analisis estadistico de datos para estudios de bioequivalencia niselman ada viviana cátedra de...

ANALISIS ESTADISTICO DE DATOS PARA ESTUDIOS DE BIOEQUIVALENCIA

NISELMAN ADA VIVIANACátedra de Matemática

Facultad de Farmacia y BioquímicaUniversidad de Buenos Aires

Número de voluntarios

El número de voluntarios de un estudio de bioequivalencia deberá ser calculado

teniendo en cuenta la Variabilidad Intraindividual,

la Máxima diferencia a ser detectada (20%; 0,20)

y los errores de Tipo I (Alfa =0,05) y Tipo II (Beta=0,20).

El cálculo del número de voluntarios,deberá figurar en el protocolo, así como la fórmula utilizada para su

cálculo y las asunciones estadísticas.

el tamaño total de muestra N , se podrá calcular de acuerdo a la siguiente fórmula

propuesta por Marzo y Balant (1995):

N > 15,68 x CV intraindividual2 / Δ2

Donde: CV es el Coeficiente de Variación

Intraindividual

Δ2 = 0,202 = 0,04.

Análisis estadístico

La metodología estadística deberá estar expresada en el protocolo

en el informe final

estableciendo los “límites de riesgo” de declarar falsamente

la bioequivalencia entre dos productos.

En la metodología se debe incluir estadística descriptiva estadística inferencial.

Análisis estadístico

La metodología estadística deberá estar expresada en el protocolo

en el informe final

estableciendo los “límites de riesgo” de declarar falsamente

la bioequivalencia entre dos productos.

En la metodología se debe incluir estadística descriptiva estadística inferencial.

Estadística descriptiva

1.2. - Para cada individuo:

a) Unidad de medida.

b) Valores en cada tiempo.

c) Secuencia.

d) Producto recibido (Test o Ref).

- Para cada concentración/tiempo:

a) Media aritmética . b) Mediana.

c) Desvío estándar. d) Coeficiente de Variación por ciento (CV%).

e) Valor mínimo (Mn). f) 1° cuartilo. g) 3° cuartilo

h) Valor máximo.(Mx).

Gráficos Exigidos

1) concentración/tiempo de cada voluntario con

las formulaciones Test y Referencia

(dos gráficos por voluntario).

2) Estas figuras se presentarán con los datos no transformados

logarítmicamente.

3) una figura resumen con los datos promedio (no transformados logarítmicamente) de cada tiempo (“Curvas resumen”).

4) Se deberán presentar todos los datos, incluso los de aquellos voluntarios

que hayan abandonado el estudio o representen valores extremos o atípicos.

e) Concentración máxima (Cmáx).

f) Tiempo en alcanzar Cmáx. (Tmáx). g) Constante de

eliminación (ke). h) Vida media (T½).

i) Área bajo la curva a tiempo t (AUCt)

j) Área bajo la curva a infinito (AUCinf).

. Tabla de la Secuencia para cada voluntario y cada tratamiento con:

a) Cmáx. b) Tmáx.

c) Ke. d) T½.

e) AUC0-t. f) AUCinf.

Para cada uno de los parámetros, expresar: • Media aritmética (Md).

• Mediana (Mn). • Media geométrica (MG).

• Desvío estándar. • Coeficiente de Variación por ciento (CV%).

• Valor mínimo (Mn). • 1° cuartilo. • 3° cuartilo

• Valor máximo.(Mx).

0.80 1.25T

R

Criterio de BE actual

Diseño ross-over 2x2

Transformación logaritmo

IC al 90% para GMR contenido en (0.80,1.25)

Análisis de Variancia (ANOVA)

ANOVA de los (ln) de (Cmáx, AUC0-t y AUCInf).

Se presentará la tabla del ANOVAde cada uno de los parámetros

Especificando las fuentes de variación (Secuencia/arrastre, Período, Tratamiento),

grados de libertad, suma de cuadrados, cuadrados medios,

valor del estadístico F y los valores correspondientes de p.

