TRTR.RTRT {replicateBE}

Reference Datasets for TRTR|RTRT Designs

Description

Datasets from the public domain, edited, or obtained by simulations to be evaluated by method.A() and/or method.B().

Format

• Reference dataset 01
  77 subjects.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (seven missings in sequence TRTR and three in sequence RTRT). Missings / period: 0/1, 1/2, 7/3, 2/4. Two outliers (subjects 45 and 52) in sequence RTRT.
  A data frame with 298 observations on the following 6 variables:

  rds01

  subject	a factor with 77 levels: 1, 2, ..., 78
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)
  logPK	a numeric vector of the natural logarithms of PK

  In the source evaluated by SAS v9.1 for ABEL. Reported results:

  SAS Proc GLM

  CVwR	47.0%
  PE	115.66% (Method A)
  	115.73% (Method B)
  90% CI	107.11% – 124.89% (Method A)
  	107.17% – 124.97% (Method B)

• Reference dataset 06
  Based on rds01. 77 subjects. Responses of T and R switched.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (seven missings in sequence TRTR and three in sequence RTRT). Missings / period: 0/1, 1/2, 7/3, 2/4. No outliers.
  A data frame with 298 observations on the following 6 variables:

  rds06

  subject	a factor with 77 levels: 1, 2, ..., 78
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 08
  Simulated with slight heteroscedasticity (CV_wT = 70%, CV_wR = 80%), CV_bT = CV_bR = 150%, GMR = 0.85. 222 subjects.
  Balanced (222 subjects in both sequences) and complete. No outliers.
  The extreme sample size results from high variability, an assumed true GMR 0.85, and target power 90%.
  A data frame with 888 observations on the following 5 variables:

  rds08

  subject	a factor with 222 levels: 1, 2, ..., 222
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 09
  Based on rds08. Wide numeric range (data of last 37 subjects multiplied by 1,000,000). 222 subjects.
  Balanced (222 subjects in both sequences) and complete. No outliers.
  A data frame with 888 observations on the following 5 variables:

  rds09

  subject	a factor with 222 levels: 1, 2, ..., 222
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 12
  Simulated with extreme intra- and intersubject variability, GMR = 1.6487. 77 subjects.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (seven missings in sequence TRTR and three in sequence RTRT). Missings / period: 0/1, 1/2, 7/3, 2/4. No outliers.
  A data frame with 298 observations on the following 6 variables:

  rds12

  subject	a factor with 77 levels: 1, 2, ..., 78
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 13
  Based on rds08. Highly incomplete (approx. 50% of period 4 data deleted). 222 subjects.
  Balanced (111 subjects in both sequences) and incomplete (56 missings in both sequences). Missings / period: 0/0, 0/0, 0/0, 112/4. No outliers.
  A data frame with 776 observations on the following 5 variables:

  rds13

  subject	a factor with 222 levels: 1, 2, ..., 222
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 14
  Simulated with high variability, GMR = 1. Dropouts as a hazard function growing with period. 77 subjects.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (18 missings in sequence TRTR and 17 in sequence RTRT). Missings / period: 0/1, 4/2, 12/3, 19/4. No outliers.
  A data frame with 273 observations on the following 6 variables:

  rds14

  subject	a factor with 77 levels: 1, 2, ..., 78
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 15
  Based on ref08. Highly incomplete (approx. 50% of period 4 data coded as missing 'NA'). 222 subjects.
  Balanced (111 subjects in both sequences) and incomplete (56 missings in both sequences). Missings / period: 0/1, 0/2, 0/3, 112/4. No outliers.
  A data frame with 888 observations (112 NA) on the following 5 variables

  rds15

  subject	a factor with 222 levels: 1, 2, ..., 222
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 18
  Data set based on rds14. Removed T data of subjects 63–78. 77 subjects.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (32 missings in sequence TRTR and 31 in sequence RTRT). Missings / period: 8/1, 12/2, 18/3, 25/4. No outliers.
  A data frame with 245 observations on the following 6 variables:

  rds18

  subject	a factor with 77 levels: 1, 2, ..., 78
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 19
  Data set based on rds18. Removed data of subjects 63–78. 61 subjects.
  Unbalanced (31 subjects in sequence TRTR and 30 in RTRT) and incomplete (14 missings in both sequences). Missings / period: 0/1, 4/2, 9/3, 15/4. Two outliers (subjects 18 and 51 in sequence RTRT).
  A data frame with 216 observations on the following 6 variables:

  rds19

  subject	a factor with 61 levels: 1, 2, ..., 62
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 20
  Data set based on rds19. Extreme outlier of R (subject 1) introduced: original value ×100). 61 subjects.
  Unbalanced (31 subjects in sequence TRTR and 30 in RTRT) and incomplete (14 missings in both sequences). Missings / period: 0/1, 4/2, 9/3, 15/4. Two outliers (subjects 1 and 51 in sequence RTRT).
  A data frame with 216 observations on the following 6 variables:

