Exploring package adaptIVPT, function rss() [Two-Stage / GS Designs]

posted by Helmut Homepage – Vienna, Austria, 2023-12-20 14:27 (121 d 20:34 ago) – Posting: # 23798
Views: 1,956

Dear all,

I was wrong in this post; the adjusted α can be specified indeed.
By trial and error (the documentation is not particularly helpful) I discovered that only a 2×2×4 full replicate design is implemented. Con­trary to the functions of PowerTOST unequal variances of T and R are not supported. The total sample size (N) can be an odd number and has to be rounded up in order to obtain balanced sequences.
I could reproduce the examples of my yesterday’s post. [image]-script at the end.

The first example:

RSS(n1 = 16, CVwR = 0.3, GMR = 0.95)
Sample size re-estimation by package ‘adaptIVPT’;
only the 2x2x4 full replicate design is supported!
adjusted alpha : 0.0294
n1             : 16
futility on N  : 100
CVwR           : 0.3000 (observed)
swR            : 0.2936 (observed)
GMR            : 0.9500 (fixed)
target power   : 0.8000 (fixed)
Stage 2 initiated (insufficent power in stage 1)
n2             :  6
N              : 22; less than the FDA’s minimum of 24 subjects!


However, it is not possible to estimate power and the empirical Type I Error.
By ‘hand’ with yesterday’s GMR 0.92 in the final analysis:

library(PowerTOST)
x <- setNames(c(power.RSABE(alpha = 0.0294, CV = 0.3, n = 22, design = "2x2x4", theta0 = 0.92),
                power.RSABE(alpha = 0.0294, CV = 0.3, n = 22, design = "2x2x4",
                            theta0 = scABEL(CV = 0.3, regulator = "FDA")[["upper"]],
                            nsims = 1e6)), c("power", "TIE"))
print(round(x, 4))
 power    TIE
0.7093 0.0861


Verdict:Comment:

I discovered that some tweaks are needed. It’s bad coding practice in simulations that the seed of the PRNG is not fixed (obviously it’s random). The user should have the option to use a random seed to assess re­pro­du­­ci­­bility (hence, in the functions of PowerTOST and Power2Stage the argument setseed). Working with seeds in parallel computing requires special attention. How­ever, I saw no improvement with only one core. Still some irreproducibility with 105 simulations (the function’s default are only 1,000). With 106 results are stable but that’s brute force.
In the script I opted for multiple calls of rss() and use the maximum of the re-estimated stage 2 sample sizes.

Why the heck do we have to debug code – for free! – which was developed in a project sponsored by the FDA?

[image]If debugging is the process of removing bugs,
then programming must be the process of putting them in.
   Edsger W. Dijkstra



RSS <- function(adj = 0.0294, n1, CVwR, GMR = 0.95, nmax = 100, target = 0.8,
                calls = 10, details = TRUE, inter = FALSE) {
  suppressMessages(require(adaptIVPT))
  up2even <- function(x) { 2 * (x %/% 2 + as.logical(x %% 2)) }
  if (missing(n1)) stop ("n1 must be given.")
  if (missing(CVwR)) stop ("CVwR mst be given.")
  if (GMR <= 0.8 | GMR >= 1.25) stop ("GMR must be within 0.8-1.25.")
  if (nmax <= n1) stop ("nmax <= n1 does not make sense.")
  if (target <= 0.5 | target >= 1) stop ("target ", target, " does not make sense.")
  if (calls <= 1) stop ("calls must be at > 1 (at least 5 recommended).")
  swR     <- sqrt(log(CVwR^2 + 1))
  n2      <- integer(calls)
  params  <- list(GMR = GMR, sig_level = adj, nmax = nmax, target_power = target)
  ncores  <- NULL
  if (!nchar(system.file(package = "parallel")) == 0) {
    cores  <- parallel::detectCores()
    ncores <- cores - 1
  }
  txt     <- paste("Sample size re-estimation by package ‘adaptIVPT’;",
                   "\nonly the 2x2x4 full replicate design is supported!",
                   sprintf("\nadjusted alpha : %.4f", adj),
                   sprintf("\nn1             : %2.0f", n1),
                   "\nfutility on N  : nmax),
                   sprintf("\nCVwR           : %.4f (observed)", CVwR),
                   sprintf("\nswR            : %.4f (observed)", swR),
                   sprintf("\nGMR            : %.4f (fixed)", GMR),
                   sprintf("\ntarget power   : %.4f (fixed)", target))
  # workaround because of random seeds (irreproducible results)
  for (j in seq_along(n2)) {
    res   <- unlist(rss(n = n1, r = 2, S_WR = swR, params = params,
                        ncores = ncores)) # r must be 2
    N     <- up2even(res[["rss"]])        # might be odd
    n2[j] <- N - n1
  }
  if (inter) { # show intermediate n2 estimates
    ns <- data.frame(n2 = sort(unique(n2)), times = NA_integer_)
    for (j in 1:nrow(ns)) {
      ns$times[j] <- length(which(n2 == ns$n2[j]))
    }
    print(ns, row.names = FALSE); cat("\n")
  }
  n2      <- max(n2)
  N       <- n1 + n2
  if (N == nmax) {
    txt <-  paste(txt, sprintf("\nN              : %2.0f >= nmax (%.0f)",
                  N, nmax), "\nStudy stopped in stage 1 for futility.\n")
  } else {
    if (N > n1) {
      txt <- paste(txt, "\nStage 2 initiated (insufficent power in stage 1)",
                   sprintf("\nn2             : %2.0f", n2),
                   sprintf("\nN              : %2.0f", N))
      if (N < 24) {
        txt <- paste0(txt, "; less than the FDA’s minimum of 24 subjects!\n")
      } else {
        txt <- paste0(txt, "\n")
      }
    } else {
      txt <- paste(txt, "\nStudy stopped in stage 1 (sufficient power)\n")
      n2  <- N <- NA
    }
  }
  if (details) { # output to the console
    cat(txt)
  } else {       # data.frame of results
    result <- data.frame(alpha.adj = adj, n1 = n1, CVwR = CVwR, GMR = GMR,
                         target = target, n2 = n2, N = N, futile = FALSE)
    if (N == nmax) result$futile <- TRUE
    return(result)
  }
}