Análisis de Variancia (ANOVA)

La Hipótesis Nula a testear con el ANOVA es:

H0: μ T = μ R

CMAX

IND Seq

Period1

Period2

A TR 122 126

B RT 207 102

C RT 123 202

E TR 59 37

F RT 85 66

G TR 54 55

H RT 219 101

I TR 90 182

K RT 60 155

L TR 57 26

M TR 23 57

N RT 47 38

O RT 71 43

P TR 68 97

Q RT 88 28

R TR 99 60

Analysis of variance table: CMAX

df SS MS F P-Value

Inter-Subjects

Carry-over 1 0.5464 0.5464 1.0373 0.3257

Residuals 14 7.3738 0.5267 2.5147 0.0478

Intra-Subjects

Drug 1 0.1821 0.1821 0.8694 0.3669

Period 1 0.1109 0.1109 0.5293 0.4789

Residuals 14 2.9323 0.2095

Total 31 11.1454

AUCt

ID Seq

Period1

Period2

A TR 365 375

B RT 405 595

C RT 703 471

E TR 233 190

F RT 247 257

G TR 178 175

H RT 246 382

I TR 408 361

K RT 315 218

L TR 140 92

M TR 165 269

N RT 88 106

O RT 183 290

P TR 122 230

Q RT 68 144

R TR 275 344

Analysis of variance table: AUCt

df SS MS F P-Value

Inter-Subjects

Carry-over

1 0.054 0.054 0.090 0.767

Residuals 14 8.426 0.601 8.226 0.002

Intra-Subjects

Drug 1 0.024 0.024 0.332 0.573

Period 1 0.138 0.138 1.889 0.190

Residuals 14 1.024 0.073

Total 31 9.667

La Tabla modelo de análisis de variancia: debe especificará el CV Intraindividual %,Con datos log-transformados puede

calcularse con la siguiente formula:

100CV MSE

Ejemplo de Cálculo del CV

La raiz cuadrada del Cuadrado Medio del Error Residual estima el Coeficiente de Variación Intra –Sujeto.

27.00731.0 CMresCV

AUCinf

ID SeqPeriod1

Period2

A TR 409 418

B RT 613 432

C RT 492 774

E TR 256 224

F RT 285 265

G TR 205 190

H RT 398 263

I TR 433 406

K RT 236 372

L TR 331 105

M TR 195 327

N RT 125 113

O RT 313 215

P TR 148 266

Q RT 156 113

R TR 292 369

Analysis of variance table: AUCinf

df SS MS F P-Value

Inter-Subjects

Seq o Carry-over

1 0.0120 0.0120 0.0273 0.8711

Suj dentro de Seq o

Residuals

14 6.1520 0.4394 4.2245 0.0054

Intra-Subjects

Drug 1 0.0138 0.0138 0.1328 0.7210

Period 1 0.0195 0.0195 0.1879 0.6713

Residuals 14 1.4563 0.1040

Total 31 7.6537

In which cases may a non-parametric statistical model be used?Statistical analysis: “AUC and Cmax should be analysed using ANOVA after

log transformation.”The reasons for this request are the following:

a) the AUC and Cmax values as biological parameters are usually not normally distributed;

c) after log transformation the distribution may allow a parametric analysis.

d) due to the small sample size, is not recommended pre-test for normality.

e) Parametric testing using ANOVA on log-transformed data should be the rule.

f) For tmax, the use of non-parametric methods on the original data set is recommended.

TMAX

IND Seq Period1 P2

A TR 1,5 1,5

B RT 1,5 1,5

C RT 1,5 0,6

E TR 3 1

F RT 2 1

G TR 1,5 1,5

H RT 1 1

I TR 1,5 0,6

K RT 1,5 1,5

L TR 1 2

M TR 4 1,5

N RT 0,6 0,6

O RT 1,5 1

P TR 0,6 1,5

Q RT 1,5 1,5

R TR 2 2

INTERVALO DE CONFIANZA

- Relación T/R (Punto Estimado) y su intervalo de confianza 90%.

Se expresará para cada parámetro (Cmáx, AUC0-t y AUCinf),

la razón T/R (Punto Estimado) y el intervalo de confianza 90% de la misma.

Classical (shortest) IC: CMAXConfidence Bounds

ObservedWithin Equivalence

Limits?

