safety profile when administered to patients under the conditions administered to patients under the conditions specified in the labeling.specified in the labeling.

Dokaz bioekvivalenceDokaz bioekvivalence

• Farmakokinetična raziskavaFarmakokinetična raziskava• Farmakodinamična raziskavaFarmakodinamična raziskava• Klinična raziskavaKlinična raziskava• In VitroIn Vitro raziskava raziskava

Testno in referenčno Testno in referenčno zdravilozdravilo

Referenčno zdraviloReferenčno zdravilo

Klinično dokazana učinkovitost in Klinično dokazana učinkovitost in varnostvarnost

Èas

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Parametri biološke Parametri biološke uporabnostiuporabnosti

• AUCAUCtt, AUC, AUCinfinf, , AUCAUC7272, , CCmaxmax, t, tmaxmax, Ae, Aett, , AeAeinfinf, C, Cmaxmax/AUC, MRT/AUC, MRT

• AUCAUC, C, Cmaxmax, C, Cminmin, PTF, PTF

Hitrost absorpcijeHitrost absorpcije

• Drug exposure (FDA)Drug exposure (FDA)• Early drug exposure (površina pod Early drug exposure (površina pod

plazemsko koncentracijsko krivuljo od plazemsko koncentracijsko krivuljo od 0 do mediane t0 do mediane tmaxmax za referenčno za referenčno zdravilo)zdravilo)

• Peak (CPeak (Cmaxmax))

• Total (AUCTotal (AUCinfinf, AUC, AUCtt))

Pristop dokazovanja Pristop dokazovanja bioekvivalencebioekvivalence

• Bioekvivalenčni kriterijBioekvivalenčni kriterij• Interval zaupanjaInterval zaupanja• Limita bioekvivalenceLimita bioekvivalence

0.8 1.25

ProtokolProtokolraziskave bioekvivalenceraziskave bioekvivalence

BIOEQUIVALENCE STUDY PROTOCOL I. Title

A. Principle investigator (study director) B. Project/protocol number and date

II. Study objective III. Study design

A. Design B. Drug products

1. Test product(s) 2. Reference product

C. Dosage regimen D. Sample collection schedule E. Housing/confinement F. Fasting/meals schedule G. Analytical methods

IV. Study population A. Subjects B. Subject selection

1. Medical history 2. Physical examination 3. Laboratory tests

C. Inclusion/exclusion criteria 1. Inclusion criteria 2. Exclusion criteria

D. Restrictions/prohibitions

V. Clinical procedures A. Dosage and drug administration B. Biological sampling schedule and

handling procedures C. Activity of subjects

VI. Ethical considerations A. Basic principles B. Institutional review board C. Informed consent D. Indications for subject withdrawal E. Adverse reactions and emergency

procedures VII. Facilities VIII. Data analysis

A. Analytical validation procedure B. Statistical treatment of data

IX. Drug accountability X. Appendix

Načrt raziskaveNačrt raziskave

• Vrsta raziskaveVrsta raziskave• eno ali več testnih zdravileno ali več testnih zdravil• en odmerek ali več - stacionarno stanjeen odmerek ali več - stacionarno stanje• na tešče ali s hranona tešče ali s hrano

• Eksperimentalni načrtEksperimentalni načrt• Vzporedni (parallel)Vzporedni (parallel) ali navzkrižni (crossover) ali navzkrižni (crossover)• Ponovljena navzkrižna raziskavaPonovljena navzkrižna raziskava

Paralelni in navzkrižni Paralelni in navzkrižni eksperimentalni načrteksperimentalni načrt

Testne osebe

RANDOMIZACIJA Skupina 1

Skupina 2

Testnozdravilo

Referenčnozdravilo

Testne osebe

RANDOMIZACIJA Sekvenca 1

Sekvenca 2

Testnozdravilo

Referenčnozdravilo

Testnozdravilo

Referenčnozdravilo

Perioda 1 Perioda 2

• Sekvenca - g (TR ali RT)Sekvenca - g (TR ali RT)• Perioda - p (1 ali 2)Perioda - p (1 ali 2)• ZdraviloZdravilo - t (T ali R) - t (T ali R)• g × p navzkrižni eksperimentalni g × p navzkrižni eksperimentalni

načrtnačrt• Doba izpiranja in preneseniDoba izpiranja in preneseni učinek učinek

Navzkrižni Navzkrižni eksperimentalni načrteksperimentalni načrt

Navzkrižni Navzkrižni eksperimentalni načrteksperimentalni načrt

• Vsak osebek dobi testno in Vsak osebek dobi testno in referenčno referenčno zdravilozdravilo

• Vsak osebek je sam sebi kontrola - Vsak osebek je sam sebi kontrola - odstranimo vpliv interindividualne odstranimo vpliv interindividualne variabilnostivariabilnosti

• Z ustrezno randomizacijo osebkov v Z ustrezno randomizacijo osebkov v sekvence dobimo najboljšo oceno za sekvence dobimo najboljšo oceno za razliko v biološki uporabostirazliko v biološki uporabosti

I II1 T T2 R R3 T R4 R T

PeriodaSekvenca

I II III1 T R R2 R T T

SekvencaPerioda

I II III IV1 T T R R2 R R T T3 T R R T4 R T T R

SekvencaPerioda

Ponovljeni navzkrižni Ponovljeni navzkrižni eksperimentalni načrteksperimentalni načrt

Kateri eksperimentalni načrt je Kateri eksperimentalni načrt je najprimernejši?najprimernejši?

