Defaults

Note that analysis of untransformed data (logscale = FALSE) is not supported. The terminology of the design argument follows this pattern: treatments x sequences x periods.

Function `pa.ABE()`

Parameter	Argument	Purpose	Default
CV	`CV`	CV	none
\(\theta_{0}\)	`theta0`	‘True’ or assumed deviation of T from R	`0.95`
\(\pi\)	`targetpower`	Minimum desired power	`0.80`
\(\pi\)	`minpower`	Minimum acceptable power	`0.70`
design	`design`	Planned design	`"2x2x2"`
passed	`...`	Arguments to `power.TOST()`	none

If no addtional arguments are passed, the defaults of power.TOST() are applied, namely alpha = 0.05, theta1 = 0.80, theta2 = 1.25.

Arguments targetpower, minpower, theta0, theta1, theta2, and CV have to be given as fractions, not percent.
The CV is generally the within-subject coefficient of variation. Only for design = "parallel" it is the total (a.k.a. pooled) CV.

The conventional TR|RT (a.k.a. AB|BA) design can be abbreviated as "2x2". Some call the "parallel" design a ‘one-sequence’ design. The "paired" design has two periods but no sequences, e.g., in studying linear pharmacokinetics a single dose is followed by multiple doses. A profile in steady state (T) is compared to the one after the single dose (R). Note that the underlying model assumes no period effects.

With x <- pa.ABE(...) results are given as an S3-object which can be printed, plotted, or both.

The estimated sample sizes give always the total number of subjects (not subject/sequence in crossovers or subjects/group in parallel designs – like in some other software packages).

Function `pa.scABE()`

Parameter	Argument	Purpose	Default
CV	`CV`	CV	none
\(\theta_{0}\)	`theta0`	‘True’ or assumed deviation of T from R	`0.90`
\(\pi\)	`targetpower`	Minimum desired power	`0.80`
\(\pi\)	`minpower`	Minimum acceptable power	`0.70`
design	`design`	Planned replicate design	`"2x2x3"`
regulator	`regulator`	‘target’ jurisdiction	`"EMA"`
nsims	`nsims`	Number of simultions	`1e5`
passed	`...`	Arguments to `power.scABEL()` or `power.RSABE()`	none

If no addtional arguments are passed, the defaults of power.scABEL() and power.RSABE() are applied, namely alpha = 0.05, theta1 = 0.80, theta2 = 1.25.

Arguments targetpower, minpower, theta0, theta1, theta2, and CV have to be given as fractions, not percent. The CV is the within-subject coefficient of variation, where only homoscedasticity (CV_wT = CV_wR) is supported.

With x <- pa.scABE(...) results are given as an S3-object which can be printed, plotted, or both.

Function `pa.NTIDFDA()`

Parameter	Argument	Purpose	Default
CV	`CV`	CV	none
\(\theta_{0}\)	`theta0`	‘True’ or assumed deviation of T from R	`0.975`
\(\pi\)	`targetpower`	Minimum desired power	`0.80`
\(\pi\)	`minpower`	Minimum acceptable power	`0.70`
design	`design`	Planned replicate design	`"2x2x4"`
nsims	`nsims`	Number of simultions	`1e5`
passed	`...`	Arguments to `power.NTIDFDA()`	none

If no addtional arguments are passed, the defaults of power.NTIDFDA() are applied, namely alpha = 0.05, theta1 = 0.80, theta2 = 1.25.

With x <- pa.NTIDFDA(...) results are given as an S3-object which can be printed, plotted, or both.

Examples

Average Bioequivalence

Example 1

Example 3 of vignette ABE. Assumed \(\theta_{0}\) 0.92, CV 0.20.

pa.ABE(CV = 0.20, theta0 = 0.92)
# Sample size plan ABE
#  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power
#     2x2  0.05 0.2   0.92    0.8   1.25          28       0.822742
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV= 0.2377, theta0= 0.9001
#  n = 21 (power= 0.7104)

Fig. 1 Power Analysis (in each panel one argument is varied and others kept constant)

The most critical parameter is \(\theta_{0}\), whereas dropouts are the least important. We will see such a pattern in other approaches as well.

Reference-scaled Average Bioequivalence

Highly Variable Drugs / Drug Products

EMA

Example 2

Assumed intra-subject CV 0.55 (CV_wT = CV_wR).

pa.scABE(CV = 0.55)
# Sample size plan scABE (EMA/ABEL)
#  Design alpha CVwT CVwR theta0 theta1 theta2 Sample size Achieved power
#   2x3x3  0.05 0.55 0.55    0.9    0.8   1.25          42        0.80848
#  Target power
#           0.8
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV= 0.6668, theta0= 0.8689
#  n = 33 (power= 0.7085)

Fig. 2 Power Analysis (in each panel one argument is varied and others kept constant)

The idea behing reference-scaling is to preserve power even for high variability without requiring extreme sample sizes. However, we make two interesting observations. At CV_wR 0.55 already the upper cap of scaling (50%) cuts in and the expanded limits are the same as at CV_wR 0.50. Therefore, if the variability increases, power decreases. On the other hand, if the CV decreases, power increases first (because being affected by the upper cap is less likely) and then decreases again (because we can expand the limits less).