Lower [10.00]% Conf. limit

0.6918 No

Upper [10.00]% Conf. limit

1.0690 Yes

Antilogged point estimate =0.86 00

Classical (shortest) Confidence Interval: AUCtConfidence Bounds

Observed

Within Equivalence

Limits?

Lower [10.00]% Conf. limit

0.9291 Yes

Upper [10.00]% Conf. limit

1.2017 Yes

Antilogged point estimate = 1.0567

Classical (shortest) Confidence Interval: AUCinfConfidence Bounds

ObservedWithin Equivalence

Limits?

Lower [10.00]% Conf. limit 0.8229 Yes

Upper [10.00]% Conf. limit 1.1183 Yes

Antilogged point estimate = 0.9593

Parámetro

Geo Mean

Media Test

Ratio estimado

IC

Cmax 80.89 69.56 0.86 0.69-1.06

AUCt 276.97 265.70 1.05 0.93-1.20

AUCinf 227.80 240.71 0.96 0.82-1.11

Test de la hipótesis intervalarAnderson Hauck

0 ) 0.80 1.25T T

R R

H o

0 ) 0.80 1.25T

R

H

Test de 2 las hipótesis unilateralesSchuirmann

/ 0.80 / 0.80) ) >H H01 11T R T R

/ 1.25 / 1.25) ) <H H02 12T R T R

Schuirmann:CMAX

t-Value One-sided p-value toreject non-

equivalence

Specified

Observed Specified Observed

Null Hypothesis L t-statistic

1.7613 0.4467 0.0500 0.3310

Null Hypothesis U t-statistic

-1.7613 -2.3115 0.0500 0.0183

Schuirmann AUCtt-Value One-sided p-value to

reject non-equivalence

SpecifiedObserved Specifie

dObserve

d

Null Hypothesis L t-

statistic

1.7613 2.9100 0.0500 0.0057

Null Hypothesis U

t-statistic

-1.7613 -1.7568 0.0500 0.0504

Schuirmann AUCinft-Value One-sided p-value to

reject non-equivalence

SpecifiedObserved Specified Observed

Null Hypothesis L t-

statistic

1.7613 1.5925 0.0500 0.0668

Null Hypothesis U

t-statistic

-1.7613 -2.3213 0.0500 0.0179

Conclusión Preliminar

AUCt y AUCinf satisfacen la cond de BE.

Cmax no la cumple con límites 0.80/1.25

Cmax la cumple con límites 0.70/1.33

Country/Region AUC 90% CI

Criteria

Cmax 90% CI

Criteria

Canada (most drugs) 80 – 125% none (point estimate only)

Europe (some drugs) 80 – 125% 75 – 133%

South Africa (most drugs)

80 – 125% 75 – 133% (or broader if justified)

Japan (some drugs) 80 – 125% Some drugs wider than 80 – 125%

Worldwide (WHO) 80 – 125% “acceptance range for Cmax may be wider than for AUC”

Criterios de aceptación de bioequivalencia

Wilcoxon-Mann-Whitney TMAXNull Hypothesis L: Mean T- Mean R <= Lower Bound Null Hypothesis U: Mean T- Mean R >= Upper Bound

Rank Sums

SpecifiedObserved

Null Hypothesis L test statistic

48.0000 42.0000

Null Hypothesis U test statistic

16.0000 21.0000

Hodges-Lehmann Interval: TMAXHodges-Lehmann estimate (median of all possible pairwise differences) = 0.0000

Confidence Bounds

Specified

Observed

Within Equivalence

Limits?

Lower [5.00]% Conf. limit

-0.2853 -0.4200 No

Upper [5.00]% Conf. limit

0.2853 0.5000 No

Suj Seq Period1 Period2 T/R

B RT 207 102 0,49275362

C RT 123 202 1,64227642

F RT 85 66 0,77647059

H RT 219 101 0,46118721

K RT 60 155 2,58333333

N RT 47 38 0,80851064

O RT 71 43 0,6056338

Q RT 88 28 0,31818182

A TR 122 126 0,96825397

E TR 59 37 1,59459459

G TR 54 55 0,98181818

I TR 90 182 0,49450549

L TR 57 26 2,19230769

P TR 68 97 0,70103093

R TR 99 60 1,65

Media 1,08472389

Desvio 0,68714366

2desvios 1,37428732

Med+/-2 desv -0,28956344 2,06143098

Bioavailability is defined as the rate and extent to which the active drug

ingredient is absorbed and becomes available at the site of drug action

Two drug products are said to be

bioequivalent if they are pharmaceutical equivalent or

pharmaceutical alternatives, and if their rates and extents of absorption do not show a significant difference.

