sampleN2.TOST {Power2Stage}

Sample size re-estimation of adaptive 2-stage BE studies in 2x2 crossover and parallel designs based on power of TOST

Description

This function estimates the necessary sample size of stage 2 to have at least a given power.

Usage

sampleN2.TOST(alpha = 0.0294, CV, n1, theta0 = 0.95,
              theta1 = 0.8, theta2 = 1.25, targetpower = 0.8,
              design = "2x2", method = "exact", imax = 100)

Arguments

alpha

Alpha value for the final analysis of pooled data. Defaults to Pocock’s alpha setting ⁠alpha=0.0294⁠.

CV

Coefficient of variation of the intra-subject variability as ratio.

n1

Sample size of stage 1.

theta0

True ratio of T/R for simulating. Defaults to 0.95 argument if missing.

theta1

Lower bioequivalence limit. Defaults to 0.8.

theta2

Upper bioequivalence limit. Defaults to 1.25.

targetpower

Power to achieve at least. Must be >0 and <1.

design

Character string describing the study design. Implemented are ⁠"2x2"⁠ and ⁠"parallel"⁠.

method

Method for calculation of the power. Implemented are ⁠"exact"⁠ (exact calculation via Owen’s Q), ⁠"nct"⁠ (approximate calculation via non-central t-distribution, and ⁠"shifted"⁠ (approximate calculation via shifted central t-distribution like in the paper of Potvin et al.
Defaults to ⁠"exact"⁠.

imax

Maximum number of steps in sample size search.
Defaults to 100. Adaption only in rare cases needed.

Details

The sample size is calculated via iterative evaluation of power of the TOST procedure.
Start value for the sample size search is taken from a large sample approximation according to Zhang, modified.

Value

A data.frame with the input and results will be returned.
The "Sample size" column contains the sample size for the second stage.

Note

Since in the final analysis one degree of freedom less than in a fixed sample design (or in stage 1) is used, power will be slightly lower than the one obtained with function ⁠sampleN.TOST⁠ of package ⁠PowerTOST⁠. However, different sample sizes are extremely unlikely.

Author(s)

H. Schütz, D. Labes

References

Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ, Smith RA.
Sequential design approaches for bioequivalence studies with crossover designs.
Pharm Stat. 2008; 7(4):245–62. doi: 10.1002/pst.294

Zhang P. A Simple Formula for Sample Size Calculation in Equivalence Studies.
J Biopharm Stat. 2003; 13(3):529–38. doi: 10.1081/BIP-120022772

Examples

# using all the defaults, CV of 25% and 12 subjects in stage 1
print(sampleN2.TOST(CV=0.25, n1=12), row.names=FALSE)
# should give a stage 2 sample size of 22 and achieved power ~0.812
# CV 10% and 12 subjects in stage 1
print(sampleN2.TOST(CV=0.1, n1=12), row.names=FALSE)
# should give a sample size of 0 (second stage not reasonable
# since power ~0.973 was already achieved in stage 1)