Test of reproducibility

suppressMessages(library(PowerTOST))
suppressMessages(library(adaptIVPT))
swR    <- CV2se(0.3)
adj    <- 0.0294
calls  <- 2500L # time consuming
params <- list(sig_level = adj)
ncores <- NULL
if (!nchar(system.file(package = "parallel")) == 0) {
  cores  <- parallel::detectCores()
  ncores <- cores - 1
}
comp   <- data.frame(n2.rss = rep(NA_integer_, calls), rt.rss.1 = NA_real_,
                     rt.rss.2 = NA_real_, n2.PT = NA_integer_, rt.PT = NA_real_)
# target_power = 0.8 is the default in both functions
for (j in 1L:calls) {
  pt               <- proc.time()[[3]]
  res              <- unlist(rss(n = 16, r = 2, S_WR = swR,
                                 params = params, ncores = ncores))
  comp$rt.rss.2[j] <- proc.time()[[3]] - pt # measured runtime
  comp$rt.rss.1[j] <- res[8]                # reported runtime
  N                <- res[["rss"]]          # as reported, no rounding
  comp$n2.rss[j]   <- N - 16
  # We use random seeds in the function as well (not the default);
  # however, it will always return balanced sequences (even numbers)

  pt               <- proc.time()[[3]]
  comp$n2.PT[j]    <- sampleN.RSABE(alpha = adj, CV = 0.3, theta0 = 0.95,
                                    design = "2x2x4", print = FALSE, details = FALSE,
                                    setseed = FALSE)[["Sample size"]] - 16
  comp$rt.PT[j]    <- proc.time()[[3]] - pt
}
names(comp)[2:3] <- c("rt.rss.reported", "rt.rss.measured")
ns     <- sort(unique(c(as.integer(unlist(comp[1])),
                        as.integer(unlist(comp[4])))))
vals   <- data.frame(n2 = ns, rss = NA_character_, PT = NA_character_)
for (j in seq_along(ns)) {
  vals$rss[j] <- sprintf("%5.2f%%", 100 * sum(comp$n2.rss == ns[j]) / calls)
  vals$PT[j]  <- sprintf("%5.2f%%", 100 * sum(comp$n2.PT == ns[j]) / calls)
}
txt    <- paste("\nMean runtimes",
                sprintf("%-34s %6.2f", "\n rss() measured / reported",
                        mean(comp[[3]]) / mean(comp[[2]])),
                sprintf("%-34s %6.2f", "\n sampleN.RSABE() / rss() reported",
                        mean(comp[[5]]) / mean(comp[[2]])),
                sprintf("%-34s %6.2f", "\n sampleN.RSABE() / rss() measured",
                        mean(comp[[5]]) / mean(comp[[3]])), "\n")
summary(comp, digits = 5); print(vals, row.names = FALSE); cat(txt)


Result (if you call the script, yours will be different):
     n2.rss      rt.rss.reported   rt.rss.measured        n2.PT            rt.PT
 Min.   :3.000   Min.   :0.00000   Min.   :0.030000   Min.   :4.0000   Min.   :0.14000
 1st Qu.:4.000   1st Qu.:0.00000   1st Qu.:0.040000   1st Qu.:6.0000   1st Qu.:0.19000
 Median :5.000   Median :0.00000   Median :0.050000   Median :6.0000   Median :0.19000
 Mean   :4.552   Mean   :0.00204   Mean   :0.044624   Mean   :5.9968   Mean   :0.19408
 3rd Qu.:5.000   3rd Qu.:0.00000   3rd Qu.:0.050000   3rd Qu.:6.0000   3rd Qu.:0.20000
 Max.   :6.000   Max.   :0.02000   Max.   :0.070000   Max.   :6.0000   Max.   :0.24000
 n2    rss     PT
  3  3.32%  0.00%
  4 43.68%  0.16%
  5 47.48%  0.00%
  6  5.52% 99.84%

Mean runtimes
 rss() measured / reported         21.87
 sampleN.RSABE() / rss() reported  95.14
 sampleN.RSABE() / rss() measured   4.35


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