Fundamental Bioequivalence Assumption

When a generic drug is claimed bioequivalent to a brand-name drug, it is assumed that they are

therapeutically equivalent.

Bioequivalence is claimed if the ratio of average bioavailabilities between test and reference products is within (80%,

125%) with 90% assurance (log-transformed data).

Confidence IntervalThe classical (shortest) confidence interval

Interval Hypotheses TestingShuirmann’s two one-sided tests procedure

FDA guidance on Statistical Approaches to Establishing

Bioequivalence (January, 2001)

FDA guidance on Bioavailability and Bioequivalence Studies for

Orally Administered Drug Products – General Considerations (July,

2002)

Most regulatory agencies including the U.S. Food and Drug Administration

(FDA) require evidence of bioequivalence in average

bioavailabilities between drug products.This type of bioequivalence is

referred to as ABE.

Based on the 2001 FDA guidance, bioequivalence may be established via

population and individual bioequivalence provided that the

observed ratio of geometric means is within the bioequivalence limits of 80%

and 125%.

A generic drug can be used as a substitute for the brand-name drug if it has been shown to be bioequivalent to

the brand-name drug.

Current regulations do not indicate that two generic copies of the same brand-

name drug can be used interchangeably,

even though they are bioequivalent to the same brand-name drug.

Bioequivalence between generic copies of a brand-name drug is not required.

Generic Drugs They’re cheaper, but do they work as

well?

Average Bioequivalence (ABE)Current regulatory requirement

Population Bioequivalence (PBE)Prescribability

Individual Bioequivalence (IBE)Switchability

Aggregate criterionMoment-based approach

Scaling methodWeighing factors

One-sided test

Drug PrescribabilityBrand-name vs. its generic copiesGeneric copies vs. generic copies

Drug SwitchabilityBrand-name vs. its generic copiesGeneric copies vs. generic copies

Current regulation for ABE does not guarantee drug prescribability and drug

switchability

Population Bioequivalence (PBE)Anderson and Hauck (1990)

Chow and Liu (1992)

The physician’s choice for prescribing an appropriate drug for his/her patients between the brand-name drug and its

generic copies

General Approaches for IBE/PBE

is a measure of the relative difference between the

mean squared errors of yR- yT and yR -

is the within-subject variance of the

reference formulation

for PBE

for IBE

' 2( ) 2R RE y y

2 2 2

2 20

( )

max{ , }T R TT TR

TR

2 2 2 2

2 20

( ) ( )

max{ , }T R D WT WR

WR

'Ry

Individual Bioequivalence (IBE)Anderson and Hauck (1990)

Schall and Luus (1993)Holder and Hsuan (1993)

Esinhart and Chinchilli (1994)

The switch from a drug (e.g., a brand-name drug or its generic copies) to

another (e.g., a generic copy) within the same patient whose concentration of the drug has been titrated to a steady,

efficacious and safe level

Notations

mT = mean of the test product

mR = mean of the reference product

sWT2 = within-subject variability for the test product

sWR2 = within-subject variability for the reference product

sD2 = variability due to the subject-by-formulation interaction

IBE Criterion

2 2 2 2

2 20

( ) ( )

max( , )T R D WT WR

IWR W

2

20

(ln1.25)I

W

Where

2 2 2 2

2 20

( ) ( )

max( , )T R D WT WR

IWR W

2 2 2 2

2 20

( ) ( )

max( , )T R D WT WR

IWR W

General Approaches for IBE/PBE

is a measure of the relative difference between the

mean squared errors of yR- yT and yR -

is the within-subject variance of the

reference formulation

for PBE

for IBE

' 2( ) 2R RE y y

2 2 2

2 20

( )

max{ , }T R TT TR

TR

2 2 2 2

2 20

( ) ( )

max{ , }T R D WT WR

WR

'Ry

Assessment of IBE

Hypotheses Testing

versus

IBE is claimed if a 95% confidence upper bound of is

less than and the observed ratio of geometric means

is within bioequivalence limits of 80% and 125%.

