R/f_analysis_base_rates.R

In rpact: Confirmatory Adaptive Clinical Trial Design and Analysis

## |
## |  *Analysis of rates with group sequential and combination test*
## |
## |  This file is part of the R package rpact:
## |  Confirmatory Adaptive Clinical Trial Design and Analysis
## |
## |  Author: Gernot Wassmer, PhD, and Friedrich Pahlke, PhD
## |  Licensed under "GNU Lesser General Public License" version 3
## |  License text can be found here: https://www.r-project.org/Licenses/LGPL-3
## |
## |  RPACT company website: https://www.rpact.com
## |  rpact package website: https://www.rpact.org
## |
## |  Contact us for information about our services: info@rpact.com
## |
## |  File version: $Revision: 7126 $
## |  Last changed: $Date: 2023-06-23 14:26:39 +0200 (Fr, 23 Jun 2023) $
## |  Last changed by: $Author: pahlke $
## |

#' @include f_logger.R
NULL

#' @title
#' Get Analysis Results Rates
#'
#' @description
#' Returns an analysis result object.
#'
#' @param design The trial design.
#'
#' @return Returns a \code{AnalysisResultsRates} object.
#'
#' @keywords internal
#'
#' @noRd
#'
.getAnalysisResultsRates <- function(..., design, dataInput) {
    if (.isTrialDesignGroupSequential(design)) {
        return(.getAnalysisResultsRatesGroupSequential(
            design = design,
            dataInput = dataInput, ...
        ))
    }

    if (.isTrialDesignInverseNormal(design)) {
        return(.getAnalysisResultsRatesInverseNormal(
            design = design,
            dataInput = dataInput, ...
        ))
    }

    if (.isTrialDesignFisher(design)) {
        return(.getAnalysisResultsRatesFisher(
            design = design,
            dataInput = dataInput, ...
        ))
    }

    .stopWithWrongDesignMessage(design, inclusiveConditionalDunnett = FALSE)
}

.getAnalysisResultsRatesInverseNormal <- function(..., design,
        dataInput, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, pi1 = NA_real_, pi2 = NA_real_, nPlanned = NA_real_,
        allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    .assertIsTrialDesignInverseNormal(design)
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design)
    .warnInCaseOfUnknownArguments(
        functionName = ".getAnalysisResultsRatesInverseNormal",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    results <- AnalysisResultsInverseNormal(design = design, dataInput = dataInput)

    .getAnalysisResultsRatesAll(
        results = results, design = design, dataInput = dataInput,
        stage = stage, directionUpper = directionUpper, normalApproximation = normalApproximation,
        thetaH0 = thetaH0, pi1 = pi1, pi2 = pi2, nPlanned = nPlanned,
        allocationRatioPlanned = allocationRatioPlanned,
        tolerance = tolerance
    )

    return(results)
}

.getAnalysisResultsRatesGroupSequential <- function(..., design,
        dataInput, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, pi1 = NA_real_, pi2 = NA_real_, nPlanned = NA_real_,
        allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    .assertIsTrialDesignGroupSequential(design)
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design)
    .warnInCaseOfUnknownArguments(
        functionName = ".getAnalysisResultsRatesGroupSequential",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    results <- AnalysisResultsGroupSequential(design = design, dataInput = dataInput)

    .getAnalysisResultsRatesAll(
        results = results, design = design, dataInput = dataInput,
        stage = stage, directionUpper = directionUpper, normalApproximation = normalApproximation,
        thetaH0 = thetaH0, pi1 = pi1, pi2 = pi2, nPlanned = nPlanned,
        allocationRatioPlanned = allocationRatioPlanned,
        tolerance = tolerance
    )

    return(results)
}

.getAnalysisResultsRatesFisher <- function(..., design,
        dataInput, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, pi1 = NA_real_, pi2 = NA_real_, nPlanned = NA_real_,
        allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT,
        iterations = C_ITERATIONS_DEFAULT, seed = NA_real_) {
    .assertIsTrialDesignFisher(design)
    .assertIsValidIterationsAndSeed(iterations, seed, zeroIterationsAllowed = FALSE)
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design)
    .warnInCaseOfUnknownArguments(
        functionName = ".getAnalysisResultsRatesFisher",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    results <- AnalysisResultsFisher(design = design, dataInput = dataInput)
    .setValueAndParameterType(results, "iterations", as.integer(iterations), C_ITERATIONS_DEFAULT)
    .setValueAndParameterType(results, "seed", seed, NA_real_)

    .getAnalysisResultsRatesAll(
        results = results, design = design, dataInput = dataInput,
        stage = stage, directionUpper = directionUpper, normalApproximation = normalApproximation,
        thetaH0 = thetaH0, pi1 = pi1, pi2 = pi2, nPlanned = nPlanned,
        allocationRatioPlanned = allocationRatioPlanned,
        tolerance = tolerance,
        iterations = iterations, seed = seed
    )

    return(results)
}

#'
#' The following parameters will be taken from 'design':
#' stages, informationRates, criticalValues, futilityBounds, alphaSpent, stageLevels
#'
#' @noRd
#'
.getAnalysisResultsRatesAll <- function(..., results, design, dataInput, stage,
        directionUpper, normalApproximation, thetaH0, pi1, pi2,
        nPlanned, allocationRatioPlanned, tolerance,
        iterations, seed) {
    startTime <- Sys.time()
    stageResults <- .getStageResultsRates(
        design = design, dataInput = dataInput,
        stage = stage, thetaH0 = thetaH0, directionUpper = directionUpper,
        normalApproximation = normalApproximation
    )
    results$.setStageResults(stageResults)
    .logProgress("Stage results calculated", startTime = startTime)


    pi1User <- pi1
    .assertIsSingleNumber(pi1, "pi1", naAllowed = TRUE)
    pi1 <- .assertIsValidPi1(pi1, stageResults, stage)
    if (identical(pi1, pi1User)) {
        .setValueAndParameterType(results, "pi1", pi1, NA_real_)
    } else {
        results$pi1 <- pi1
        results$.setParameterType("pi1", C_PARAM_GENERATED)
    }

    if (dataInput$getNumberOfGroups() == 2) {
        pi2User <- pi2
        .assertIsSingleNumber(pi2, "pi2", naAllowed = TRUE)
        pi2 <- .assertIsValidPi2(pi2, stageResults, stage)
        if (identical(pi2, pi2User)) {
            .setValueAndParameterType(results, "pi2", pi2, NA_real_)
        } else {
            results$pi2 <- pi2
            results$.setParameterType("pi2", C_PARAM_GENERATED)
        }
    } else {
        if (!all(is.na(pi2))) {
            warning("'pi2' (", .arrayToString(pi2), ") will be ignored ",
                "because the specified data has only one group",
                call. = FALSE
            )
        }
        results$pi2 <- NA_real_
        results$.setParameterType("pi2", C_PARAM_NOT_APPLICABLE)
    }
    .warnInCaseOfUnusedConditionalPowerArgument(results, nPlanned, "pi1", pi1)
    .warnInCaseOfUnusedConditionalPowerArgument(results, nPlanned, "pi2", pi2)

    .setValueAndParameterType(results, "directionUpper", directionUpper, C_DIRECTION_UPPER_DEFAULT)
    .setValueAndParameterType(
        results, "normalApproximation",
        normalApproximation, C_NORMAL_APPROXIMATION_RATES_DEFAULT
    )
    .setValueAndParameterType(results, "thetaH0", thetaH0, C_THETA_H0_RATES_DEFAULT)
    .setConditionalPowerArguments(results, dataInput, nPlanned, allocationRatioPlanned)

    #  test actions
    results$testActions <- getTestActions(stageResults = stageResults)
    results$.setParameterType("testActions", C_PARAM_GENERATED)

    if (design$kMax > 1) {
        # conditional power
        startTime <- Sys.time()
        if (.isTrialDesignFisher(design)) {
            results$.conditionalPowerResults <- .getConditionalPowerRates(
                stageResults = stageResults,
                nPlanned = nPlanned, allocationRatioPlanned = allocationRatioPlanned,
                pi1 = pi1, pi2 = pi2, iterations = iterations, seed = seed
            )
            .synchronizeIterationsAndSeed(results)
        } else {
            results$.conditionalPowerResults <- .getConditionalPowerRates(
                stageResults = stageResults,
                nPlanned = nPlanned, allocationRatioPlanned = allocationRatioPlanned,
                pi1 = pi1, pi2 = pi2
            )
            results$conditionalPower <- results$.conditionalPowerResults$conditionalPower
            results$.setParameterType("conditionalPower", C_PARAM_GENERATED)
        }
        .logProgress("Conditional power calculated", startTime = startTime)

        # CRP - conditional rejection probabilities
        startTime <- Sys.time()
        if (.isTrialDesignFisher(design) && isTRUE(.getOptionalArgument("simulateCRP", ...))) {
            results$.setParameterType("seed", ifelse(is.na(seed), C_PARAM_DEFAULT_VALUE, C_PARAM_USER_DEFINED))
            seed <- results$.conditionalPowerResults$seed
            crp <- getConditionalRejectionProbabilities(
                stageResults = stageResults, iterations = iterations, seed = seed
            )
            results$conditionalRejectionProbabilities <- crp$crpFisherSimulated
            paramTypeSeed <- results$.conditionalPowerResults$.getParameterType("seed")
            if (paramTypeSeed != C_PARAM_TYPE_UNKNOWN) {
                results$.setParameterType("seed", paramTypeSeed)
            }
            results$seed <- seed
        } else {
            results$conditionalRejectionProbabilities <-
                getConditionalRejectionProbabilities(stageResults = stageResults)
        }
        results$.setParameterType("conditionalRejectionProbabilities", C_PARAM_GENERATED)
        .logProgress("Conditional rejection probabilities (CRP) calculated", startTime = startTime)
    }

