R/ADSSMod.r

In MedianaDesigner: Power and Sample Size Calculations for Clinical Trials

ADSSMod = function(parameters) {

  # Error checks

  if (typeof(parameters) != "list") stop("Function parameters must be a list of named values.", call. = FALSE)
  
  if (is.null(parameters$random_seed)) {
    
    random_seed = 49283

  } else {

    random_seed = ContinuousErrorCheck(parameters$random_seed, 
                                 1, 
                                 lower_values = 1,
                                 lower_values_sign = c(">="),
                                 upper_values = 100000,
                                 upper_values_sign = c("<="),
                                 "Seed for the random number generator (random_seed)",
                                 c("Value"),
                                 "int",
                                 NA) 

  }

  parameters$random_seed = random_seed

  # Set the seed of R's random number generator.
  # It also takes effect to Rcpp random generation functions.
  # https://stackoverflow.com/questions/60119621/get-the-same-sample-of-integers-from-rcpp-as-base-r
  suppressWarnings(RNGkind(sample.kind = "Rounding"))
  set.seed(random_seed)
    
  if (is.null(parameters$endpoint_type)) stop("Endpoint type (endpoint_type): Value must be specified.", call. = FALSE)

  if (!tolower(parameters$endpoint_type) %in% tolower(endpoint_list)) stop("Endpoint type (endpoint_type): Value must be Normal, Binary or Time-to-event.", call. = FALSE)

  parameters$endpoint_index = 1  

  for (i in 1:length(endpoint_list)) {
      if (tolower(endpoint_list[i]) == tolower(parameters$endpoint_type)) parameters$endpoint_index = i
  }   

  endpoint_index = parameters$endpoint_index

  if (is.null(parameters$direction)) {
        parameters$direction_index = 1
  } else {
        if (!tolower(parameters$direction) %in% c("higher", "lower")) stop("Direction of favorable outcome (direction): Value must be specified.", call. = FALSE)
  }

  if (tolower(parameters$direction) == "higher") parameters$direction_index = 1    
  if (tolower(parameters$direction) == "lower") parameters$direction_index = 2    

  if (is.null(parameters$sample_size)) stop("Number of enrolled patients in the two arms (sample_size): Value must be specified.", call. = FALSE)

  sample_size = ContinuousErrorCheck(parameters$sample_size, 
                                     2, 
                                     lower_values = 0,
                                     lower_values_sign = ">",
                                     upper_values = 1000,
                                     upper_values_sign = "<=",
                                     "Number of enrolled patients in the two arms (sample_size)",
                                     NA,
                                     "int",
                                     NA) 

  if (is.null(parameters$info_frac)) stop("Information fractions at IA1, IA2, FA (info_frac): Value must be specified.", call. = FALSE)

  info_frac = ContinuousErrorCheck(parameters$info_frac, 
                                     4, 
                                     lower_values = 0,
                                     lower_values_sign = ">",
                                     upper_values = 3,
                                     upper_values_sign = "<=",
                                     "Information fractions at IA1, IA2, FA (info_frac)",
                                     NA,
                                     "double",
                                     NA) 

  if (info_frac[1] >= info_frac[2]) stop("Information fractions at IA1, IA2, FA (info_frac): Information fraction at IA1 must be less than Information fraction at IA2.", call. = FALSE)

  if (info_frac[2] >= info_frac[3]) stop("Information fractions at IA1, IA2, FA (info_frac): Information fraction at IA2 must be less than Information fraction at FA", call. = FALSE)

  if (info_frac[3] != 1) stop("Information fractions at IA1, IA2, FA (info_frac): Information fraction at FA before sample size/event count adjustment must be equal to 1.", call. = FALSE)

  if (info_frac[3] >= info_frac[4]) stop("Information fractions at IA1, IA2, FA (info_frac): Information fraction at FA before sample size/event count adjustment must be less than Information fraction at FA after sample size/event count adjustment must be.", call. = FALSE)

  if (is.null(parameters$futility_threshold)) stop("Futility threshold at IA1 (futility_threshold): Value must be specified.", call. = FALSE)

