power.dp {PowerTOST}

Power of dose-proportionality studies evaluated via Power model

Description

Calculates the power of dose-proportionality studies using the power model for crossover (Latin square) or parallel group designs via a confidence interval equivalence criterion.

Usage

power.dp(alpha = 0.05, CV, doses, n, beta0, theta1 = 0.8, theta2 = 1/theta1, 
         design = c("crossover", "parallel", "IBD"), dm = NULL, CVb)

Arguments

alpha

Type 1 error. Commonly set to 0.05.

CV

Coefficient of variation for intra-subject variability if design="crossover" or CV of total variability in case of design="parallel".

doses

Vector of dose levels. At least two doses have to be given.

n

Number of subjects. Is total number if given as scalar, else number of subjects in the (sequence) groups. In the latter case the length of n vector has to be the same as length of vector doses.
n has to be >2.

beta0

‘True’ slope of power model. If missing defaults to 1+log(0.95)/log(rd) where rd is the ratio of highest to lowest dose.

theta1

Lower acceptance limit for the ratio of dose normalized means (Rdmn).
Transformes into slope acceptance range as described under item beta0.

theta2

Upper acceptance limit for the ratio of dose normalized means (Rdmn).

design

Crossover design (default), parallel group design or incomplete block design (IBD).
Crossover design means Latin square design with number of doses as dimension.

dm

'Design matrix' of the incomplete block design (IBD) if design="IBD".
This matrix contains the sequences in rows and periods in columns. The entry (i, j) of the design matrix corresponds to the dose (index) a subject with i-th sequence gets in the j-th period. Can be obtained f.i. via functions of package crossdes or via function bib.CL().

CVb

Coefficient of variation of the between-subject variability.
Only necessary if design="IBD". Will be set to 2*CV if missing. This is only a crude rule of thumb. Better obtain an estimate of CVb from a previous crossover study.

Set CVb=0 if an all-effects-fixed model shall be used. This model gives higher power than the random subject effects model.

Details

The power calculations are based on TOST for testing equivalence of the slope of the power model with alternativ hypothesis slope = 1.
Power is calculated via non-central t-approximation only.
The calculations are based on mixed effects model (random intercept aka random subject effect). For design="cossover" or design="parallel" the results coincide with all-effects-fixed model.

Value

Value of power according to the input arguments.

Warning

This function is ‘experimental’ only since it is not thorougly tested yet. Especially for design="IBD" reliable test cases are missing.

Author(s)

D. Labes

References

Patterson S, Jones B. Bioequivalence and Statistics in Clinical Pharmacology. Boca Raton: Chapman & Hall/CRC: 2006. p. 239.
(contains presumably a bug)

Sethuraman VS, Leonov S, Squassante L, Mitchell TR, Hale MD. Sample size calculation for the Power Model for dose proportionality studies. Pharm Stat. 2007;6(1):35–41. doi:10.1002/pst.241

Hummel J, McKendrick S, Brindley C, French R. Exploratory assessment of dose proportionality: review of current approaches and proposal for a practical criterion. Pharm. Stat. 2009;8(1):38–49. doi:10.1002/pst.326

See Also

sampleN.dp, bib.CL

Examples

# using all the defaults, i.e. latin square crossover design, alpha=0.05, 
# beta0=1+log(0.95)/log(rd), theta1=0.8, theta2=1.25
power.dp(CV = 0.2, doses = c(1,2,8), n = 15)
#
# period balanced IBD with 3 doses, 2 periods and 3 sequences,
ibd <- matrix(c(1, 2, 3, 2, 3, 1), nrow = 3, ncol = 2)
power.dp(CV = 0.2, doses = c(1,2,8), n = 12, design = "IBD", dm = ibd)
# considerably lower than 3x3 Latin square