    # RCI - repeated confidence interval
    startTime <- Sys.time()
    repeatedConfidenceIntervals <- .getRepeatedConfidenceIntervalsRates(
        design = design, dataInput = dataInput, stage = stage,
        normalApproximation = normalApproximation, tolerance = tolerance
    )
    results$repeatedConfidenceIntervalLowerBounds <- repeatedConfidenceIntervals[1, ]
    results$repeatedConfidenceIntervalUpperBounds <- repeatedConfidenceIntervals[2, ]
    results$.setParameterType("repeatedConfidenceIntervalLowerBounds", C_PARAM_GENERATED)
    results$.setParameterType("repeatedConfidenceIntervalUpperBounds", C_PARAM_GENERATED)
    .logProgress("Repeated confidence interval calculated", startTime = startTime)

    # repeated p-value
    startTime <- Sys.time()
    results$repeatedPValues <- getRepeatedPValues(
        stageResults = stageResults, tolerance = tolerance
    )
    results$.setParameterType("repeatedPValues", C_PARAM_GENERATED)
    .logProgress("Repeated p-values calculated", startTime = startTime)

    if (design$kMax > 1) {
        # final p-value
        startTime <- Sys.time()
        finalPValue <- getFinalPValue(stageResults, showWarnings = FALSE)
        results$finalPValues <- .getVectorWithFinalValueAtFinalStage(
            kMax = design$kMax,
            finalValue = finalPValue$pFinal, finalStage = finalPValue$finalStage
        )
        results$.setParameterType("finalPValues", C_PARAM_GENERATED)
        results$finalStage <- finalPValue$finalStage
        results$.setParameterType("finalPValues", C_PARAM_GENERATED)
        results$.setParameterType("finalStage", C_PARAM_GENERATED)
        .logProgress("Final p-value calculated", startTime = startTime)

        # final confidence interval & median unbiased estimate
        startTime <- Sys.time()
        finalConfidenceIntervals <- .getFinalConfidenceIntervalRates(
            design = design, dataInput = dataInput,
            thetaH0 = thetaH0, stage = stage, directionUpper = directionUpper,
            normalApproximation = normalApproximation, tolerance = tolerance
        )
        if (!is.null(finalConfidenceIntervals)) {
            finalStage <- finalConfidenceIntervals$finalStage
            results$finalConfidenceIntervalLowerBounds <- .getVectorWithFinalValueAtFinalStage(
                kMax = design$kMax,
                finalValue = finalConfidenceIntervals$finalConfidenceInterval[1], finalStage = finalStage
            )
            results$finalConfidenceIntervalUpperBounds <- .getVectorWithFinalValueAtFinalStage(
                kMax = design$kMax,
                finalValue = finalConfidenceIntervals$finalConfidenceInterval[2], finalStage = finalStage
            )
            results$medianUnbiasedEstimates <- .getVectorWithFinalValueAtFinalStage(
                kMax = design$kMax,
                finalValue = finalConfidenceIntervals$medianUnbiased, finalStage = finalStage
            )
            results$.setParameterType("finalConfidenceIntervalLowerBounds", C_PARAM_GENERATED)
            results$.setParameterType("finalConfidenceIntervalUpperBounds", C_PARAM_GENERATED)
            results$.setParameterType("medianUnbiasedEstimates", C_PARAM_GENERATED)
            .logProgress("Final confidence interval calculated", startTime = startTime)
        }
    }

    return(results)
}

#' @title
#' Get Stage Results Rates
#'
#' @description
#' Returns a stage results object.
#'
#' @param design the trial design.
#'
#' @return Returns a \code{StageResultsRates} object.
#'
#' @keywords internal
#'
#' @noRd
#'
.getStageResultsRates <- function(..., design, dataInput, thetaH0 = NA_real_,
        directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        stage = NA_integer_, userFunctionCallEnabled = FALSE) {
    .assertIsDatasetRates(dataInput)
    .assertIsValidThetaH0DataInput(thetaH0, dataInput)
    .assertIsValidDirectionUpper(directionUpper, design$sided,
        userFunctionCallEnabled = userFunctionCallEnabled
    )
    .assertIsSingleLogical(normalApproximation, "normalApproximation")
    .warnInCaseOfUnknownArguments(
        functionName = "getStageResultsRates",
        ignore = .getDesignArgumentsToIgnoreAtUnknownArgumentCheck(design, powerCalculationEnabled = TRUE), ...
    )
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design, stage = stage)

    effectSizes <- rep(NA_real_, design$kMax)

    if (dataInput$getNumberOfGroups() == 1) {
        if (is.na(thetaH0)) {
            stop(C_EXCEPTION_TYPE_MISSING_ARGUMENT, "'thetaH0' must be defined")
        }

        if (normalApproximation) {
            overallTestStatistics <- c((dataInput$getOverallEventsUpTo(stage) /
                dataInput$getOverallSampleSizesUpTo(stage) - thetaH0) /
                sqrt(thetaH0 * (1 - thetaH0)) *
                sqrt(dataInput$getOverallSampleSizesUpTo(stage)), rep(NA_real_, design$kMax - stage))
            if (directionUpper) {
                overallPValues <- 1 - stats::pnorm(overallTestStatistics)
            } else {
                overallPValues <- stats::pnorm(overallTestStatistics)
            }
        } else {
            overallTestStatistics <- rep(NA_real_, design$kMax)
            if (directionUpper) {
                overallPValues <- stats::pbinom(dataInput$getOverallEventsUpTo(stage) - 1,
                    dataInput$getOverallSampleSizesUpTo(stage), thetaH0,
                    lower.tail = FALSE
                )
            } else {
                overallPValues <- stats::pbinom(dataInput$getOverallEventsUpTo(stage),
                    dataInput$getOverallSampleSizesUpTo(stage), thetaH0,
                    lower.tail = TRUE
                )
            }
            overallTestStatistics <- .getOneMinusQNorm(overallPValues)
        }
        effectSizes[1:stage] <- dataInput$getOverallEventsUpTo(stage) /
            dataInput$getOverallSampleSizesUpTo(stage)
    }

    if (dataInput$getNumberOfGroups() == 2) {
        if (is.na(thetaH0)) {
            thetaH0 <- C_THETA_H0_RATES_DEFAULT
        }

        overallEvents1 <- dataInput$getOverallEvents(group = 1)
        overallEvents2 <- dataInput$getOverallEvents(group = 2)

        overallTestStatistics <- rep(NA_real_, design$kMax)
        overallPValues <- rep(NA_real_, design$kMax)

        for (k in 1:stage) {
            if (normalApproximation) {
                if (thetaH0 == 0) {
                    if ((overallEvents1[k] + overallEvents2[k] == 0) ||
                            (overallEvents1[k] + overallEvents2[k] ==
                                sum(dataInput$getSampleSizesUpTo(k, 1)) +
                                    sum(dataInput$getSampleSizesUpTo(k, 2)))) {
                        overallTestStatistics[k] <- 0
                    } else {
                        overallRateH0 <- (overallEvents1[k] + overallEvents2[k]) /
                            (sum(dataInput$getSampleSizesUpTo(k, 1)) + sum(dataInput$getSampleSizesUpTo(k, 2)))
                        overallTestStatistics[k] <-
                            (overallEvents1[k] / sum(dataInput$getSampleSizesUpTo(k, 1)) -
                                overallEvents2[k] / sum(dataInput$getSampleSizesUpTo(k, 2)) - thetaH0) /
                                sqrt(overallRateH0 * (1 - overallRateH0) *
                                    (1 / sum(dataInput$getSampleSizesUpTo(k, 1)) +
                                        1 / sum(dataInput$getSampleSizesUpTo(k, 2))))
                    }
                } else {
                    y <- .getFarringtonManningValues(
                        rate1 = overallEvents1[k] / sum(dataInput$getSampleSizesUpTo(k, 1)),
                        rate2 = overallEvents2[k] / sum(dataInput$getSampleSizesUpTo(k, 2)),
                        theta = thetaH0, allocation = sum(dataInput$getSampleSizesUpTo(k, 1)) /
                            sum(dataInput$getSampleSizesUpTo(k, 2)), "diff"
                    )

                    overallTestStatistics[k] <-
                        (overallEvents1[k] / sum(dataInput$getSampleSizesUpTo(k, 1)) -
                            overallEvents2[k] / sum(dataInput$getSampleSizesUpTo(k, 2)) - thetaH0) /
                            sqrt(y$ml1 * (1 - y$ml1) / sum(dataInput$getSampleSizesUpTo(k, 1)) +
                                y$ml2 * (1 - y$ml2) / sum(dataInput$getSampleSizesUpTo(k, 2)))
                }

                if (directionUpper) {
                    overallPValues[k] <- 1 - stats::pnorm(overallTestStatistics[k])
                } else {
                    overallPValues[k] <- stats::pnorm(overallTestStatistics[k])
                }
            } else {
                if (thetaH0 != 0) {
                    stop(
                        C_EXCEPTION_TYPE_CONFLICTING_ARGUMENTS,
                        "thetaH0 must be equal 0 for performing Fisher's exact test"
                    )
                }

                if (directionUpper) {
                    overallPValues[k] <- stats::phyper(overallEvents1[k] - 1,
                        overallEvents1[k] + overallEvents2[k],
                        sum(dataInput$getSampleSizesUpTo(k, 1)) + sum(dataInput$getSampleSizesUpTo(k, 2)) -
                            overallEvents1[k] - overallEvents2[k],
                        sum(dataInput$getSampleSizesUpTo(k, 1)),
                        lower.tail = FALSE
                    )
                } else {
                    overallPValues[k] <- stats::phyper(overallEvents1[k],
                        overallEvents1[k] + overallEvents2[k],
                        sum(dataInput$getSampleSizesUpTo(k, 1)) + sum(dataInput$getSampleSizesUpTo(k, 2)) -
                            overallEvents1[k] - overallEvents2[k],
                        sum(dataInput$getSampleSizesUpTo(k, 1)),
                        lower.tail = TRUE
                    )
                }
                overallTestStatistics <- .getOneMinusQNorm(overallPValues)
            }
        }
        effectSizes[1:stage] <- overallEvents1[1:stage] / cumsum(dataInput$getSampleSizesUpTo(stage, 1)) -
            overallEvents2[1:stage] / cumsum(dataInput$getSampleSizesUpTo(stage, 2))
    }