  futility_threshold = 
        ContinuousErrorCheck(parameters$futility_threshold, 
                             1, 
                             lower_values = c(0),
                             lower_values_sign = c(">="),
                             upper_values = c(0.999),
                             upper_values_sign = c("<"),
                             "Futility threshold at IA1 (futility_threshold)",
                             c("Value"),
                             "double",
                             NA) 

  if (is.null(parameters$promising_interval)) stop("Promising interval at IA2 (promising_interval): Value must be specified.", call. = FALSE)

  promising_interval = 
        ContinuousErrorCheck(parameters$promising_interval, 
                             2, 
                             lower_values = c(0.001),
                             lower_values_sign = c(">"),
                             upper_values = c(0.999),
                             upper_values_sign = c("<"),
                             "Promising interval at IA2 (promising_interval)",
                             c("Value"),
                             "double",
                             NA) 

  if (parameters$promising_interval[1] > parameters$promising_interval[2]) stop("Promising interval at IA2 (promising_interval): Lower and upper limits are not correctly specified.", call. = FALSE)        

  if (is.null(parameters$target_power)) stop("Target conditional power (target_power): Value must be specified.", call. = FALSE)

  target_power = 
        ContinuousErrorCheck(parameters$target_power, 
                             1, 
                             lower_values = c(0.001),
                             lower_values_sign = c(">"),
                             upper_values = c(0.999),
                             upper_values_sign = c("<"),
                             "Target conditional power (target_power)",
                             c("Value"),
                             "double",
                             NA) 

  if (!is.null(parameters$dropout_rate)) {

    dropout_rate = 
      ContinuousErrorCheck(parameters$dropout_rate, 
                           1, 
                           lower_values = c(0),
                           lower_values_sign = c(">="),
                           upper_values = c(1),
                           upper_values_sign = c("<"),
                           "Patient dropout rate (dropout_rate)",
                           c("Value"),
                           "double",
                           NA) 

  } else {
    parameters$dropout_rate = 0
  }

  if (!is.null(parameters$nsims)) {

    nsims = 
      ContinuousErrorCheck(parameters$nsims, 
                           1, 
                           lower_values = c(1),
                           lower_values_sign = c(">="),
                           upper_values = c(10000),
                           upper_values_sign = c("<="),
                           "Number of simulations (nsims)",
                           c("Value"),
                           "int",
                           NA) 

  } else {
    parameters$nsims = 1000
  }

  if (!is.null(parameters$ncores)) {
    # nocov start
    # Maximum number of cores
    max_ncores = parallel::detectCores()

    ncores = 
      ContinuousErrorCheck(parameters$ncores, 
                           1, 
                           lower_values = c(1),
                           lower_values_sign = c(">="),
                           upper_values = c(max_ncores),
                           upper_values_sign = c("<="),
                           "Number of cores for parallel calculations (ncores)",
                           c("Value"),
                           "int",
                           NA)

    if (!is.doRGN && ncores > 1) {
      warning("Please install the doRNG package to use multi-core simulation. Only one core will be used.")
      ncores = 1
    }

    parameters$ncores = ncores
    # nocov end
  } else {
    parameters$ncores = 1
  }

  # Number of simulations per core
  parameters$nsims_per_core = ceiling(parameters$nsims / parameters$ncores)   

  if (!is.null(parameters$alpha)) {

    alpha = 
          ContinuousErrorCheck(parameters$alpha, 
                               1, 
                               lower_values = c(0.001),
                               lower_values_sign = c(">"),
                               upper_values = c(0.5),
                               upper_values_sign = c("<"),
                               "One-sided Type I error rate (alpha)",
                               c("Value"),
                               "double",
                               NA) 
  } else {
    parameters$alpha = 0.025
  }

