# Sample R script for sample size calculations using PowerTOST
# Developed by Nathan Teuscher
# January 2025

# Load PowerTOST functions
library(PowerTOST)

# Example 1
# 2-way crossover BE study
# alpha = 0.05
# CV = 0.2
# Test/Reference = 0.95
# BE limits = 0.8 to 1.25
# Power = 0.8
# you can type ?sampleN.TOST in the console to see all of the options for this function

sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.2,
             theta0 = 0.95, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2x2 crossover 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.95,  CV = 0.2
# 
# Sample size (total)
# n     power
# 20   0.834680 

# Try again with test/reference of 98%
sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.2,
             theta0 = 0.98, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2x2 crossover 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.98,  CV = 0.2
# 
# Sample size (total)
# n     power
# 16   0.817447 


# Try again with CV of 30% and test/reference of 95%
sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.3,
             theta0 = 0.95, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2x2 crossover 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.95,  CV = 0.3
# 
# Sample size (total)
# n     power
# 40   0.815845 

# What is power for a specific study design and sample size
power.TOST(n = 16, alpha = 0.05, CV = 0.2,
             theta0 = 0.95, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")

# What happens if you underestimate the CV?
power.TOST(n = 20, alpha = 0.05, CV = 0.3,
           theta0 = 0.95, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Real-life example
sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.23,
             theta0 = 0.93, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2x2 crossover 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.93,  CV = 0.23
# 
# Sample size (total)
# n     power
# 30   0.804800 

# CV% could be as high as 27%
# test/reference could be as low as 90%
# Is 30 the right number of subjects?

# Check CV of 27%
power.TOST(n = 30, alpha = 0.05, CV = 0.27,
           theta0 = 0.93, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Check test/reference of 90%
power.TOST(n = 30, alpha = 0.05, CV = 0.23,
           theta0 = 0.90, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Check test/reference of 90% and CV is 27%
power.TOST(n = 30, alpha = 0.05, CV = 0.27,
           theta0 = 0.90, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Calculate sample for "worst" situation
sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.23,
             theta0 = 0.90, theta1 = 0.8, theta2 = 1.25,
             design = "2x2")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2x2 crossover 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.9,  CV = 0.23
# 
# Sample size (total)
# n     power
# 48   0.804809 

# Now what if we have 48 subjects in those same situations as was originally described?
# Check CV of 27%
power.TOST(n = 48, alpha = 0.05, CV = 0.27,
           theta0 = 0.93, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Check test/reference of 90%
power.TOST(n = 48, alpha = 0.05, CV = 0.23,
           theta0 = 0.90, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Check test/reference of 90% and CV is 27%
power.TOST(n = 48, alpha = 0.05, CV = 0.27,
           theta0 = 0.90, theta1 = 0.8, theta2 = 1.25,
           design = "2x2")

# Parallel design example
sampleN.TOST(alpha = 0.05, targetpower = 0.8, CV = 0.2,
             theta0 = 0.95, theta1 = 0.8, theta2 = 1.25,
             design = "parallel")
# +++++++++++ Equivalence test - TOST +++++++++++
#   Sample size estimation
# -----------------------------------------------
#   Study design: 2 parallel groups 
# log-transformed data (multiplicative model)
# 
# alpha = 0.05, target power = 0.8
# BE margins = 0.8 ... 1.25 
# True ratio = 0.95,  CV = 0.2
# 
# Sample size (total)
# n     power
# 36   0.809940