    # calculation of stage-wise test statistics and combination tests
    testStatistics <- rep(NA_real_, design$kMax)
    pValues <- rep(NA_real_, design$kMax)
    combInverseNormal <- rep(NA_real_, design$kMax)
    combFisher <- rep(NA_real_, design$kMax)
    weightsInverseNormal <- .getWeightsInverseNormal(design)
    weightsFisher <- .getWeightsFisher(design)
    for (k in 1:stage) {
        if (dataInput$getNumberOfGroups() == 1) {
            if (normalApproximation) {
                # stage-wise test statistics
                testStatistics[k] <- (dataInput$getEvent(k) / dataInput$getSampleSize(k) - thetaH0) /
                    sqrt(thetaH0 * (1 - thetaH0)) * sqrt(dataInput$getSampleSize(k))
                pValues[k] <- 1 - stats::pnorm(testStatistics[k])
                if (!directionUpper) {
                    pValues[k] <- 1 - pValues[k]
                }
            } else {
                testStatistics[k] <- NA_real_
                if (directionUpper) {
                    pValues[k] <- stats::pbinom(dataInput$getEvent(k) - 1, dataInput$getSampleSize(k),
                        thetaH0,
                        lower.tail = FALSE
                    )
                } else {
                    pValues[k] <- stats::pbinom(dataInput$getEvent(k), dataInput$getSampleSize(k),
                        thetaH0,
                        lower.tail = TRUE
                    )
                }
            }
        } else if (dataInput$getNumberOfGroups() == 2) {
            if (normalApproximation) {
                # stage-wise test statistics
                if (thetaH0 == 0) {
                    if ((dataInput$getEvent(k, 1) + dataInput$getEvent(k, 2) == 0) ||
                            (dataInput$getEvent(k, 1) + dataInput$getEvent(k, 2) ==
                                dataInput$getSampleSize(k, 1) + dataInput$getSampleSize(k, 2))) {
                        testStatistics[k] <- 0
                    } else {
                        rateH0 <- (dataInput$getEvent(k, 1) + dataInput$getEvent(k, 2)) /
                            (dataInput$getSampleSize(k, 1) + dataInput$getSampleSize(k, 2))
                        testStatistics[k] <-
                            (dataInput$getEvent(k, 1) / dataInput$getSampleSize(k, 1) -
                                dataInput$getEvent(k, 2) / dataInput$getSampleSize(k, 2) - thetaH0) /
                                sqrt(rateH0 * (1 - rateH0) *
                                    (1 / dataInput$getSampleSize(k, 1) + 1 / dataInput$getSampleSize(k, 2)))
                    }
                } else {
                    y <- .getFarringtonManningValues(
                        rate1 = dataInput$getEvent(k, 1) / dataInput$getSampleSize(k, 1),
                        rate2 = dataInput$getEvent(k, 2) / dataInput$getSampleSize(k, 2), theta = thetaH0,
                        allocation = dataInput$getSampleSize(k, 1) / dataInput$getSampleSize(k, 2), method = "diff"
                    )

                    testStatistics[k] <- (dataInput$getEvent(k, 1) / dataInput$getSampleSize(k, 1) -
                        dataInput$getEvent(k, 2) / dataInput$getSampleSize(k, 2) - thetaH0) /
                        sqrt(y$ml1 * (1 - y$ml1) / dataInput$getSampleSize(k, 1) +
                            y$ml2 * (1 - y$ml2) / dataInput$getSampleSize(k, 2))
                }

                if (directionUpper) {
                    pValues[k] <- 1 - stats::pnorm(testStatistics[k])
                } else {
                    pValues[k] <- stats::pnorm(testStatistics[k])
                }
            } else {
                testStatistics[k] <- NA_real_
                if (directionUpper) {
                    pValues[k] <- stats::phyper(dataInput$getEvent(k, 1) - 1,
                        dataInput$getEvent(k, 1) + dataInput$getEvent(k, 2),
                        dataInput$getSampleSize(k, 1) + dataInput$getSampleSize(k, 2) -
                            dataInput$getEvent(k, 1) - dataInput$getEvent(k, 2),
                        dataInput$getSampleSize(k, 1),
                        lower.tail = FALSE
                    )
                } else {
                    pValues[k] <- stats::phyper(dataInput$getEvent(k, 1),
                        dataInput$getEvent(k, 1) + dataInput$getEvent(k, 2),
                        dataInput$getSampleSize(k, 1) + dataInput$getSampleSize(k, 2) -
                            dataInput$getEvent(k, 1) - dataInput$getEvent(k, 2),
                        dataInput$getSampleSize(k, 1),
                        lower.tail = TRUE
                    )
                }
            }
        }

        # inverse normal test
        combInverseNormal[k] <- (weightsInverseNormal[1:k] %*% .getOneMinusQNorm(pValues[1:k])) /
            sqrt(sum(weightsInverseNormal[1:k]^2))

        # Fisher combination test
        combFisher[k] <- prod(pValues[1:k]^weightsFisher[1:k])
    }

    direction <- ifelse(directionUpper, C_DIRECTION_UPPER, C_DIRECTION_LOWER)

    stageResults <- StageResultsRates(
        design = design,
        dataInput = dataInput,
        stage = as.integer(stage),
        overallTestStatistics = .fillWithNAs(overallTestStatistics, design$kMax),
        overallPValues = .fillWithNAs(overallPValues, design$kMax),
        effectSizes = effectSizes,
        overallEvents = .fillWithNAs(dataInput$getOverallEventsUpTo(stage, group = 1), design$kMax),
        overallSampleSizes = .fillWithNAs(dataInput$getOverallSampleSizesUpTo(stage, 1), design$kMax),
        testStatistics = testStatistics,
        pValues = pValues,
        combInverseNormal = combInverseNormal,
        combFisher = combFisher,
        weightsInverseNormal = weightsInverseNormal,
        weightsFisher = weightsFisher,
        thetaH0 = thetaH0,
        direction = ifelse(directionUpper, C_DIRECTION_UPPER, C_DIRECTION_LOWER),
        normalApproximation = normalApproximation
    )

    if (dataInput$getNumberOfGroups() == 1) {
        stageResults$overallEvents <- .fillWithNAs(dataInput$getOverallEventsUpTo(stage, group = 1), design$kMax)
        stageResults$overallSampleSizes <- .fillWithNAs(dataInput$getOverallSampleSizesUpTo(stage, 1), design$kMax)
        stageResults$overallPi1 <- stageResults$overallEvents / stageResults$overallSampleSizes
        stageResults$.setParameterType("overallPi1", C_PARAM_GENERATED)
    } else if (dataInput$getNumberOfGroups() == 2) {
        stageResults$overallEvents1 <- .fillWithNAs(dataInput$getOverallEventsUpTo(stage, group <- 1), design$kMax)
        stageResults$overallEvents2 <- .fillWithNAs(dataInput$getOverallEventsUpTo(stage, group <- 2), design$kMax)
        stageResults$overallSampleSizes1 <- .fillWithNAs(dataInput$getOverallSampleSizesUpTo(stage, 1), design$kMax)
        stageResults$overallSampleSizes2 <- .fillWithNAs(dataInput$getOverallSampleSizesUpTo(stage, 2), design$kMax)
        stageResults$overallPi1 <- stageResults$overallEvents1 / stageResults$overallSampleSizes1
        stageResults$overallPi2 <- stageResults$overallEvents2 / stageResults$overallSampleSizes2
        stageResults$.setParameterType("overallPi1", C_PARAM_GENERATED)
        stageResults$.setParameterType("overallPi2", C_PARAM_GENERATED)
    }

    if (.isTrialDesignFisher(design)) {
        stageResults$.setParameterType("combFisher", C_PARAM_GENERATED)
        stageResults$.setParameterType("weightsFisher", C_PARAM_GENERATED)
    } else if (.isTrialDesignInverseNormal(design)) {
        stageResults$.setParameterType("combInverseNormal", C_PARAM_GENERATED)
        stageResults$.setParameterType("weightsInverseNormal", C_PARAM_GENERATED)
    }

    return(stageResults)
}

#'
#' Calculation of lower and upper limits of repeated confidence intervals (RCIs) for Rates
#'
#' @noRd
#'
.getRepeatedConfidenceIntervalsRates <- function(..., design) {
    if (.isTrialDesignGroupSequential(design)) {
        return(.getRepeatedConfidenceIntervalsRatesGroupSequential(design = design, ...))
    }

    if (.isTrialDesignInverseNormal(design)) {
        return(.getRepeatedConfidenceIntervalsRatesInverseNormal(design = design, ...))
    }

    if (.isTrialDesignFisher(design)) {
        return(.getRepeatedConfidenceIntervalsRatesFisher(design = design, ...))
    }