  # Treatment effect assumptions 

  if (endpoint_index == 1) {

    if (is.null(parameters$control_mean)) stop("Mean effect in the control arm (control_mean): Value must be specified.", call. = FALSE)

    control_mean = 
          ContinuousErrorCheck(parameters$control_mean, 
                               1, 
                               lower_values = c(NA),
                               lower_values_sign = c(NA),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Mean effect in the control arm (control_mean)",
                               c("Value"),
                               "double",
                               NA) 

    if (is.null(parameters$treatment_mean)) stop("Mean effect in the treatment arm (treatment_mean): Value must be specified.", call. = FALSE)

    treatment_mean = 
          ContinuousErrorCheck(parameters$treatment_mean, 
                               1, 
                               lower_values = c(NA),
                               lower_values_sign = c(NA),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Mean effect in the treatment arm (treatment_mean)",
                               c("Value"),
                               "double",
                               NA) 

    if (is.null(parameters$control_sd)) stop("Standard deviation in the control arm (control_sd): Value must be specified.", call. = FALSE)

    control_sd = 
          ContinuousErrorCheck(parameters$control_sd, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Standard deviation in the control arm (control_sd)",
                               c("Value"),
                               "double",
                               NA) 


    if (is.null(parameters$treatment_sd)) stop("Standard deviation in the treatment arm (treatment_sd): Value must be specified.", call. = FALSE)

    treatment_sd = 
          ContinuousErrorCheck(parameters$treatment_sd, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Standard deviation in the treatment arm (treatment_sd)",
                               c("Value"),
                               "double",
                               NA) 

  }

  if (endpoint_index == 2) {

    if (is.null(parameters$control_rate)) stop("Response rate in the control arm (control_rate): Value must be specified.", call. = FALSE)

    control_rate = 
          ContinuousErrorCheck(parameters$control_rate, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(1),
                               upper_values_sign = c("<"),
                               "Response rate in the control arm (control_rate)",
                               c("Value"),
                               "double",
                               NA) 

    if (is.null(parameters$treatment_rate)) stop("Response rate in the treatment arm (treatment_rate): Value must be specified.", call. = FALSE)

    treatment_rate = 
          ContinuousErrorCheck(parameters$treatment_rate, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(1),
                               upper_values_sign = c("<"),
                               "Response rate in the treatment arm (treatment_rate)",
                               c("Value"),
                               "double",
                               NA) 

  }

  if (endpoint_index == 3) {

    if (is.null(parameters$control_time)) stop("Median time in the control arm (control_time): Value must be specified.", call. = FALSE)

    control_time = 
          ContinuousErrorCheck(parameters$control_time, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Median time in the control arm (control_time)",
                               c("Value"),
                               "double",
                               NA) 

    if (is.null(parameters$treatment_time)) stop("Median time in the treatment arm (treatment_time): Value must be specified.", call. = FALSE)

    treatment_time = 
          ContinuousErrorCheck(parameters$treatment_time, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Median time in the treatment arm (treatment_time)",
                               c("Value"),
                               "double",
                               NA) 

    if (is.null(parameters$enrollment_period)) stop("Patient enrollment period (enrollment_period): Value must be specified.", call. = FALSE)

    enrollment_period = 
          ContinuousErrorCheck(parameters$enrollment_period, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(NA),
                               upper_values_sign = c(NA),
                               "Patient enrollment period (enrollment_period)",
                               c("Value"),
                               "double",
                               NA)           

    if (is.null(parameters$enrollment_parameter)) stop("Median enrollment time (enrollment_parameter): Value must be specified.", call. = FALSE)

    enrollment_parameter = 
          ContinuousErrorCheck(parameters$enrollment_parameter, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(parameters$enrollment_period),
                               upper_values_sign = c("<"),
                               "Median enrollment time (enrollment_parameter)",
                               c("Value"),
                               "double",
                               NA)   

    if (is.null(parameters$event_count)) stop("Target number of events at FA (event_count): Value must be specified.", call. = FALSE)

    event_count = 
          ContinuousErrorCheck(parameters$event_count, 
                               1, 
                               lower_values = c(0),
                               lower_values_sign = c(">"),
                               upper_values = c(sum(parameters$sample_size)),
                               upper_values_sign = c("<"),
                               "Target number of events at FA (event_count)",
                               c("Value"),
                               "int",
                               NA)   