References 1. FDA (1999). In Vivo Bioequivalence Studies Based on Population and Individual

Bioequivalence Approaches. Food and Drug Administration, Rockville, Maryland,

August, 1999.

2. FDA (2001). Guidance for Industry: Statistical Approaches to Establishing

Bioequivalence. Food and Drug Administration, Rockville, Maryland, January, 2001.

0 : IBEH 0 : IBEH

IBE

Special IssuesChow, S.C. (Ed.) Special issue on Bioavailability and Bioequivalence of Drug Information Journal, Vol. 29,

No. 3, 1995Chow, S.C. (Ed.) Special issue on Bioavailability and

Bioequivalence of Journal of Biopharmaceutical Statistics, Vol. 7, No. 1, 1997

Chow, S.C. and Liu, J.P. (Ed.) Special issue on Individual Bioequivalence of Statistics in Medicine, Vol.

19, No. 20, October, 2000.

Review of FDA GuidancesChow, S. C. and Liu, J. P. (1994). Recent statistical

development in bioequivalence trials - a review of FDA guidance. Drug Information Journal, 28, 851-864.

Liu, J. P. and Chow, S. C. (1996). Statistical issues on FDA conjugated estrogen tablets guideline. Drug

Information Journal, 30, 881-889.Chow, S. C. (1999). Individual bioequivalence - a review of FDA draft guidance. Drug Information

Journal, 33, 435-444.Wang, H., Shao, J., and Chow, S.C. (2001). On FDA’s

statistical approach to establishing population

bioequivalence. Unpublished manuscript.

BooksChow, S.C. and Liu, J.P. (1998). Design and Analysis

of Bioavailability and Bioequivalence Studies, 2nd edition, Marcel Dekker, New York, New York.

Chow, S.C. and Shao, J. (2002). Statistics in Drug Research, Marcel Dekker, New York, New York.

Chow, S.C., Shao, J., and Wang, H. (2003). Sample Size Calculation in Clinical Research, Marcel Dekker,

Inc., New York, New York.

Original ArticlesShao, J., Chow, S. C., and Wang, B. (2000). Bootstrap

methods for individual bioequivalence. Statistics in Medicine, 19, 2741-2754.

Chow, S.C., Shao, J., and Wang, H. (2002). Individual bioequivalence testing under 2x3 crossover designs.

Statistics in Medicine, 21, 629-648. Chow, S.C. and Shao, J. (2002). In vitro

bioequivalence testing. Statistics in Medicine, 22, 55-68 .

Chow, S.C., Shao, J., and Wang, H. (2003). Statistical tests for population bioequivalence. Statistica Sinica,

13, 539-554.

OBJETIVOa) Discernir entre formulaciones

b) Evaluar el efecto producido en la disolución por los cambios en las variables del proceso de manufactura

aseguramiento de la calidad uniformidad de lote a lote

¿cómo cuantificar el grado de similitudo diferencia entre dos curvas?

FDA. Center for Drug Evaluation and Research, Guidance for Industry:

Modified Release Solid Oral Dosage Forms. Scale-up and Post-Approval Changes:

Chemistry, Manufacturing and Controls In Vitro, and In Vivo Bioequivalence Documentation

[SUPAC- MR ]; 1997 

FDA. CDER Guidance for

Industry Dissolution Testing

of Immediate Release Solid Oral Dosage

Forms. [SUPAC-IR]; 1997

METODO MODELO NO DEPENDIENTE, EMPLEANDO LOS FACTORES DE AJUSTE.

Jeffrey W. Moore et al (1996)

Se compara la diferencia en el % disuelto por unidad de tiempo entre referencia y prueba.

Estos factores son

f1 (factor de diferenciación)

f2 (factor de similitud) : 

Un valor f2 menor de 50 no indica necesariamente falta de similitud.

Si el patrocinador opina que las diferenciasen f2 son típicas para el producto

se puede presentar la justificación apropiada Como suplemento de aprobación previa.

Esta justificación deberá incluir análisis estadísticos de respaldo

(p.ej., un análisis de intervalo de confianza del 90%).