    .stopWithWrongDesignMessage(design, inclusiveConditionalDunnett = FALSE)
}

.getRootThetaRates <- function(..., design, dataInput, stage, directionUpper, normalApproximation,
        firstParameterName, secondValue, tolerance, acceptResultsOutOfTolerance, callingFunctionInformation) {
    if (dataInput$getNumberOfGroups() == 2) {
        thetaLow <- -1 + tolerance
    } else {
        thetaLow <- tolerance
    }
    thetaUp <- 1 - tolerance

    if (dataInput$getNumberOfGroups() == 1 && !normalApproximation) {
        acceptResultsOutOfTolerance <- FALSE
    }

    result <- .getOneDimensionalRoot(
        function(theta) {
            stageResults <- .getStageResultsRates(
                design = design, dataInput = dataInput,
                stage = stage, thetaH0 = theta, directionUpper = directionUpper,
                normalApproximation = normalApproximation
            )
            firstValue <- stageResults[[firstParameterName]][stage]
            if (.isTrialDesignGroupSequential(design)) {
                firstValue <- .getOneMinusQNorm(firstValue)
            }
            return(firstValue - secondValue)
        },
        lower = thetaLow, upper = thetaUp, tolerance = tolerance,
        acceptResultsOutOfTolerance = acceptResultsOutOfTolerance,
        callingFunctionInformation = callingFunctionInformation
    )

    return(result)
}

.getRepeatedConfidenceIntervalsRatesAll <- function(..., design, dataInput,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        directionUpper = C_DIRECTION_UPPER_DEFAULT, tolerance = C_ANALYSIS_TOLERANCE_DEFAULT, firstParameterName) {
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design)

    if (!normalApproximation && dataInput$getNumberOfGroups() == 2) {
        normalApproximation <- TRUE
        message("Repeated confidence intervals will be calculated under the normal approximation")
    }

    futilityCorr <- rep(NA_real_, design$kMax) # necessary for adjustment for binding futility boundaries

    criticalValues <- design$criticalValues

    if (.isTrialDesignFisher(design)) {
        bounds <- design$alpha0Vec
        border <- C_ALPHA_0_VEC_DEFAULT
        conditionFunction <- .isFirstValueSmallerThanSecondValue
    } else {
        criticalValues[is.infinite(criticalValues) & criticalValues > 0] <- C_QNORM_MAXIMUM
        criticalValues[is.infinite(criticalValues) & criticalValues < 0] <- C_QNORM_MINIMUM
        bounds <- design$futilityBounds
        border <- C_FUTILITY_BOUNDS_DEFAULT
        conditionFunction <- .isFirstValueGreaterThanSecondValue
    }

    repeatedConfidenceIntervals <- matrix(NA_real_, 2, design$kMax)
    for (k in (1:stage)) {
        startTime <- Sys.time()
        if (criticalValues[k] < C_QNORM_MAXIMUM) {
            # finding upper and lower RCI limits through root function
            if (dataInput$getNumberOfGroups() == 1) {
                if (dataInput$overallEvents[k] == 0) {
                    repeatedConfidenceIntervals[1, k] <- 0
                } else {
                    repeatedConfidenceIntervals[1, k] <- .getRootThetaRates(
                        design = design, dataInput = dataInput, stage = k,
                        directionUpper = C_DIRECTION_UPPER_DEFAULT, normalApproximation = normalApproximation,
                        firstParameterName = firstParameterName, secondValue = criticalValues[k], tolerance = tolerance,
                        acceptResultsOutOfTolerance = TRUE,
                        callingFunctionInformation = paste0("Repeated confidence interval [1, ", k, "]")
                    )
                }

                if (dataInput$overallEvents[k] == dataInput$overallSampleSizes[k]) {
                    repeatedConfidenceIntervals[2, k] <- 1
                } else {
                    repeatedConfidenceIntervals[2, k] <- .getRootThetaRates(
                        design = design, dataInput = dataInput, stage = k,
                        directionUpper = FALSE, normalApproximation = normalApproximation,
                        firstParameterName = firstParameterName, secondValue = criticalValues[k], tolerance = tolerance,
                        acceptResultsOutOfTolerance = TRUE,
                        callingFunctionInformation = paste0("Repeated confidence interval [2, ", k, "]")
                    )
                }
            } else if (dataInput$getNumberOfGroups() == 2) {
                repeatedConfidenceIntervals[1, k] <- .getRootThetaRates(
                    design = design, dataInput = dataInput, stage = k,
                    directionUpper = C_DIRECTION_UPPER_DEFAULT, normalApproximation = normalApproximation,
                    firstParameterName = firstParameterName, secondValue = criticalValues[k], tolerance = tolerance,
                    acceptResultsOutOfTolerance = TRUE,
                    callingFunctionInformation = paste0("Repeated confidence interval [1, ", k, "]")
                )

                repeatedConfidenceIntervals[2, k] <- .getRootThetaRates(
                    design = design, dataInput = dataInput, stage = k,
                    directionUpper = FALSE, normalApproximation = normalApproximation,
                    firstParameterName = firstParameterName, secondValue = criticalValues[k], tolerance = tolerance,
                    acceptResultsOutOfTolerance = TRUE,
                    callingFunctionInformation = paste0("Repeated confidence interval [1, ", k, "]")
                )
            }

            # adjustment for binding futility bounds
            if (k > 1 && !is.na(bounds[k - 1]) && conditionFunction(bounds[k - 1], border) && design$bindingFutility) {
                parameterName <- ifelse(.isTrialDesignFisher(design), "pValues", firstParameterName)

                futilityCorr[k] <- .getRootThetaRates(
                    design = design, dataInput = dataInput, stage = k - 1,
                    directionUpper = directionUpper, normalApproximation = normalApproximation,
                    firstParameterName = parameterName, secondValue = bounds[k - 1], tolerance = tolerance,
                    acceptResultsOutOfTolerance = TRUE,
                    callingFunctionInformation = paste0("Repeated confidence interval, futility correction [", k, "]")
                )

                if (directionUpper) {
                    repeatedConfidenceIntervals[1, k] <- min(min(futilityCorr[2:k]), repeatedConfidenceIntervals[1, k])
                } else {
                    repeatedConfidenceIntervals[2, k] <- max(max(futilityCorr[2:k]), repeatedConfidenceIntervals[2, k])
                }
            }
            .logProgress("Repeated confidence interval of stage %s calculated", startTime = startTime, k)
        }

        if (!is.na(repeatedConfidenceIntervals[1, k]) && !is.na(repeatedConfidenceIntervals[2, k]) &&
                repeatedConfidenceIntervals[1, k] > repeatedConfidenceIntervals[2, k]) {
            repeatedConfidenceIntervals[, k] <- rep(NA_real_, 2)
        }
    }

    return(repeatedConfidenceIntervals)
}

#'
#' RCIs based on group sequential method
#'
#' @noRd
#'
.getRepeatedConfidenceIntervalsRatesGroupSequential <- function(...,
        design, dataInput,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        directionUpper = C_DIRECTION_UPPER_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    .warnInCaseOfUnknownArguments(
        functionName =
            ".getRepeatedConfidenceIntervalsRatesGroupSequential",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    return(.getRepeatedConfidenceIntervalsRatesAll(
        design = design, dataInput = dataInput,
        normalApproximation = normalApproximation, directionUpper = directionUpper,
        firstParameterName = "overallPValues", tolerance = tolerance, ...
    ))
}

#'
#' RCIs based on inverse normal combination test
#'
#' @noRd
#'
.getRepeatedConfidenceIntervalsRatesInverseNormal <- function(...,
        design, dataInput,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        directionUpper = C_DIRECTION_UPPER_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    .warnInCaseOfUnknownArguments(
        functionName =
            ".getRepeatedConfidenceIntervalsRatesInverseNormal",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    return(.getRepeatedConfidenceIntervalsRatesAll(
        design = design, dataInput = dataInput,
        normalApproximation = normalApproximation, directionUpper = directionUpper,
        firstParameterName = "combInverseNormal", tolerance = tolerance, ...
    ))
}

#'
#' RCIs based on Fisher's combination test
#'
#' @noRd
#'
.getRepeatedConfidenceIntervalsRatesFisher <- function(...,
        design, dataInput,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        directionUpper = C_DIRECTION_UPPER_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    .warnInCaseOfUnknownArguments(
        functionName =
            ".getRepeatedConfidenceIntervalsRatesFisher",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(
            design,
            powerCalculationEnabled = TRUE
        ), "stage"), ...
    )

    return(.getRepeatedConfidenceIntervalsRatesAll(
        design = design, dataInput = dataInput,
        normalApproximation = normalApproximation, directionUpper = directionUpper,
        firstParameterName = "combFisher", tolerance = tolerance, ...
    ))
}