  }

  #############################################

  parameters$means = 0
  parameters$sds = 0
  parameters$rates = 0
  parameters$hazard_rates = 0
  parameters$dropout_parameter = 0
  parameters$enrollment_distribution = 2
  parameters$sample_size_ia1 = 0
  parameters$sample_size_ia2 = 0
  parameters$sample_size_fa1 = 0
  parameters$sample_size_fa2 = 0
  parameters$event_count_ia1 = 0
  parameters$event_count_ia2 = 0
  parameters$event_count_fa1 = 0
  parameters$event_count_fa2 = 0
  parameters$weight = info_frac[2]

  # All means and SDs
  if (endpoint_index == 1) {
    parameters$means = c(parameters$control_mean, parameters$treatment_mean)
    parameters$sds = c(parameters$control_sd, parameters$treatment_sd)
    parameters$enrollment_period = 0
    parameters$enrollment_parameter = 0
  }

  # All rates
  if (endpoint_index == 2) {
    parameters$rates = c(parameters$control_rate, parameters$treatment_rate)
    parameters$enrollment_period = 0
    parameters$enrollment_parameter = 0
  }

  # All hazard rates
  if (endpoint_index == 3) {
    parameters$times = c(parameters$control_time, parameters$treatment_time)
    parameters$hazard_rates = log(2) / c(parameters$control_time, parameters$treatment_time)
    parameters$dropout_parameter = c(parameters$dropout_rate, dropout_period = 12)
    parameters$event_count_ia1 = floor(parameters$event_count * info_frac[1])
    parameters$event_count_ia2 = floor(parameters$event_count * info_frac[2])
    parameters$event_count_fa1 = floor(parameters$event_count * info_frac[3])
    parameters$event_count_fa2 = floor(parameters$event_count * info_frac[4])
  }

  # Total sample size after accounting for dropout rates
  if (endpoint_index != 3) {
    parameters$sample_size_ia1 = floor(parameters$sample_size * (1 - parameters$dropout_rate) * info_frac[1])
    parameters$sample_size_ia2 = floor(parameters$sample_size * (1 - parameters$dropout_rate) * info_frac[2])
    parameters$sample_size_fa1 = floor(parameters$sample_size * (1 - parameters$dropout_rate) * info_frac[3])
    parameters$sample_size_fa2 = floor(parameters$sample_size * (1 - parameters$dropout_rate) * info_frac[4])
  }

  ###########################################################

  # Run simulations on multiple cores to compute key characteristics

  if (parameters$ncores > 1) {
    # nocov start
    cl = parallel::makeCluster(parameters$ncores)

    # Export all functions in the global environment to each node
    parallel::clusterExport(cl, ls(envir = .GlobalEnv))

    doParallel::registerDoParallel(cl)
    simulation_list = foreach(counter=(1:parameters$ncores), .packages = c("MedianaDesigner")) %dorng% { 
      ADSSModSingleCore(parameters)
    }
    stopCluster(cl)

    # Combine the simulation results across the cores 

    sim_results = NULL

    for (i in 1:parameters$ncores) {

      sim_results = rbind(sim_results, simulation_list[[i]]$sim_results)

    }
    # nocov end
  } else {

    simulations = ADSSModSingleCore(parameters)
    sim_results = simulations$sim_results

  }

  # Add column names
  column_names = c("futility_flag", "not_used", "increase_flag", "adapt_sign_outcome", "ia1_time", "ia2_time", "fa_time", "ia1_cp", "ia2_cp", "ia1_event_count", "ia2_event_count", "fa_event_count", "increase", "ia1_hr", "ia2_hr", "fa_hr", "stage1_pvalue", "stage2_pvalue", "trad_sign_outcome")
  colnames(sim_results) = column_names

  sim_summary = list()

  nsims = nrow(sim_results)

  sim_summary$futility = mean(sim_results[, 1])
  sim_summary$increase = mean(sim_results[, 3])
  sim_summary$ad_power = mean(sim_results[, 4])

  sim_summary$look_time1 = mean(sim_results[, 5])
  sim_summary$look_time2 = mean(sim_results[sim_results[, 6] != 0 , 6])
  sim_summary$look_time3 = mean(sim_results[sim_results[, 7] != 0 & sim_results[, 3] == 0, 7])
  sim_summary$look_time4 = mean(sim_results[sim_results[, 7] != 0 & sim_results[, 3] == 1 , 7])

  promising_interval = parameters$promising_interval

  cp = sim_results[, 9]
  ad_outcome = sim_results[, 4]

