R/saFAB.R In spencerwoody/saFAB: Create Bayes-optimal Selection-adjusted Intervals via the saFAB Procedure

Documented in saFAB

```#' Create selection-adjusted FAB intervals, given the spending function
#'
#' @param theta vector of thetas from spending function
#' @param w vector for spending function
#' @param t truncation point
#' @param alpha confidence level
#' @param yMin minimal value of y for the confidence interval
#' @param yMax maxmimal value of y for the confidence interval
#' @param yNum length of vector of y's at which to make confidence interval
#' @param verbose logical; if TRUE (default), print progress bars
#'
#' @export

saFAB <- function(theta, w, t, sigma, alpha = 0.10,
yMin = -5, yMax = 5, yNum = 5000, verbose = TRUE) {
require(dplyr)
require(rootSolve)
require(splines)

numTheta <- length(theta)

# Create vectors for upper and lower acceptance regions
Al <- rep(NA, numTheta)
Au <- rep(NA, numTheta)

if (verbose) cat("\nCreating acceptance regions...\n")

# Fill create acceptance regions
prog <- progress_estimated(numTheta)
for (i in 1:numTheta) {

# Tail regions
wl <- alpha * w[i]
wu <- 1 - alpha + wl

# saFAB acceptance regions
Al[i] <- qtnorm(wl, theta[i], sigma, t)
Au[i] <- qtnorm(wu, theta[i], sigma, t)

# Print progress update
if (verbose) prog\$tick()\$print()

}

# Make data.frame for acceptance regions
theta = rep(theta, 2),
A = c(Al, Au),
ul = c(rep("lower", numTheta), rep("upper", numTheta))
)

# Create spline functions for acceptance regions
AlFun <- splinefun(theta, Al)
AuFun <- splinefun(theta, Au)

# Create confidence intervals along a sequence of y values
yGrid <- seq(yMin, yMax, length.out = yNum)

Cdf <- data.frame(
y = yGrid,
intervals = I(vector("list", length(yGrid))),
numIntervals = NA,
intervalLength = NA
)

if (verbose) cat("\nCreating confidence intervals...\n")
prog <- progress_estimated(yNum)
for (i in 1:length(yGrid)) {

# Temporary auxillary functions
Lfun <- function(x) {
AlFun(x) - yGrid[i]
}

Ufun <- function(x) {
AuFun(x) - yGrid[i]
}

# Roots of auxillary functions
rootsL <- uniroot.all(Lfun, range(theta))
rootsU <- uniroot.all(Ufun, range(theta))

# Intervals come from roots of auxillary functions
Cdf\$intervals[[i]] <- c(rootsU, rootsL)

# Number of disjoint intervals
Cdf\$numIntervals[i] <- length(Cdf\$intervals[[i]]) / 2

# Length of intervals
Cdf\$intervalLength[i] <- totalLength(Cdf\$intervals[[i]])

# Print progress bar
if (verbose) prog\$tick()\$print()
}

# Output the confidence interval dataframe for plotting

# Confidence interval dataframe for plotting
CdfPlotting <- data.frame(
y = rep(NA, sum(Cdf\$numIntervals)),
lower = NA,
upper = NA
)

rowCount <- 1

for (j in 1:nrow(Cdf)) {
numIntervalsJ <- Cdf\$numIntervals[j]

Rows <- (rowCount):(rowCount + numIntervalsJ - 1)

CdfPlotting\$y[Rows] <- rep(Cdf\$y[j], numIntervalsJ)

CdfPlotting\$lower[Rows] <- Cdf\$intervals[[j]][seq(1, numIntervalsJ * 2, by = 2)]
CdfPlotting\$upper[Rows] <- Cdf\$intervals[[j]][seq(2, numIntervalsJ * 2, by = 2)]

rowCount <- rowCount + numIntervalsJ

}

# Output
return(list(