.calculateThetaH1 <- function(stageResults, pi1, pi2, stage, kMax, nPlanned, allocationRatioPlanned) {
    # Shifted decision region for use in getGroupSequentialProbabilities
    # Inverse normal method
    condError <- getConditionalRejectionProbabilities(stageResults = stageResults)[stage]

    if (stageResults$isOneSampleDataset()) {
        if (condError < 1e-12) {
            adjustment <- 0
        } else {
            adjustment <- .getOneMinusQNorm(condError) * (1 - sqrt(stageResults$thetaH0 * (1 - stageResults$thetaH0)) /
                sqrt(pi1 * (1 - pi1))) / sqrt(sum(nPlanned[(stage + 1):kMax]))
        }

        if (stageResults$direction == "upper") {
            thetaH1 <- (pi1 - stageResults$thetaH0) / sqrt(pi1 * (1 - pi1)) + adjustment
        } else {
            thetaH1 <- -(pi1 - stageResults$thetaH0) / sqrt(pi1 * (1 - pi1)) + adjustment
        }

        return(list(thetaH1 = thetaH1, nPlanned = nPlanned))
    }

    .assertIsSingleNumber(allocationRatioPlanned, "allocationRatioPlanned")
    .assertIsInOpenInterval(allocationRatioPlanned, "allocationRatioPlanned", 0, C_ALLOCATION_RATIO_MAXIMUM)

    x <- .getFarringtonManningValues(
        rate1 = pi1, rate2 = pi2, theta = stageResults$thetaH0,
        allocation = allocationRatioPlanned
    )

    if (condError < 1e-12) {
        adjustment <- 0
    } else {
        adjustment <- .getOneMinusQNorm(condError) * (1 -
            sqrt(x$ml1 * (1 - x$ml1) + allocationRatioPlanned * x$ml2 * (1 - x$ml2)) /
                sqrt(pi1 * (1 - pi1) + allocationRatioPlanned * pi2 * (1 - pi2))) *
            (1 + allocationRatioPlanned) / sqrt(allocationRatioPlanned *
                sum(nPlanned[(stage + 1):kMax]))
    }

    if (stageResults$direction == "upper") {
        thetaH1 <- (pi1 - pi2 - stageResults$thetaH0) /
            sqrt(pi1 * (1 - pi1) + allocationRatioPlanned * pi2 *
                (1 - pi2)) * sqrt(1 + allocationRatioPlanned) + adjustment
    } else {
        thetaH1 <- -(pi1 - pi2 - stageResults$thetaH0) /
            sqrt(pi1 * (1 - pi1) + allocationRatioPlanned * pi2 *
                (1 - pi2)) * sqrt(1 + allocationRatioPlanned) + adjustment
    }

    nPlanned <- allocationRatioPlanned / (1 + allocationRatioPlanned)^2 * nPlanned
    return(list(thetaH1 = thetaH1, nPlanned = nPlanned))
}

#'
#' Calculation of conditional power based on group sequential / inverse normal method
#'
#' @noRd
#'
.getConditionalPowerRatesInverseNormalOrGroupSequential <- function(..., stageResults, stage = stageResults$stage,
        nPlanned, allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT, pi1, pi2) {
    design <- stageResults$.design
    .assertIsTrialDesignInverseNormalOrGroupSequential(design)
    .assertIsValidStage(stage, design$kMax)
    .warnInCaseOfUnknownArguments(
        functionName = ".getConditionalPowerRatesInverseNormalOrGroupSequential",
        ignore = c("design", "stageResultsName", "grid", "pi1H1", "pi2H1"), ...
    )

    kMax <- design$kMax
    conditionalPower <- rep(NA_real_, kMax)
    weights <- stageResults$weightsInverseNormal
    informationRates <- design$informationRates
    nPlanned <- c(rep(NA, stage), nPlanned)
    if (stage == kMax) {
        .logDebug(
            "Conditional power will be calculated only for subsequent stages ",
            "(stage = ", stage, ", kMax = ", design$kMax, ")"
        )
        return(list(
            nPlanned = nPlanned,
            conditionalPower = conditionalPower
        ))
    }

    criticalValuesInverseNormal <- design$criticalValues

    resultList <- .calculateThetaH1(stageResults, pi1, pi2, stage, kMax, nPlanned, allocationRatioPlanned)
    thetaH1 <- resultList$thetaH1
    nPlanned <- resultList$nPlanned

    shiftedDecisionRegionUpper <- criticalValuesInverseNormal[(stage + 1):kMax] *
        sqrt(sum(weights[1:stage]^2) + cumsum(weights[(stage + 1):kMax]^2)) /
        sqrt(cumsum(weights[(stage + 1):kMax]^2)) -
        c(weights[1:stage] %*% .getOneMinusQNorm(stageResults$pValues[1:stage])) /
            sqrt(cumsum(weights[(stage + 1):kMax]^2)) -
        thetaH1 * cumsum(sqrt(nPlanned[(stage + 1):kMax]) * weights[(stage + 1):kMax]) /
            sqrt(cumsum(weights[(stage + 1):kMax]^2))

    if (design$sided == 2) {
        shiftedDecisionRegionLower <- -criticalValuesInverseNormal[(stage + 1):kMax] *
            sqrt(sum(weights[1:stage]^2) + cumsum(weights[(stage + 1):kMax]^2)) /
            sqrt(cumsum(weights[(stage + 1):kMax]^2)) -
            c(weights[1:stage] %*% .getOneMinusQNorm(stageResults$pValues[1:stage])) /
                sqrt(cumsum(weights[(stage + 1):kMax]^2)) -
            thetaH1 * cumsum(sqrt(nPlanned[(stage + 1):kMax]) * weights[(stage + 1):kMax]) /
                sqrt(cumsum(weights[(stage + 1):kMax]^2))
    }
    if (stage == kMax - 1) {
        shiftedFutilityBounds <- c()
    } else {
        shiftedFutilityBounds <- design$futilityBounds[(stage + 1):(kMax - 1)] *
            sqrt(sum(weights[1:stage]^2) + cumsum(weights[(stage + 1):(kMax - 1)]^2)) /
            sqrt(cumsum(weights[(stage + 1):(kMax - 1)]^2)) -
            c(weights[1:stage] %*% .getOneMinusQNorm(stageResults$pValues[1:stage])) /
                sqrt(cumsum(weights[(stage + 1):(kMax - 1)]^2)) -
            thetaH1 * cumsum(sqrt(nPlanned[(stage + 1):(kMax - 1)]) * weights[(stage + 1):(kMax - 1)]) /
                sqrt(cumsum(weights[(stage + 1):(kMax - 1)]^2))
    }

    # Scaled information for use in getGroupSeqProbs
    scaledInformation <- (informationRates[(stage + 1):kMax] - informationRates[stage]) /
        (1 - informationRates[stage])

    if (design$sided == 2) {
        decisionMatrix <- matrix(c(shiftedDecisionRegionLower, shiftedDecisionRegionUpper), nrow = 2, byrow = TRUE)
    } else {
        decisionMatrix <- matrix(c(
            shiftedFutilityBounds, C_FUTILITY_BOUNDS_DEFAULT,
            shiftedDecisionRegionUpper
        ), nrow = 2, byrow = TRUE)
    }
    probs <- .getGroupSequentialProbabilities(
        decisionMatrix = decisionMatrix,
        informationRates = scaledInformation
    )

    if (design$twoSidedPower) {
        conditionalPower[(stage + 1):kMax] <- cumsum(probs[3, ] - probs[2, ] + probs[1, ])
    } else {
        conditionalPower[(stage + 1):kMax] <- cumsum(probs[3, ] - probs[2, ])
    }

    if (stageResults$isTwoSampleDataset()) {
        nPlanned <- (1 + allocationRatioPlanned)^2 / allocationRatioPlanned * nPlanned
    }

    return(list(
        nPlanned = nPlanned,
        conditionalPower = conditionalPower
    ))
}

#'
#' Calculation of conditional power based on Fisher combination test
#'
#' @noRd
#'
.getConditionalPowerRatesFisher <- function(..., stageResults, stage = stageResults$stage,
        nPlanned, allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT,
        pi1, pi2, iterations = C_ITERATIONS_DEFAULT, seed = NA_real_) {
    design <- stageResults$.design
    .assertIsTrialDesignFisher(design)
    .assertIsValidStage(stage, design$kMax)
    .assertIsValidIterationsAndSeed(iterations, seed, zeroIterationsAllowed = FALSE)
    .warnInCaseOfUnknownArguments(
        functionName = ".getConditionalPowerRatesFisher",
        ignore = c("design", "stageResultsName", "grid", "pi1H1", "pi2H1"), ...
    )

    kMax <- design$kMax
    conditionalPower <- rep(NA_real_, kMax)
    seed <- .setSeed(seed)
    simulated <- FALSE
    nPlanned <- c(rep(NA, stage), nPlanned)

    resultList <- .calculateThetaH1(stageResults, pi1, pi2, stage, kMax, nPlanned, allocationRatioPlanned)
    thetaH1 <- resultList$thetaH1
    nPlanned <- resultList$nPlanned

    criticalValues <- design$criticalValues
    weightsFisher <- stageResults$weightsFisher
    pValues <- stageResults$pValues