• Lastnosti učinkovineLastnosti učinkovine• Namen raziskaveNamen raziskave• Število razpoložljivih prostovoljcevŠtevilo razpoložljivih prostovoljcev• Inter in intraindividualna variabilnostInter in intraindividualna variabilnost• Trajanje raziskave (maksimalno Trajanje raziskave (maksimalno

število period)število period)• Verjetnost, da prostovoljec ne konča Verjetnost, da prostovoljec ne konča

raziskaveraziskave

Statistični modelStatistični model

ijkkjkjjikkijk eCFPSGY ),1(),(

Yijk farmakokinetični parameter pri osebku i, v sekvenci k in periodi j

celokupna aritmetična sredinaGk vpliv sekvence k (k=1,…,g) Gj = 0Sik vpliv osebka i v sekvenci k (k=1,…,g) - interindividualna

variabilnost: N(0,s2)

Pj vpliv periode j (j=1,…,p) Pj = 0F(j,k) vpliv zdravila v periodi j in sekvenci k F(j,k) = 0C(j-1,k) vpliv “carryover” učinka prvega reda za zdravilo v sekvenci

k s periodo j-1 C(0,k) = 0 in C(j-1,k) = 0eijk nepojasnjena varianca - intraindividualna variabilnost:

N(0,t2) t = 1,…,l

kn

1iijk

kjk Y

n

1Y j = 1,…,p in k = 1,…,g

(g × p - 1) prostostnih stopenj(g × p - 1) = (g - 1)+(p - 1)+(g - 1)(p - 1)

Vpliv sekvence

Vpliv interakcije med periodo in sekvenco

= Vpliv zdravila (T ali R) + “carryover”

Vpliv periode

2 × 2 navzkrižni 2 × 2 navzkrižni eksperimentalni načrteksperimentalni načrt

I II

1 (RT) 11 = + P1 + FR

21 = + P2 + FT + CR

2 (TR) 12 = + P1 + FT

22 = + P2 + FR + CT

PeriodaSekvenca

Št. prostostnih stopenj je 3: 1 perioda, 1 sekvenca, 1 njuna interakcija.

I II

1 (RT) 11 = + P1 + FR

21 = + P2 + FT + CR

2 (TR) 12 = + P1 + FT

22 = + P2 + FR + CT

PeriodaSekvenca

11 -

21 )

-

12 - 22 )

2 (FR - FT) - (CR - CT)

ANOVAANOVA

Interval zaupanjaInterval zaupanja

90 % interval zaupanja:

21

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L, U - limiti bioekvivalence

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Dvojni Schuirmannov Dvojni Schuirmannov enostranski t-testenostranski t-test

LRlnTln01 :H LRlnTln1a :H

URlnTln2a :H URlnTln02 :H

PrimerPrimer

Sekvenca Form. T Form. R Form. T Form. R1 TR 290 210 5,670 5,3472 RT 201 163 5,303 5,0943 TR 187 116 5,231 4,7544 TR 168 77 5,124 4,3445 RT 200 220 5,298 5,3946 RT 151 133 5,017 4,8907 TR 294 140 5,684 4,9428 RT 97 190 4,575 5,2479 RT 228 168 5,429 5,12410 TR 250 161 5,521 5,08111 TR 293 240 5,680 5,48112 RT 154 188 5,037 5,236

Mean 209,42 167,17 5,298 5,078sd 63,34 46,31 0,331 0,315

SubjektAUC ln(AUC)

ANOVAANOVA

Tests of Between-Subjects Effects

Dependent Variable: LNAUC

6.130E-02 1 6.130E-02 .46 .5131.332 10 .133 2.96 .051.450 1 .450 10.02 .010.290 1 .290 6.44 .029.450 10 4.496E-02

2.583 23

SourceSEQENCESUBJECT(SEQUENCE)PERIODTREATMENErrorTotal

Type III Sumof Squares df Mean Square F Sig.

“carryover” učinek 513.01332.0

0613.0FP 10,1

ANOVAANOVA

Tests of Between-Subjects Effects

Dependent Variable: LNAUC

6.130E-02 1 6.130E-02 .46 .5131.332 10 .133 2.96 .051.450 1 .450 10.02 .010.290 1 .290 6.44 .029.450 10 4.496E-02

2.583 23

SourceSEQENCESUBJECT(SEQUENCE)PERIODTREATMENErrorTotal

Type III Sumof Squares df Mean Square F Sig.

078.5R

298.5T

21

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1

n

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2tRT

376.0,063.06

1

6

1

281.122.0

2e

(1.065,1.457)

interval zaupanja

• Začetek 20. stoletja - prve raziskave biološke Začetek 20. stoletja - prve raziskave biološke uporabnostiuporabnosti

• BioekvivalencaBioekvivalenca• 1970-1984 1970-1984 Drugs price competition and patent Drugs price competition and patent

term restoration actterm restoration act

• 1984-1992 1984-1992 Guidance on statistical procedures Guidance on statistical procedures for bioequivalence studies using a for bioequivalence studies using a standard two-treatment crossover standard two-treatment crossover designdesign

• 1992-1992- Koncept populacijske in individualne Koncept populacijske in individualne bioekvivalence bioekvivalence ((generično predpisovanjegenerično predpisovanje, , generična generična zamenljivostzamenljivost))

Razvoj raziskav Razvoj raziskav bioekvivalencebioekvivalence

Populacijska in individualna Populacijska in individualna bbioekvivalenca ioekvivalenca

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“Bioekvivalenca gre naprej!”