## Plot the passing-rate curve and the passing-rate surface in IVPT

### Description

This function plots the power (passing-rate) curve and power (passing-rate) surface of the mixed scaling (MS) approach. A power curve shows the statistical power across different effect sizes. In IVPT studies, the effect size is captured by the difference between the means of log-measurements of the test and reference products (i.e., logGMR). For the passing-rate surface, the corresponding function considers different values of the standard deviation.

### Usage

PRsurface(
n,
r,
observed_GMR = 0.95,
observed_sigmaWR = 0.294,
GMR_grid = seq(0.75, 1.3, length.out = 100),
sigmaWR_grid = seq(0.2, 1, length.out = 100),
params = list(),
nsim = 1000,
ncores = NULL,
verbose = FALSE,
plot = TRUE
)


### Arguments

 n The number of donors in each simulation. r The number of replicates from each donor for each simulated dataset. observed_GMR The observed (estimated) GMR of the user's data. Along with the observed sigmaWR, the corresponding passing rate will be displayed in the 3D plot as a vertical line parallel to the z-axis. observed_sigmaWR The observed (estimated) sigmaWR of the user's data. Along with the observed GMR, the corresponding passing rate will be displayed in the 3D plot as a vertical line parallel to the z-axis. GMR_grid The grid of GMR values to be used for plotting the 3D surface of passing rates. sigmaWR_grid The grid of sigmaWR values to be used for plotting the 3D surface of passing rates. params (Optional) The list of true parameters to be assumed in data generation. sigma_W0 - A regulatory constant set by the FDA. Defaults to 0.25. sigma_WT - The true standard deviation of the test formulation population. sigma_WR - The true standard deviation of the reference formulation population. GMR - The geometric mean ratio of the test and reference values of the pharmacokinetic measures (e.g., Jmax or AUC). If the test-formulation measure is greater than that of the reference formulation, then GMR is typically set to 1.05, which is the initial value of this function. If the reference-formulation measure is bigger, then GMR is typically 0.95. Defaults to 0.95. m - Another regulatory constant that determines the bounds within which the estimated GMR should fall for bioequivalence to be established. Defaults to 1.25, representing 80-125% average BE limits, which is the FDA recommendation. sig_level - The significance level (alpha-level). Defaults to 0.05. nsim (Optional) The number of total simulations to be conducted. Defaults to 1,000. ncores (Optional) The number of CPU cores to use for parallel processing (OpenMP). If R hasn't been installed with OpenMP configured, this will not take effect. When OpenMP is available, it should not exceed the number of existing cores. If unspecified, it will default to 2 cores or the number of existing cores, whichever is smaller. verbose (Optional) A logical value (TRUE/FALSE) indicating whether to display the progress bar. plot (Optional) A logical value (TRUE/FALSE) indicating whether to generate a 3D interactive plot of the surface. If FALSE, the function will return the (x, y, z) values as a list.

### Value

A list

• GMR - A list of true parameter settings.

• passing_rate - The estimated passing rate.

• runtime - The total elapsed time charged for the execution of the program.

### Author(s)

Daeyoung Lim, daeyoung.lim@uconn.edu

### References

Davit, B. M., Chen, M. L., Conner, D. P., Haidar, S. H., Kim, S., Lee, C. H., Lionberger, R. A., Makhlouf, F. T., Nwakama, P. E., Patel, D. T., Schuirmann, D. J., & Yu, L. X. (2012). Implementation of a reference-scaled average bioequivalence approach for highly variable generic drug products by the US Food and Drug Administration. The AAPS journal, 14(4), 915-924.

### Examples

out <- PRsurface(6, 3, GMR_grid = c(0.90, 1), sigmaWR_grid = c(0.2, 0.5), nsim = 2, plot = FALSE)