    if (stage < kMax - 1) {
        for (k in (stage + 1):kMax) {
            reject <- 0
            for (i in 1:iterations) {
                reject <- reject + .getRejectValueConditionalPowerFisher(
                    kMax = kMax, alpha0Vec = design$alpha0Vec,
                    criticalValues = criticalValues, weightsFisher = weightsFisher,
                    pValues = pValues, currentKMax = k, thetaH1 = thetaH1,
                    stage = stage, nPlanned = nPlanned
                )
            }
            conditionalPower[k] <- reject / iterations
        }
        simulated <- TRUE
    }

    if (stage == kMax - 1) {
        divisor <- prod(pValues[1:(kMax - 1)]^weightsFisher[1:(kMax - 1)])
        result <- 1 - (criticalValues[kMax] / divisor)^(1 / weightsFisher[kMax])
        if (result <= 0 || result >= 1) {
            warning("Calculation not possible: could not calculate conditional power for stage ", kMax, call. = FALSE)
            conditionalPower[kMax] <- NA_real_
        } else {
            conditionalPower[kMax] <- 1 - stats::pnorm(.getQNorm(result) - thetaH1 * sqrt(nPlanned[kMax]))
        }
    }

    if (stageResults$isTwoSampleDataset()) {
        nPlanned <- (1 + allocationRatioPlanned)^2 / allocationRatioPlanned * nPlanned
    }

    return(list(
        nPlanned = nPlanned,
        conditionalPower = conditionalPower,
        iterations = as.integer(iterations),
        seed = seed,
        simulated = simulated
    ))
}

.getConditionalPowerRates <- function(..., stageResults, nPlanned,
        allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT, pi1 = NA_real_, pi2 = NA_real_) {
    pi1H1 <- .getOptionalArgument("pi1H1", ...)
    if (!is.null(pi1H1) && !is.na(pi1H1)) {
        if (!is.na(pi1)) {
            warning(sQuote("pi1"), " will be ignored because ", sQuote("pi1H1"), " is defined", call. = FALSE)
        }
        pi1 <- pi1H1
    }

    pi2H1 <- .getOptionalArgument("pi2H1", ...)
    if (!is.null(pi2H1) && !is.na(pi2H1)) {
        if (!is.na(pi2)) {
            warning(sQuote("pi2"), " will be ignored because ", sQuote("pi2H1"), " is defined", call. = FALSE)
        }
        pi2 <- pi2H1
    }

    stage <- stageResults$stage
    pi1 <- .assertIsValidPi1(pi1, stageResults, stage)

    if (!stageResults$isOneSampleDataset()) {
        pi2 <- .assertIsValidPi2(pi2, stageResults, stage)
    }

    results <- ConditionalPowerResultsRates(
        .stageResults = stageResults,
        .design = stageResults$.design, nPlanned = nPlanned,
        allocationRatioPlanned = allocationRatioPlanned, pi1 = pi1, pi2 = pi2
    )

    if (any(is.na(nPlanned))) {
        return(results)
    }

    if (!.isValidNPlanned(nPlanned = nPlanned, kMax = stageResults$.design$kMax, stage = stage)) {
        return(results)
    }

    if (.isTrialDesignInverseNormalOrGroupSequential(stageResults$.design)) {
        cp <- .getConditionalPowerRatesInverseNormalOrGroupSequential(...,
            stageResults = stageResults, nPlanned = nPlanned,
            allocationRatioPlanned = allocationRatioPlanned, pi1 = pi1, pi2 = pi2
        )
    } else if (.isTrialDesignFisher(stageResults$.design)) {
        cp <- .getConditionalPowerRatesFisher(...,
            stageResults = stageResults, nPlanned = nPlanned,
            allocationRatioPlanned = allocationRatioPlanned, pi1 = pi1, pi2 = pi2
        )
        results$iterations <- cp$iterations
        results$seed <- cp$seed
        results$simulated <- cp$simulated
        .updateParameterTypeOfIterationsAndSeed(results, ...)
    } else {
        .stopWithWrongDesignMessage(stageResults$.design, inclusiveConditionalDunnett = FALSE)
    }

    results$nPlanned <- cp$nPlanned
    results$conditionalPower <- cp$conditionalPower
    results$.setParameterType("nPlanned", C_PARAM_GENERATED)
    results$.setParameterType("conditionalPower", C_PARAM_GENERATED)
    results$.setParameterType(
        "allocationRatioPlanned",
        ifelse(allocationRatioPlanned == C_ALLOCATION_RATIO_DEFAULT, C_PARAM_DEFAULT_VALUE, C_PARAM_USER_DEFINED)
    )
    results$.setParameterType("pi1", ifelse(is.na(pi1), C_PARAM_DEFAULT_VALUE, C_PARAM_USER_DEFINED))
    results$.setParameterType("pi2", ifelse(is.na(pi2), C_PARAM_DEFAULT_VALUE, C_PARAM_USER_DEFINED))

    return(results)
}

.getConditionalPowerPlotRates <- function(..., stageResults, stage,
        nPlanned, allocationRatioPlanned = C_ALLOCATION_RATIO_DEFAULT, piTreatmentRange, pi2) {
    if (stageResults$isOneSampleDataset()) {
        .associatedArgumentsAreDefined(nPlanned = nPlanned, piTreatmentRange = piTreatmentRange)
        pi2 <- NA_real_
    } else {
        .associatedArgumentsAreDefined(nPlanned = nPlanned, pi2 = pi2, piTreatmentRange = piTreatmentRange)
    }

    .assertIsValidAllocationRatioPlanned(
        allocationRatioPlanned,
        stageResults$getDataInput()$getNumberOfGroups()
    )
    .assertIsValidPi(pi2, "pi2")
    piTreatmentRange <- .assertIsValidPiTreatmentRange(piTreatmentRange = piTreatmentRange)

    .warnInCaseOfUnknownArguments(
        functionName = ".getConditionalPowerPlotRates",
        ignore = c("iterations", "seed", "stageResultsName", "grid"), ...
    )

    condPowerValues <- rep(NA, length(piTreatmentRange))
    likelihoodValues <- rep(NA, length(piTreatmentRange))

    design <- stageResults$.design

    warningMessages <- c()
    withCallingHandlers(
        if (stageResults$isOneSampleDataset()) {
            mu <- stageResults$effectSizes[stage]
            stdErr <- sqrt(stageResults$effectSizes[stage] * (1 - stageResults$effectSizes[stage]) /
                stageResults$overallSampleSizes[stage])

            for (i in seq(along = piTreatmentRange)) {
                if (.isTrialDesignInverseNormalOrGroupSequential(design)) {
                    condPowerValues[i] <- .getConditionalPowerRatesInverseNormalOrGroupSequential(
                        stageResults = stageResults, nPlanned = nPlanned,
                        allocationRatioPlanned = allocationRatioPlanned,
                        pi1 = piTreatmentRange[i], pi2 = pi2
                    )$conditionalPower[design$kMax]
                } else if (.isTrialDesignFisher(design)) {
                    condPowerValues[i] <- .getConditionalPowerRatesFisher(
                        stageResults = stageResults, nPlanned = nPlanned,
                        allocationRatioPlanned = allocationRatioPlanned,
                        pi1 = piTreatmentRange[i], pi2 = pi2
                    )$conditionalPower[design$kMax]
                }
                likelihoodValues[i] <- stats::dnorm(piTreatmentRange[i], mu, stdErr) / stats::dnorm(0, 0, stdErr)
            }
        },
        warning = function(w) {
            m <- w$message
            if (!(m %in% warningMessages)) {
                warningMessages <<- c(warningMessages, m)
            }
            invokeRestart("muffleWarning")
        },
        error = function(e) {
            e
        }
    )

    if (stageResults$isTwoSampleDataset()) {
        mu <- stageResults$overallEvents1[stage] / stageResults$overallSampleSizes1[stage]
        stdErr <- sqrt(stageResults$overallEvents1[stage] / stageResults$overallSampleSizes1[stage] *
            (1 - stageResults$overallEvents1[stage] / stageResults$overallSampleSizes1[stage]) /
            stageResults$overallSampleSizes1[stage])

        withCallingHandlers(
            for (i in seq(along = piTreatmentRange)) {
                if (.isTrialDesignInverseNormalOrGroupSequential(design)) {
                    condPowerValues[i] <- .getConditionalPowerRatesInverseNormalOrGroupSequential(
                        stageResults = stageResults, stage = stage, nPlanned = nPlanned,
                        allocationRatioPlanned = allocationRatioPlanned,
                        pi1 = piTreatmentRange[i], pi2 = pi2
                    )$conditionalPower[design$kMax]
                } else if (.isTrialDesignFisher(design)) {
                    condPowerValues[i] <- .getConditionalPowerRatesFisher(
                        stageResults = stageResults, stage = stage, nPlanned = nPlanned,
                        allocationRatioPlanned = allocationRatioPlanned,
                        pi1 = piTreatmentRange[i], pi2 = pi2
                    )$conditionalPower[design$kMax]
                }
                likelihoodValues[i] <- stats::dnorm(piTreatmentRange[i], mu, stdErr) / stats::dnorm(0, 0, stdErr)
            },
            warning = function(w) {
                m <- w$message
                if (!(m %in% warningMessages)) {
                    warningMessages <<- c(warningMessages, m)
                }
                invokeRestart("muffleWarning")
            },
            error = function(e) {
                e
            }
        )
    }

    if (length(warningMessages) > 0) {
        for (m in warningMessages) {
            warning(m, call. = FALSE)
        }
    }

    if (stageResults$isOneSampleDataset()) {
        subtitle <- paste0("Stage = ", stage, ", # of remaining subjects = ", sum(nPlanned))
    } else {
        subtitle <- paste0(
            "Stage = ", stage, ", # of remaining subjects = ", sum(nPlanned),
            ", pi2 = ", .formatSubTitleValue(pi2, "pi2"),
            ", allocation ratio = ", .formatSubTitleValue(allocationRatioPlanned, "allocationRatioPlanned")
        )
    }

    return(list(
        xValues = piTreatmentRange,
        condPowerValues = condPowerValues,
        likelihoodValues = likelihoodValues,
        main = C_PLOT_MAIN_CONDITIONAL_POWER_WITH_LIKELIHOOD,
        xlab = "pi1",
        ylab = C_PLOT_YLAB_CONDITIONAL_POWER_WITH_LIKELIHOOD,
        sub = subtitle
    ))
}