  rds20

  subject	a factor with 61 levels: 1, 2, ..., 62
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 21
  Based on ds01. 77 subjects. One extreme result of subjects 45 & 52 set to NA.
  Unbalanced (39 subjects in sequence TRTR and 38 in RTRT) and incomplete (seven missings in sequence TRTR and five in sequence RTRT). Missings / period: 1/1, 1/2, 8/3, 2/4. No outliers.
  A data frame with 298 observations (2 NA) on the following 6 variables:

  rds21

  subject	a factor with 61 levels: 1, 2, ..., 62
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 25
  Simulated with heteroscedasticity (CV_wT = 50%, CV_wR = 80%), CV_bT = CV_bR = 130%, GMR = 0.85. 70 subjects.
  Balanced (70 subjects in both sequences) and complete. No outliers.
  A data frame with 280 observations on the following 5 variables:

  rds25

  subject	a factor with 70 levels: 1, 2, ..., 70
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

• Reference dataset 26
  54 subjects.
  Balanced (27 subjects in both sequences) and incomplete (two missings in both sequences). Missings / period: 0/1, 0/2, 2/3, 2/4. One outlier (subject 49) in sequence RTRT.
  A data frame with 216 observations on the following 5 variables:

  rds26

  subject	a factor with 54 levels: 1, 2, ..., 57
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (here Cmax)

  In the source evaluated by SAS for ABEL. Reported results (Method A):

  SAS Proc GLM

  CVwR	60.25%
  PE	151.3%
  90% CI	133.5% – 171.4%

• Reference dataset 29
  Simulated with heteroscedasticity (CV_wT = 14%, CV_wR = 28%, CV_bT = 28%, CV_bR = 56%), GMR = 0.90. 12 subjects.
  Imbalanced (five subjects in sequence TRTR and seven in sequence RTRT) and incomplete (three missings in sequence TRTR and four in sequence RTRT). Missings / period: 0/1, 1/2, 2/3, 4/4. One outlier (subject 11) in sequence RTRT.
  A data frame with 41 observations on the following 5 variables:

  rds29

  subject	a factor with 12 levels: 1, 2, ..., 20
  period	a factor with 4 levels: 1, 2, 3, 4
  sequence	a factor with 2 levels: TRTR, RTRT
  treatment	a factor with 2 levels: T, R
  PK	a numeric vector of pharmacokinetic responses acceptable for reference-scaling (generally Cmax)

Details

Dataset	N	CVwR (%)	Evaluation
rds01	77	>30	method.A(), method.B()
rds06	77	>30	method.A(), method.B()
rds08	222	>30	method.A(), method.B()
rds09	222	>30	method.A(), method.B()
rds12	77	>30	method.A(), method.B()
rds13	222	>30	method.A(), method.B()
rds14	77	>30	method.A(), method.B()
rds15	222	>30	method.A(), method.B()
rds18	77	>30	method.A(), method.B()
rds19	61	>30	method.A(), method.B()
rds20	61	>30	method.A(), method.B()
rds21	77	>30	method.A(), method.B()
rds25	70	>30	method.A(), method.B()
rds26	54	>30	method.A(), method.B()
rds29	12	<30	method.A(), method.B(), ABE()

Note

In software sequences and treatments are ranked in lexical order. Hence, executing str() or summary() will show sequence as "RTRT", "TRTR" and treatment as "R", "T". In BE – by convention – sequences are ordered with T first. The package follows this convention.

Author(s)

Helmut Schütz (R-code for simulations by Detlew Labes), Michael Tomashevskiy (simulations in Phoenix NLME)

Source

Dataset	Origin	Description
rds01	EMA	Annex II.
rds06	rds01 edited	T and R switched.
rds08	R	Large simulated data set with slight heteroscedasticity.
rds09	rds08	Wide numeric range (data of last 37 subjects multiplied by 1,000,000).
rds12	Phoenix NLME	Simulated with extreme intra- and intersubject variability.
rds13	rds08 edited	Highly incomplete (approx. 50% of period 4 data deleted).
rds14	Phoenix NLME	Simulated with high intra-/intersubject variability and
		number of dropouts increasing with period.
rds15	rds08 edited	Highly incomplete (approx. 50% of period 4 data coded as missing 'NA').
rds18	rds14 edited	Removed T data of subjects 63–78.
rds19	rds18 edited	Removed data of subjects 63–78.
rds20	rds19 edited	Outlier of R (subject 1) introduced: original value ×100.
rds21	rds01 edited	One extreme result of subjects 45 & 52 set to NA.
rds25	R	Simulated with heteroscedasticity.
rds26	Patterson & Jones	Cmax data given in Tables 4.40 and 4.31.
rds29	R	Simulated with heteroscedasticity; imbalanced and incomplete.

References

European Medicines Agency. London, 21 September 2016. Annex I, Annex II.

Patterson SD, Jones B. Bioequivalence and Statistics in Clinical Pharmacology. Boca Raton: CRC Press; 2^nd edition 2016. p105–6.

Examples

str(rds01)
summary(rds01[2:6])