  # Traditional design that accounts for futility stopping
  trad_outcome = sim_results[, 19] * (sim_results[, 1] == 0)

  sim_summary$trad_power = mean(trad_outcome)

  sim_summary$ad_under = mean(ad_outcome * (cp < promising_interval[1])) / mean(cp < promising_interval[1])
  sim_summary$trad_under = mean(trad_outcome * (cp < promising_interval[1])) / mean(cp < promising_interval[1]) 

  sim_summary$ad_prom = mean(ad_outcome * (cp >= promising_interval[1] & cp <= promising_interval[2])) / mean(cp >= promising_interval[1] & cp <= promising_interval[2]) 
  sim_summary$trad_prom = mean(trad_outcome * (cp >= promising_interval[1] & cp <= promising_interval[2])) / mean(cp >= promising_interval[1] & cp <= promising_interval[2])  

  sim_summary$ad_over = mean(ad_outcome * (cp > promising_interval[2])) / mean(cp > promising_interval[2]) 
  sim_summary$trad_over = mean(trad_outcome * (cp > promising_interval[2])) / mean(cp > promising_interval[2]) 

  results = list(parameters = parameters,
                 sim_results = sim_results,
                 sim_summary = sim_summary)

  class(results) = "ADSSModResults"

  return(results)


}    

ADSSModReportDoc = function(results) {

   #############################################################################

   # Error checks

   if (!is(results, "ADSSModResults")) stop("The object was not created by the ADSSMod function", call. = FALSE)

  #############################################################################

  # Trial arms
  trial_arms = c("Control", "Treatment")

  statistics = c("Lower quartile", "Median", "Mean", "Upper quartile")

  #############################################################################

  # Empty list of tables to be included in the report
  item_list = list()
  item_index = 1
  table_index = 1
  figure_index = 1

  width = 6.5
  height = 5

  parameters = results$parameters
  sim_results = results$sim_results
  sim_summary = results$sim_summary
  endpoint_index = parameters$endpoint_index
  narms = 2

  # All means and SDs
  if (endpoint_index == 1) {
    means = c(parameters$control_mean, parameters$treatment_mean)
    sds = c(parameters$control_sd, parameters$treatment_sd)
  }

  # All rates
  if (endpoint_index == 2) {
    rates = c(parameters$control_rate, parameters$treatment_rate)
  }

  # All hazard rates
  if (endpoint_index == 3) {
    times = c(parameters$control_time, parameters$treatment_time)
  }

  #############################################################################

  if (endpoint_index %in% c(1, 2)) report_title = "Adaptive design with sample size re-estimation"

  if (endpoint_index %in% c(3)) report_title = "Adaptive design with event count re-estimation"

  if (endpoint_index %in% c(1, 2)) item_list[[item_index]] = list(type = "paragraph", label = "Description", value = "The simulation report presents key operating characteristics of an adaptive design for a two-arm Phase III clinical trial with two interim analyses. The first interim analysis supports early stopping for futility and the second interim analysis supports an option to increase the sample size in the trial.")

  if (endpoint_index %in% c(3)) item_list[[item_index]] = list(type = "paragraph", label = "Description", value = "The simulation report presents key operating characteristics of an adaptive design for a two-arm Phase III clinical trial with two interim analyses. The first interim analysis supports early stopping for futility and the second interim analysis supports an option to increase the target number of events in the trial.")

