sampleN.TOST: Sample size based on power of TOST
In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

sampleN.TOST

R Documentation

Sample size based on power of TOST

Description

Estimates the necessary sample size to obtain at least a target (desired) power.

Usage

sampleN.TOST(alpha = 0.05, targetpower = 0.8, logscale = TRUE,
             theta0, theta1, theta2, CV, design = "2x2",
             method = "exact", robust = FALSE, print = TRUE,
             details = FALSE, imax=100)

Arguments

`alpha`	Significance level (one-sided). Commonly set to 0.05.
`targetpower`	Power to achieve at least. Must be >0 and <1. Typical values are 0.8 or 0.9.
`logscale`	Should the data used on log-transformed (`TRUE`) or on original scale (`FALSE`)? Defaults to `TRUE`.
`theta0`	‘True’ or assumed T/R ratio or difference. In case of `logscale = TRUE` it must be given as ratio T/R. If `logscale = FALSE`, the difference in means. In this case, the difference may be expressed in two ways: relative to the same (underlying) reference mean, i.e., as (T-R)/R = T/R - 1; or as difference in means T-R. Note that in the former case the units of `CV`, `theta1` and `theta2` need also be given relative to the reference mean (specified as ratio). Defaults to 0.95 if `logscale = TRUE` or to 0.05 if `logscale = FALSE`
`theta1`	Lower (bio-)equivalence limit. In case of `logscale = TRUE` it is given as ratio. If `logscale = FALSE`, the limit may be expressed in two ways: difference of means relative to the same (underlying) reference mean or in units of the difference of means. Note that in the former case the units of `CV`, `theta0` and `theta2` need also be given relative to the reference mean (specified as ratio). Defaults to 0.8 if `logscale = TRUE` or to -0.2 if `logscale = FALSE`.
`theta2`	Upper (bio-)equivalence limit. In case of `logscale = TRUE` it is given as ratio. If `logscale = FALSE`, the limit may be expressed in two ways: difference of means relative to the same (underlying) reference mean or in units of the difference of means. Note that in the former case the units of `CV`, `theta0` and `theta1` need also be given relative to the reference mean (specified as ratio). If not given, `theta2` will be calculated as `1/theta1` if `logscale = TRUE` or as `-theta1` if `logscale = FALSE`.
`CV`	In case of `logscale=TRUE` the (geometric) coefficient of variation given as ratio. If `logscale=FALSE` the argument refers to (residual) standard deviation of the response. In this case, standard deviation may be expressed two ways: relative to a reference mean (specified as ratio sigma/muR), i.e., again as a coefficient of variation; or untransformed, i.e., as standard deviation of the response. Note that in the former case the units of `theta0`, `theta1` and `theta2` need also be given relative to the reference mean (specified as ratio). In case of cross-over studies this is the within-subject CV, in case of a parallel-group design the CV of the total variability.
`design`	Character string describing the study design. See `known.designs()` for designs covered in this package.
`method`	Method for calculation of the power. Defaults to `"exact"` in which case the calculation is done based on formulas with Owen’s Q. The calculation via Owen’s Q can also be choosen with `method = "owenq"`. Another exact method via direct use of the bivariate non-central t-distribution may be chosen with `⁠method = "mvt"⁠`. This may have somewhat lower precision compared to Owen’s Q and has a much longer run-time. Approximate calculations can be choosen via `⁠method = "noncentral"⁠` or `⁠method = "nct"⁠` for the approximation using the non-central t-distribution. With `⁠method = "central"⁠` or `⁠method = "shifted"⁠` the relatively crude approximation via the ‘shifted’ central t-distribution is chosen. The strings for `⁠method⁠` may be abbreviated.
`robust`	Defaults to `FALSE`. With that value the usual degrees of freedom will be used. Set to `TRUE` will use the degrees of freedom according to the ‘robust’ evaluation (aka Senn’s basic estimator). These df are calculated as `n-seq`. See `known.designs()$df2` for designs covered in this package. Has only effect for higher-order crossover designs.
`print`	If `TRUE` (default) the function prints its results. If `FALSE` only the data frame with the results will be returned.
`details`	If `TRUE` the design characteristics and the steps during sample size calculations will be shown. Defaults to `FALSE`.
`imax`	Maximum number of steps in sample size search. Defaults to 100. Adaption only in rare cases needed.

Details

The sample size is estimated 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.
The sample size is bound to 4 as minimum.

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

Value

A data frame with the input and results will be returned.
The Sample size column contains the total sample size.

Warning

The function does not vectorize properly.
If you need sample sizes with varying CVs, use f.i. ⁠for⁠-loops or the ⁠apply⁠-family.

Note

Of course it is highly recommended to use the default ⁠method = "exact"⁠. :-)
There is no reason besides testing and for comparative purposes to use an approximation if the exact method is available at no extra costs.

Author(s)

D. Labes

References

Phillips KF. Power of the Two One-Sided Tests Procedure in Bioequivalence. J Pharmacokin Biopharm. 1990;18:137–44. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF01063556")}

Diletti D, Hauschke D, Steinijans VW. Sample Size Determination for Bioequivalence Assessment by Means of Confidence Intervals. Int J Clin Pharmacol Ther Toxicol. 1991;29(1):1–8.

Diletti D, Hauschke D, Steinijans VW. Sample size determination: Extended tables for the multiplicative model and bioequivalence ranges of 0.9 to 1.11 and 0.7 to 1.43. Int J Clin Pharmacol Ther Toxicol. 1992;30(Suppl 1):S59–62.

Zhang P. A Simple Formula for Sample Size Calculation in Equivalence Studies. J Biopharm Stat. 2003;13(3):529–38. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1081/BIP-120022772")}

Examples

# Exact calculation for a classical 2x2 cross-over (TR/RT),
# BE limits 80 ... 125%, assumed true BE ratio 0.95, intra-subject CV=30%,
# using all the default values
# should give n=40 power=0.815845
sampleN.TOST(CV = 0.3)

# Exact calculation for a parallel group design
# evaluation on the original (untransformed) scale
# BE limits 80 ... 120% = -20% ... +20% of reference,
# assumed true BE ratio 0.95% = -5% to reference mean,
# total CV=20%
# should give n=48 (total) power=0.815435
sampleN.TOST(logscale = FALSE, theta1 = -0.2, theta0 = -0.05,
             CV = 0.2, design = "parallel")

# A rather strange setting of theta0! Have a look at n.
# It would be better this is not the sample size but the running total
# of my bank account. But the first million is the hardest. ;-)
sampleN.TOST(CV = 0.2, theta0 = 0.8005)

PowerTOST documentation built on May 29, 2024, 4:40 a.m.