#'
#' Calculation of final confidence interval
#' based on group sequential test without SSR (general case).
#'
#' @noRd
#'
.getFinalConfidenceIntervalRatesGroupSequential <- function(..., design, dataInput, stage,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    stageResults <- .getStageResultsRates(
        design = design, dataInput = dataInput, stage = stage,
        thetaH0 = thetaH0, directionUpper = directionUpper, normalApproximation = normalApproximation
    )

    finalConfidenceIntervalGeneral <- rep(NA_real_, 2)
    medianUnbiasedGeneral <- NA_real_

    stageGroupSeq <- .getStageGroupSeq(design = design, stageResults = stageResults, stage = stage)

    finalStage <- min(stageGroupSeq, design$kMax)

    # early stopping or at end of study
    if (stageGroupSeq < design$kMax || stage == design$kMax) {
        if (stageGroupSeq == 1) {
            finalConfidenceIntervalGeneral[1] <- stageResults$overallTestStatistics[1] -
                .getOneMinusQNorm(design$alpha / design$sided)
            finalConfidenceIntervalGeneral[2] <- stageResults$overallTestStatistics[1] +
                .getOneMinusQNorm(design$alpha / design$sided)
            medianUnbiasedGeneral <- stageResults$overallTestStatistics[1]

            if (dataInput$getNumberOfGroups() == 1) {
                finalConfidenceIntervalGeneral <- finalConfidenceIntervalGeneral /
                    sqrt(stageResults$overallSampleSizes[1])
                medianUnbiasedGeneral <- medianUnbiasedGeneral /
                    sqrt(stageResults$overallSampleSizes[1])
            } else {
                finalConfidenceIntervalGeneral <- finalConfidenceIntervalGeneral *
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] + 1 / stageResults$overallSampleSizes2[finalStage])
                medianUnbiasedGeneral <- medianUnbiasedGeneral *
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] + 1 / stageResults$overallSampleSizes2[finalStage])
            }
        } else {
            finalConfidenceIntervalGeneral[1] <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "overallPValues",
                case = "finalConfidenceIntervalGeneralLower"
            )

            finalConfidenceIntervalGeneral[2] <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "overallPValues",
                case = "finalConfidenceIntervalGeneralUpper"
            )

            medianUnbiasedGeneral <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "overallPValues",
                case = "medianUnbiasedGeneral"
            )
        }
    }

    if (is.na(finalConfidenceIntervalGeneral[1]) && (stageGroupSeq > 1)) {
        finalStage <- NA_integer_
    }

    finalConfidenceInterval <- rep(NA_real_, 2)
    medianUnbiased <- NA_real_

    if (!is.na(finalStage)) {
        #  Retransformation
        if (dataInput$getNumberOfGroups() == 1) {
            stErrRates <- sqrt(stageResults$overallEvents[finalStage] / stageResults$overallSampleSizes[finalStage] *
                (1 - stageResults$overallEvents[finalStage] / stageResults$overallSampleSizes[finalStage])) /
                sqrt(stageResults$overallSampleSizes[finalStage])
        } else {
            stErrRates <- sqrt(stageResults$overallEvents1[finalStage] / stageResults$overallSampleSizes1[finalStage] *
                (1 - stageResults$overallEvents1[finalStage] / stageResults$overallSampleSizes1[finalStage]) /
                stageResults$overallSampleSizes1[finalStage] +
                stageResults$overallEvents2[finalStage] / stageResults$overallSampleSizes2[finalStage] *
                    (1 - stageResults$overallEvents2[finalStage] / stageResults$overallSampleSizes2[finalStage]) /
                    stageResults$overallSampleSizes2[finalStage])
        }

        directionUpperSign <- ifelse(directionUpper, 1, -1)

        if (stageGroupSeq == 1) {
            finalConfidenceInterval[1] <- .getRootThetaRates(
                design = design, dataInput = dataInput, stage = 1,
                directionUpper = C_DIRECTION_UPPER_DEFAULT, normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
                firstParameterName = "overallPValues", secondValue = .getOneMinusQNorm(design$alpha / design$sided),
                tolerance = tolerance, acceptResultsOutOfTolerance = TRUE,
                callingFunctionInformation = "Final confidence interval [1]"
            )

            finalConfidenceInterval[2] <- .getRootThetaRates(
                design = design, dataInput = dataInput, stage = 1,
                directionUpper = FALSE, normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
                firstParameterName = "overallPValues", secondValue = .getOneMinusQNorm(design$alpha / design$sided),
                tolerance = tolerance, acceptResultsOutOfTolerance = TRUE,
                callingFunctionInformation = "Final confidence interval [2]"
            )

            medianUnbiased <- stageResults$effectSizes[1]
        } else {
            if (dataInput$getNumberOfGroups() == 1) {
                finalConfidenceInterval[1] <- finalConfidenceIntervalGeneral[1] *
                    sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                finalConfidenceInterval[2] <- finalConfidenceIntervalGeneral[2] *
                    sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                medianUnbiased <- medianUnbiasedGeneral * sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
            } else {
                finalConfidenceInterval[1] <- finalConfidenceIntervalGeneral[1] /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                finalConfidenceInterval[2] <- finalConfidenceIntervalGeneral[2] /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                medianUnbiased <- medianUnbiasedGeneral /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
            }
        }
    }

    if (!directionUpper) {
        medianUnbiasedGeneral <- -medianUnbiasedGeneral
        finalConfidenceIntervalGeneral <- -finalConfidenceIntervalGeneral
        if (stageGroupSeq > 1) {
            medianUnbiased <- -medianUnbiased
            finalConfidenceInterval <- -finalConfidenceInterval
        }
    }

    if (!any(is.na(finalConfidenceIntervalGeneral))) {
        finalConfidenceIntervalGeneral <- sort(finalConfidenceIntervalGeneral)
    }
    if (!any(is.na(finalConfidenceInterval))) {
        finalConfidenceInterval <- sort(finalConfidenceInterval)
    }

    if (dataInput$getNumberOfGroups() == 1) {
        finalConfidenceInterval[1] <- max(0, finalConfidenceInterval[1])
        finalConfidenceInterval[2] <- min(1, finalConfidenceInterval[2])
    } else {
        finalConfidenceInterval[1] <- max(-1, finalConfidenceInterval[1])
        finalConfidenceInterval[2] <- min(1, finalConfidenceInterval[2])
    }

    return(list(
        stage = stage,
        thetaH0 = thetaH0,
        directionUpper = directionUpper,
        normalApproximation = normalApproximation,
        tolerance = tolerance,
        finalStage = finalStage,
        medianUnbiasedGeneral = medianUnbiasedGeneral,
        finalConfidenceIntervalGeneral = finalConfidenceIntervalGeneral,
        medianUnbiased = medianUnbiased,
        finalConfidenceInterval = finalConfidenceInterval
    ))
}

#'
#' Calculation of final confidence interval
#' based on inverse normal method, only valid for kMax <= 2 or no SSR.
#'
#' @noRd
#'
.getFinalConfidenceIntervalRatesInverseNormal <- function(..., design, dataInput, stage,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    stageResults <- .getStageResultsRates(
        design = design, dataInput = dataInput, stage = stage,
        thetaH0 = thetaH0, directionUpper = directionUpper, normalApproximation = normalApproximation
    )

    finalConfidenceIntervalGeneral <- rep(NA_real_, 2)
    medianUnbiasedGeneral <- NA_real_

    stageInverseNormal <- .getStageInverseNormal(design = design, stageResults = stageResults, stage = stage)
    finalStage <- min(stageInverseNormal, design$kMax)