  item_index = item_index + 1

  #############################################################################

  column_names = c("Trial arm", "Sample size")

  col1 = trial_arms
  col2 = parameters$sample_size

  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Number of enrolled patients")

  column_width = c(5, 1.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "Value")

  if (parameters$direction_index == 1) label = "A higher value of the endpoint indicates a more favorable outcome"

  if (parameters$direction_index == 2) label = "A lower value of the endpoint indicates a more favorable outcome"

  col1 = c("Endpoint type", "Direction of favorable outcome") 
  col2 = c(endpoint_list[endpoint_index], label)

  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Primary efficacy endpoint")

  column_width = c(3, 3.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Trial arm", "Parameter", "Value")

  col1 = NULL
  col2 = NULL
  col3 = NULL

  for (i in 1:narms) {

    if (endpoint_index == 1) {
      col1 = c(col1, trial_arms[i], "")
      col2 = c(col2, "Mean", "SD")
      col3 = c(col3, means[i], sds[i])
    }

    if (endpoint_index == 2) {
      col1 = c(col1, trial_arms[i])
      col2 = c(col2, "Rate (%)")
      col3 = c(col3, 100 * rates[i])
    }

    if (endpoint_index == 3) {
      col1 = c(col1, trial_arms[i])
      col2 = c(col2, "Median time")
      col3 = c(col3, times[i])
    }

  }

  data_frame = data.frame(col1, col2, col3)
  title = paste0("Table ", table_index, ". Treatment effect assumptions")

  column_width = c(2, 2, 2.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  if (endpoint_index %in% c(1, 2)) column_names = c("Decision point", "Total number of patients", "Information fraction (%)")

  if (endpoint_index %in% c(3)) column_names = c("Decision point", "Total number of events", "Information fraction (%)")

  if (endpoint_index %in% c(1, 2)) {
    col1 = c("Interim analysis 1", 
           "Interim analysis 2",
           "Final analysis (before sample size re-estimation)", 
           "Final analysis (after sample size re-estimation)")
    col2 = c(sum(parameters$sample_size_ia1), sum(parameters$sample_size_ia2), sum(parameters$sample_size_fa1), paste0("Up to ", sum(parameters$sample_size_fa2)))
    col3 = round(100 * parameters$info_frac[1:4], 1)    
  }
  if (endpoint_index %in% c(3)) {
    col1 = c("Interim analysis 1", 
           "Interim analysis 2",
           "Final analysis (before event count re-estimation)", 
           "Final analysis (after event count re-estimation)")
    col2 = c(parameters$event_count_ia1, parameters$event_count_ia2, parameters$event_count_fa1, paste0("Up to ", parameters$event_count_fa2))
    col3 = round(100 * parameters$info_frac[1:4], 1)    
  }

  data_frame = data.frame(col1, col2, col3)
  if (endpoint_index %in% c(1, 2)) title = paste0("Table ", table_index, ". Number of patients at the interim and final analyses")
  if (endpoint_index %in% c(3)) title = paste0("Table ", table_index, ". Number of events at the interim and final analyses")

  if (endpoint_index %in% c(1, 2)) footnote = "The number of patients at the interim and final analyses may be reduced due to patient dropout." else footnote = NULL 

  column_width = c(2.5, 2, 2)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "PPS (%)")

  col1 = c("Futility threshold")
  col2 = 100 * c(parameters$futility_threshold)
  
  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Decision rule at Interim analysis 1")

  footnote = "PPS: Predicted probability of success at Interim analysis 1. The trial will be stopped for futility at Interim analysis 1 if the predicted probability of success is less than the futility threshold."

  column_width = c(5, 1.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "PPS (%)")

  col1 = c("Promising interval (lower limit)", "Promising interval (upper limit)", "Target probability of success at Final analysis")
  col2 = 100 * c(parameters$promising_interval, parameters$target_power)
  
  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Decision rules at Interim analysis 2")

  if (endpoint_index %in% c(1, 2)) footnote = "PPS: Predicted probability of success at Interim analysis 2. The sample size will be increased after Interim analysis 2 to achieve the target probability of success at Final analysis if the predicted probability of success lies within the promising interval."

