Post on 23-Jan-2016
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%).