justify alpha part 2

optimal_alpha.R

optimal_alpha <- function(power_function, costT1T2 = 1, prior_H1H0 = 1, error = "minimal") {
  #Define the function to be minimized
  f = function(x, power_function, costT1T2 = 1, prior_H1H0 = 1, error = "minimal") {
    y <- 1 - eval(parse(text=paste(power_function)))
    print(c(x, y, x+y)) #optional: print alpha, beta, and objective
    if(error == "balance"){
      max((costT1T2*x - prior_H1H0*y)/(prior_H1H0+1), (prior_H1H0*y - costT1T2*x)/(prior_H1H0+1))
    } else if (error == "minimal"){
      2*(costT1T2*x + prior_H1H0*y)/(prior_H1H0+1)
    }
  }
  #Run optimize to find the minimum
  res <- optimize(f, 
                  c(0, 1), 
                  tol = 0.00001,
                  power_function = power_function,
                  costT1T2 = costT1T2, 
                  prior_H1H0 = prior_H1H0, 
                  error = error)
  if(error == "balance"){
    beta <- res$minimum - res$objective
  } else if (error == "minimal"){
    beta <- res$objective - res$minimum
  }
  x <- res$minimum
  #Store results
  invisible(list(alpha = res$minimum,
                 beta = 1 - eval(parse(text=paste(power_function))),
                 tot = res$objective
  )
  )
}