    # Early stopping or at end of study
    if (stageInverseNormal < design$kMax || stage == design$kMax) {
        if (stageInverseNormal == 1) {
            finalConfidenceIntervalGeneral[1] <- stageResults$combInverseNormal[1] -
                .getOneMinusQNorm(design$alpha / design$sided)
            finalConfidenceIntervalGeneral[2] <- stageResults$combInverseNormal[1] +
                .getOneMinusQNorm(design$alpha / design$sided)
            medianUnbiasedGeneral <- stageResults$combInverseNormal[1]

            if (dataInput$getNumberOfGroups() == 1) {
                finalConfidenceIntervalGeneral <- finalConfidenceIntervalGeneral /
                    sqrt(stageResults$overallSampleSizes[1])
                medianUnbiasedGeneral <- medianUnbiasedGeneral /
                    sqrt(stageResults$overallSampleSizes[1])
            } else {
                finalConfidenceIntervalGeneral <- finalConfidenceIntervalGeneral *
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage])
                medianUnbiasedGeneral <- medianUnbiasedGeneral *
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage])
            }
        } else {
            if ((design$kMax > 2) && !.isNoEarlyEfficacy(design)) {
                message(
                    "Calculation of final confidence interval performed for kMax = ", design$kMax,
                    " (for kMax > 2, it is theoretically shown that it is valid only ",
                    "if no sample size change was performed)"
                )
            }

            finalConfidenceIntervalGeneral[1] <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "combInverseNormal",
                case = "finalConfidenceIntervalGeneralLower"
            )

            finalConfidenceIntervalGeneral[2] <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "combInverseNormal",
                case = "finalConfidenceIntervalGeneralUpper"
            )

            medianUnbiasedGeneral <- .getDecisionMatrixRoot(
                design = design,
                stage = finalStage, stageResults = stageResults, tolerance = tolerance,
                firstParameterName = "combInverseNormal",
                case = "medianUnbiasedGeneral"
            )
        }
    }

    if (is.na(finalConfidenceIntervalGeneral[1]) && (stageInverseNormal > 1)) {
        finalStage <- NA_integer_
    }

    finalConfidenceInterval <- rep(NA_real_, 2)
    medianUnbiased <- NA_real_

    if (!is.na(finalStage)) {
        # Retransformation
        if (dataInput$getNumberOfGroups() == 1) {
            stErrRates <- sqrt(stageResults$overallEvents[finalStage] / stageResults$overallSampleSizes[finalStage] *
                (1 - stageResults$overallEvents[finalStage] / stageResults$overallSampleSizes[finalStage])) /
                sqrt(stageResults$overallSampleSizes[finalStage])
        } else {
            stErrRates <- sqrt(stageResults$overallEvents1[finalStage] / stageResults$overallSampleSizes1[finalStage] *
                (1 - stageResults$overallEvents1[finalStage] / stageResults$overallSampleSizes1[finalStage]) /
                stageResults$overallSampleSizes1[finalStage] +
                stageResults$overallEvents2[finalStage] / stageResults$overallSampleSizes2[finalStage] *
                    (1 - stageResults$overallEvents2[finalStage] / stageResults$overallSampleSizes2[finalStage]) /
                    stageResults$overallSampleSizes2[finalStage])
        }

        directionUpperSign <- ifelse(directionUpper, 1, -1)

        if (stageInverseNormal == 1) {
            finalConfidenceInterval[1] <- .getRootThetaRates(
                design = design, dataInput = dataInput, stage = 1,
                directionUpper = C_DIRECTION_UPPER_DEFAULT, normalApproximation = TRUE,
                firstParameterName = "combInverseNormal",
                secondValue = .getOneMinusQNorm(design$alpha / design$sided), tolerance = tolerance,
                acceptResultsOutOfTolerance = TRUE,
                callingFunctionInformation = "Final confidence interval [1]"
            )

            finalConfidenceInterval[2] <- .getRootThetaRates(
                design = design, dataInput = dataInput, stage = 1,
                directionUpper = FALSE, normalApproximation = TRUE,
                firstParameterName = "combInverseNormal",
                secondValue = .getOneMinusQNorm(design$alpha / design$sided), tolerance = tolerance,
                acceptResultsOutOfTolerance = TRUE,
                callingFunctionInformation = "Final confidence interval [1]"
            )

            medianUnbiased <- stageResults$effectSizes[1]
        } else {
            if (dataInput$getNumberOfGroups() == 1) {
                finalConfidenceInterval[1] <- finalConfidenceIntervalGeneral[1] *
                    sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                finalConfidenceInterval[2] <- finalConfidenceIntervalGeneral[2] *
                    sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                medianUnbiased <- medianUnbiasedGeneral * sqrt(stageResults$overallSampleSizes[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
            } else {
                finalConfidenceInterval[1] <- finalConfidenceIntervalGeneral[1] /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                finalConfidenceInterval[2] <- finalConfidenceIntervalGeneral[2] /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
                medianUnbiased <- medianUnbiasedGeneral /
                    sqrt(1 / stageResults$overallSampleSizes1[finalStage] +
                        1 / stageResults$overallSampleSizes2[finalStage]) *
                    stErrRates + directionUpperSign * thetaH0
            }
        }
    }

    if (!directionUpper) {
        medianUnbiasedGeneral <- -medianUnbiasedGeneral
        finalConfidenceIntervalGeneral <- -finalConfidenceIntervalGeneral
        if (stageInverseNormal > 1) {
            medianUnbiased <- -medianUnbiased
            finalConfidenceInterval <- -finalConfidenceInterval
        }
    }

    finalConfidenceIntervalGeneral <- sort(finalConfidenceIntervalGeneral)
    finalConfidenceInterval <- sort(finalConfidenceInterval)

    if (dataInput$getNumberOfGroups() == 1) {
        finalConfidenceInterval[1] <- max(0, finalConfidenceInterval[1])
        finalConfidenceInterval[2] <- min(1, finalConfidenceInterval[2])
    } else {
        finalConfidenceInterval[1] <- max(-1, finalConfidenceInterval[1])
        finalConfidenceInterval[2] <- min(1, finalConfidenceInterval[2])
    }

    return(list(
        stage = stage,
        thetaH0 = thetaH0,
        directionUpper = directionUpper,
        normalApproximation = normalApproximation,
        tolerance = tolerance,
        finalStage = finalStage,
        medianUnbiasedGeneral = medianUnbiasedGeneral,
        finalConfidenceIntervalGeneral = finalConfidenceIntervalGeneral,
        medianUnbiased = medianUnbiased,
        finalConfidenceInterval = finalConfidenceInterval
    ))
}

#'
#' Calculation of final confidence interval
#' based on Fisher combination test, only valid for kMax <= 2.
#'
#' @noRd
#'
.getFinalConfidenceIntervalRatesFisher <- function(..., design, dataInput, stage,
        thetaH0 = C_THETA_H0_RATES_DEFAULT, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    stageResults <- .getStageResultsRates(
        design = design, dataInput = dataInput, stage = stage,
        thetaH0 = thetaH0, directionUpper = directionUpper, normalApproximation = normalApproximation
    )

    finalConfidenceInterval <- rep(NA_real_, 2)
    medianUnbiased <- NA_real_

    stageFisher <- .getStageFisher(design = design, stageResults = stageResults, stage = stage)

    finalStage <- min(stageFisher, design$kMax)

    # Early stopping or at end of study
    if (stageFisher < design$kMax || stage == design$kMax) {
        message(
            "Calculation of final confidence interval for Fisher's ",
            "design not implemented yet"
        )
        return(list(
            finalStage = NA_integer_, medianUnbiased = NA_real_,
            finalConfidenceInterval = rep(NA_real_, design$kMax)
        ))
    }

    return(list(
        stage = stage,
        thetaH0 = thetaH0,
        directionUpper = directionUpper,
        normalApproximation = normalApproximation,
        tolerance = tolerance,
        finalStage = finalStage,
        medianUnbiased = medianUnbiased,
        finalConfidenceInterval = finalConfidenceInterval
    ))
}

.getFinalConfidenceIntervalRates <- function(..., design, dataInput,
        thetaH0 = NA_real_, directionUpper = C_DIRECTION_UPPER_DEFAULT,
        normalApproximation = C_NORMAL_APPROXIMATION_RATES_DEFAULT,
        tolerance = C_ANALYSIS_TOLERANCE_DEFAULT) {
    stage <- .getStageFromOptionalArguments(..., dataInput = dataInput, design = design)
    .assertIsValidThetaH0DataInput(thetaH0, dataInput)
    .warnInCaseOfUnknownArguments(
        functionName = "getFinalConfidenceIntervalRates",
        ignore = c(.getDesignArgumentsToIgnoreAtUnknownArgumentCheck(design, powerCalculationEnabled = TRUE), "stage"), ...
    )

    if (design$kMax == 1) {
        return(list(
            finalStage = NA_integer_,
            medianUnbiasedGeneral = NA_real_,
            finalConfidenceIntervalGeneral = c(NA_real_, NA_real_),
            medianUnbiased = NA_real_,
            finalConfidenceInterval = c(NA_real_)
        ))
    }

    if (is.na(thetaH0)) {
        thetaH0 <- C_THETA_H0_RATES_DEFAULT
    }

    if (.isTrialDesignGroupSequential(design)) {
        return(.getFinalConfidenceIntervalRatesGroupSequential(
            design = design, dataInput = dataInput, stage = stage, thetaH0 = thetaH0,
            directionUpper = directionUpper, normalApproximation = normalApproximation,
            tolerance = tolerance
        ))
    }

    if (.isTrialDesignInverseNormal(design)) {
        return(.getFinalConfidenceIntervalRatesInverseNormal(
            design = design, dataInput = dataInput, stage = stage, thetaH0 = thetaH0,
            directionUpper = directionUpper, normalApproximation = normalApproximation,
            tolerance = tolerance
        ))
    }

    if (.isTrialDesignFisher(design)) {
        return(.getFinalConfidenceIntervalRatesFisher(
            design = design, dataInput = dataInput, stage = stage, thetaH0 = thetaH0,
            directionUpper = directionUpper, normalApproximation = normalApproximation,
            tolerance = tolerance
        ))
    }

    .stopWithWrongDesignMessage(design, inclusiveConditionalDunnett = FALSE)
}