Example 3

Assumed intra-subject CV 0.40 (CV_wT = CV_wR), 4-period full replicate design.

pa.scABE(CV = 0.40, design = "2x2x4")
# Sample size plan scABE (EMA/ABEL)
#  Design alpha CVwT CVwR theta0 theta1 theta2 Sample size Achieved power
#   2x2x4  0.05  0.4  0.4    0.9    0.8   1.25          30        0.80656
#  Target power
#           0.8
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV= 0.6938, theta0= 0.8763
#  n = 23 (power= 0.7123)

Fig. 3 Power Analysis (in each panel one argument is varied and others kept constant)

Here we see a different pattern. With increasing variability power increases (due to more expanding) up to the cap of scaling where it starts to decrease like in the previous example. If the variability decreases, power decreases as well (less expanding). However, close the the switching CV (30%) power increases again. Although we cannot scale anymore, with 30 subjects the study is essentially ‘overpowered’ for ABE.

Health Canada

Example 4

Same data like in Example 2.

pa.scABE(CV = 0.55, regulator = "HC")
# Sample size plan scABE (HC/ABEL2)
#  Design alpha CVwT CVwR theta0 theta1 theta2 Sample size Achieved power
#   2x3x3  0.05 0.55 0.55    0.9    0.8   1.25          39        0.81418
#  Target power
#           0.8
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV= 0.7599, theta0= 0.8647
#  n = 30 (power= 0.7125)

Fig. 4 Power Analysis (in each panel one argument is varied and others kept constant)

Since we are close to Health Canada’s upper cap of 57.4%, power drops on both sides. Note that we need three subjects less than for the EMA’s method and CV_wR can increase to ~0.76 until we reach the minimum acceptable power – which is substantially higher than the ~0.67 for the EMA.

FDA

Example 5

Same data like in Example 2 and Example 4.

pa.scABE(CV = 0.55, regulator = "FDA")
# Sample size plan scABE (FDA/RSABE)
#  Design alpha CVwT CVwR theta0 theta1 theta2 Sample size Achieved power
#   2x3x3  0.05 0.55 0.55    0.9    0.8   1.25          30        0.80034
#  Target power
#           0.8
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV= 0.9713, theta0= 0.8652
#  n = 23 (power= 0.7001)

Fig. 5 Power Analysis (in each panel one argument is varied and others kept constant)

A similar pattern like the one of Health Canada, although due to the different regulatory constant we need nine subjects less (and twelve less than for the EMA). Caused by unlimited scaling the CV_wR can increase more.

Narrow Therapeutic Index Drugs (FDA)

Example 6

Assumed intra-subject CV 0.125.

pa.NTIDFDA(CV = 0.125)
# Sample size plan RSABE NTID
#  Design alpha  CVwT  CVwR theta0 theta1 theta2 Sample size Achieved power
#   2x2x4  0.05 0.125 0.125  0.975    0.8   1.25          16        0.82278
#  Target power
#           0.8
# 
# Power analysis
# CV, theta0 and number of subjects which lead to min. acceptable power of at least 0.7:
#  CV = (0.0716, 0.3059), theta0= 0.9569
#  n = 13 (power= 0.7064)

Fig. 6 Power Analysis (in each panel one argument is varied and others kept constant)

With decreasing variability power decreases because the scaled limits become narrower. With increasing variability we gain power because we have to scale less until at ~21.4% the additional criterion ‘must pass conventional BE limits of 80.00–125.00%’ cuts in.

function	author(s)
`pa.ABE`, `pa.scABE`	Idea and original code by Helmut Schütz with modifications by Detlew Labes
`pa.NTIDFDA`	Detlew Labes acc. to code by Helmut Schütz for `pa.ABE` and `pa.scABE`

International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use. ICH Harmonised Tripartite Guideline. Statistical Principles for Clinical Trials. 5 February 1998. E9 Step 4.↩︎

PowerTOST • Power Analysis

Details and examples of other methods are accessible via the menu bar on top of the page and in the online manual of all functions.

Defaults

Function `pa.ABE()`

Function `pa.scABE()`

Function `pa.NTIDFDA()`

Examples

Average Bioequivalence

Example 1

Reference-scaled Average Bioequivalence

Highly Variable Drugs / Drug Products

EMA

Example 2

Example 3

Health Canada

Example 4

FDA

Example 5

Narrow Therapeutic Index Drugs (FDA)

Example 6

Cave!

Authors

License

Helmut Schütz 2020-08-04

PowerTOST • Power Analysis

Details and examples of other methods are accessible via the menu bar on top of the page and in the online manual of all functions.

Defaults

Function pa.ABE()

Function pa.scABE()

Function pa.NTIDFDA()

Examples

Average Bioequivalence

Example 1

Reference-scaled Average Bioequivalence

Highly Variable Drugs / Drug Products

EMA

Example 2

Example 3

Health Canada

Example 4

FDA

Example 5

Narrow Therapeutic Index Drugs (FDA)

Example 6

Cave!

Authors

License

Helmut Schütz 2020-08-04

Function `pa.ABE()`

Function `pa.scABE()`

Function `pa.NTIDFDA()`