### Description

This function reestimates the sample size using mixed criterion required for target power, using binary search. The power (passing rate) function of mixed criterion testing lacks a closed-form expression. Thus, sample size (re-)estimation requires a binary search, after identifying an n where the passing rate exceeds the desired level.

### Usage

rss(n, r, S_WR, params = list(), nsim = 1000, ncores = NULL)


### Arguments

 n The number of donors in each simulation. r The number of replicates from each donor for each simulated dataset. S_WR The estimated standard deviation of the reference measurements. The reference-scaled average bioequivalence approach is used if S_WR > 0.249 and the average bioequivalence approach otherwise. 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. 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). nmax - The upper limit for sample size reestimation. If the sample size exceeds nmax inside estimation procedure, the function will return nmax. target_power - The threshold for power (or passing rate) for a hypothesis test to be considered powerful. Typically set at 80% and defaults to 0.8. 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.

### Value

A list of lists

• parameters - A list of true parameter settings.

• rss - The reestimated sample size.

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

### Author(s)

Daeyoung Lim, daeyoung.lim@uconn.edu

### References

Potvin, D., DiLiberti, C. E., Hauck, W. W., Parr, A. F., Schuirmann, D. J., & Smith, R. A. (2008). Sequential design approaches for bioequivalence studies with crossover designs. Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry, 7(4), 245-262.

### Examples

out <- rss(10, 6, S_WR = 0.22, nsim = 2)