  if (endpoint_index %in% c(3)) footnote = "PPS: Predicted probability of success at Interim analysis 2. The target number of events will be increased after Interim analysis 2 to achieve the target probability of success at Final analysis if the predicted probability of success lies within the promising interval."

  column_width = c(5, 1.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "Value")

  if (endpoint_index %in% c(1, 2)) {
    col1 = c("Dropout rate at the end of the treatment period (%)")
    col2 = c(100 * parameters$dropout_rate)
  }
  if (endpoint_index %in% c(3)) {
    col1 = c("Patient enrollment period", "Median enrollment time", "Annual dropout rate (%)")
    col2 = c(parameters$enrollment_period, parameters$enrollment_parameter, 100 * parameters$dropout_rate)
  }

  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Other design parameters")

  column_width = c(5, 1.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "Value")

  col1 = c("One-sided Type I error rate", "Number of simulations")
  col2 = c(sprintf("%0.3f", sum(parameters$alpha)),
           sprintf("%d", parameters$nsims))

  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Simulation parameters")

  column_width = c(5, 1.5)
  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, TRUE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Parameter", "Value")

  if (endpoint_index %in% c(1, 2)) col1 = c("Probability of stopping for futility at Interim analysis 1 (%)",
           "Probability of increasing the sample size at Interim analysis 2 (%)",
           "Traditional design: Power (%)",
           "Adaptive design: Power (%)") 

  if (endpoint_index %in% c(3)) col1 = c("Probability of stopping for futility at Interim analysis 1 (%)",
           "Probability of increasing the number of events at Interim analysis 2 (%)",
           "Traditional design: Power (%)",
           "Adaptive design: Power (%)")
            
  col2 = c(round(100 * sim_summary$futility, 1),
           round(100 * sim_summary$increase, 1),
           round(100 * sim_summary$trad_power, 1),
           round(100 * sim_summary$ad_power, 1))
  
  data_frame = data.frame(col1, col2)
  title = paste0("Table ", table_index, ". Simulation results: Outcome probabilities")

  column_width = c(5.5, 1)

  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  column_names = c("Interval", "Design", "Power (%)")

  col1 = c("Unfavorable interval", "", "Promising interval", "", "Favorable interval", "")
  col2 = rep(c("Traditional design", "Adaptive design"), 3)
  col3 = c(round(100 * sim_summary$trad_under, 1),
           round(100 * sim_summary$ad_under, 1),
           round(100 * sim_summary$trad_prom, 1),
           round(100 * sim_summary$ad_prom, 1),
           round(100 * sim_summary$trad_over, 1),
           round(100 * sim_summary$ad_over, 1))
  
  data_frame = data.frame(col1, col2, col3)
  title = paste0("Table ", table_index, ". Simulation results: Comparison of traditional and adaptive designs")

  l = 100 * parameters$promising_interval[1]
  u = 100 * parameters$promising_interval[2]

  if (endpoint_index %in% c(1, 2)) footnote = paste0("Unfavorable interval: Predicted probability of success at Interim analysis 2 (PPS) is less than ", l, "% (original sample size is retained). Promising interval: PPS is between ", l, "% and ", u, "% (sample size is increased). Favorable interval: PPS is greater than ", u, "% (original sample size is retained).")

  if (endpoint_index %in% c(3)) footnote = paste0("Unfavorable interval: Predicted probability of success at Interim analysis 2 (PPS) is less than ", l, "% (original number of events is retained). Promising interval: PPS is between ", l, "% and ", u, "% (number of events is increased). Favorable interval: PPS is greater than ", u, "% (original number of events is retained).")

  column_width = c(2.5, 2.5, 1.5)

  item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
  item_index = item_index + 1
  table_index = table_index + 1

  #############################################################################

  report = item_list

  doc = SaveReport(report, report_title)

  return(doc)

}
# End of ADSSModReportDoc

ADSSModSingleCore = function(parameters) {

  params_for_run = parameters
  params_for_run$nsims = params_for_run$nsims_per_core
  simulations = ADSSModC(params_for_run)

  return(simulations)

}