DMAR (version 1.0.0)

power_equivalence_md_plot: Plot TOST Equivalence-Test Power Curves Over a Range of True Differences

Description

For each sample size in n, draws power as a function of the true mean difference (or ratio, on the log scale), evaluated at 201 equally spaced points across the equivalence interval. Returns a ggplot2 object; the underlying numerical grid is attached as attr(<plot>, "power_grid").

Usage

power_equivalence_md_plot(
  alpha_level,
  logscale,
  theta1,
  theta2,
  sigma,
  n,
  nu,
  title = NULL,
  subtitle = NULL
)

Value

A ggplot object. The 201-row power grid (column 1: true difference; remaining columns: power for each n) is attached as

attr(<plot>, "power_grid").

Arguments

alpha_level

Type I error rate for each of the two one-sided tests.

logscale

Logical. If TRUE, the means are compared on the logarithmic scale.

theta1

Lower limit of the equivalence interval.

theta2

Upper limit of the equivalence interval.

sigma

\(\sqrt{\mathrm{error\ variance}}\).

n

Vector of sample sizes (one curve per element).

nu

Vector of degrees of freedom for sigma, the same length as n.

title

Optional plot title (default "Power of TOST").

subtitle

Optional subtitle (typically a reference like "Phillips, Figure 3").

Author

Ken Kelley [email protected]

References

Diletti, E., Hauschke, D., & Steinijans, V. W. (1991). Sample size determination of bioequivalence assessment by means of confidence intervals. International Journal of Clinical Pharmacology, Therapy and Toxicology, 29(1), 1--8.

Kelley, K. (2007a). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1--24. tools:::Rd_expr_doi("10.18637/jss.v020.i08")

Kelley, K. (2007b). Methods for the behavioral, educational, and social sciences: An R package. Behavior Research Methods, 39(4), 979--984. tools:::Rd_expr_doi("10.3758/BF03192993")

Phillips, K. F. (1990). Power of the two one-sided tests procedure in bioequivalence. Journal of Pharmacokinetics and Biopharmaceutics, 18(2), 139--144. tools:::Rd_expr_doi("10.1007/BF01063556")

Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657--680.

See Also

power_equivalence_md, power_density_equivalence_md

Other equivalence testing: equivalence_c(), equivalence_r(), equivalence_smd(), plot_equivalence(), power_density_equivalence_md(), power_equivalence_c(), power_equivalence_md(), ss_power_equivalence_c()

Other plotting: plot_R2(), plot_cfa_k(), plot_ci(), plot_equivalence(), plot_forest(), plot_irt_information(), plot_mediation_mbco(), plot_randomization_test(), plot_regions_of_significance(), plot_smd(), plot_trajectories(), plot_trajectories_fitted()

Examples

# One curve per sample size, showing power against the true mean
# difference. The seven sample sizes are the ones behind Figure 3 of
# Phillips, 1990, so the figure reproduces that one; every curve
# evaluates the power integral at 201 true differences.
n  <- c(9, 12, 18, 24, 30, 40, 60)
nu <- c(7, 10, 16, 22, 28, 38, 58)
fig <- power_equivalence_md_plot(
  alpha_level = .05, logscale = FALSE,
  theta1 = -.2, theta2 = .2, sigma = .20,
  n = n, nu = nu,
  subtitle = "Phillips Figure 3"
)
fig

# The numbers behind the curves travel with the figure, so a particular
# power value can be read off rather than eyeballed. The first column is
# the true difference and the remaining columns give power, one column
# per sample size. Power is highest where the true difference is zero.
power_grid <- attr(fig, "power_grid")
power_grid[which.min(abs(power_grid[, 1])), ]

# Figure 1c of Diletti et al., 1991, is the same idea on the log scale,
# where the equivalence limits are the 0.80 to 1.25 ratio bounds used
# in bioequivalence work.
n_d  <- c(8, 12, 18, 24, 30, 40, 60)
nu_d <- c(6, 10, 16, 22, 28, 38, 58)
power_equivalence_md_plot(
  alpha_level = .05, logscale = TRUE,
  theta1 = .8, theta2 = 1.25, sigma = .20,
  n = n_d, nu = nu_d,
  subtitle = "Diletti, Figure 1c"
)