Package 'lrstat'

Description

A comprehensive clinical trial design and analysis package with a focus on non-proportional hazards and weighted log-rank methods, plus broad support for group sequential design, adaptive design, multiplicity, dose-finding, and endpoint-specific power and sample size calculations.

Details

For proportional hazards, power is determined by the total number of events and the constant hazard ratio together with information rates and spending functions. For non-proportional hazards, the hazard ratio varies over time and calendar time determines the mean and variance of the weighted log-rank score statistic. The package uses the analytic approach in Lu (2021) and approximates the variance-covariance matrix of sequential statistics under the alternative by that under the null to leverage the independent increments structure in Tsiatis (1982) for the Fleming-Harrington family.

The package capabilities can be grouped as follows:

• Time-to-event design under proportional and non-proportional hazards: weighted log-rank statistics and design operating characteristics (for example lrstat, lrpower, lrsamplesize, lrsim, lrschoenfeld), including equivalence settings, event prediction, accrual modeling, and calendar time determination (for example accrual, caltime, nevent, pevent, patrisk, natrisk, getDurationFromNevents, getNeventsFromHazardRatio).

• Group sequential and adaptive designs: standard, adaptive, multi-arm multi-stage (MAMS), and seamless frameworks, including boundaries, conditional power, confidence intervals, and exit probabilities (for example getDesign, adaptDesign, getBound, getCP, getCI, getRCI, getADCI, getADRCI, exitprob, and their _mams and _seamless variants).

• Fixed and sequential sample size/power across endpoint types: binary, continuous, ordinal/multinomial, paired, crossover/carryover, MMRM, repeated measures ANOVA, two-way ANOVA, Wilcoxon, Fisher's exact, McNemar, one-sample exact, agreement, logistic regression, and negative binomial endpoints (for example getDesign*, power*Exact, samplesize*Exact, kmpower, rmpower, nbpower, and associated *samplesize and *equiv functions).

• Multiplicity and graphical procedures: weighted Bonferroni and graph-based updates, Bonferroni mixtures of weighted Simes and Dunnett, and gatekeeping procedures for multiple hypotheses (for example fadjpbon, fadjpsim, fadjpdun, fseqbon, fstp2seq, fstdmix, fmodmix, fwgtmat, updateGraph).

• Early-phase and dose-finding tools: Simon's two-stage, Bayesian Simon designs, mTPI-2, and BOIN utilities (for example simon2stage, simonBayesAnalysis, simonBayesSim, mTPI2Table, BOINTable).

• Estimation, confidence intervals, and supporting utilities: Clopper-Pearson, exact risk ratio/risk difference, Brookmeyer-Crowley survival quantiles, Miettinen-Nurminen and REML intervals/statistics for stratified measures, Hedges' g, piecewise-exponential distribution tools, multivariate normal integration, and model diagnostics (for example ClopperPearsonCI, riskRatioExactCI, riskDiffExactCI, survQuantile, mnRiskDiffCI, remlRiskDiff, hedgesg, dtpwexp, ptpwexp, qtpwexp, rtpwexp, pbvnorm, pmvnormr, qmvnormr, phregr, liferegr, residuals_phregr, survfit_phregr, zph_phregr).

• Interactive use: a bundled Shiny interface for exploratory design workflows (runShinyApp_lrstat).

The development of lrstat was strongly influenced by rpact, with argument naming aligned where possible for ease of adoption. Key differences include direct approximation (rather than Schoenfeld-based approximation) for weighted log-rank design calculations, explicit use of accrualDuration to define the accrual end, and treatment of final stage trial outcome when early futility stopping does not occur.

Author(s)

Kaifeng Lu, [email protected]

References

Anastasios A. Tsiatis. Repeated significance testing for a general class of statistics used in censored survival analysis. J Am Stat Assoc. 1982;77:855-861.

Christopher Jennison, Bruce W. Turnbull. Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC: Boca Raton, 2000, ISBN:0849303168

Kaifeng Lu. Sample size calculation for logrank test and prediction of number of events over time. Pharm Stat. 2021;20:229-244.

See Also

rpact, gsDesign

Examples

lrpower(kMax = 2, informationRates = c(0.8, 1),
        criticalValues = c(2.250, 2.025), accrualIntensity = 20,
        piecewiseSurvivalTime = c(0, 6),
        lambda1 = c(0.0533, 0.0309), lambda2 = c(0.0533, 0.0533),
        gamma1 = 0.00427, gamma2 = 0.00427,
        accrualDuration = 22, followupTime = 18)

Description

Obtains the number of subjects enrolled by given calendar times.

Usage

accrual(time, accrualTime, accrualIntensity, accrualDuration)

Arguments

Value

A vector of total number of subjects enrolled by the specified calendar times.

Author(s)

Kaifeng Lu, [email protected]

Examples

# Example 1: Uniform enrollment with 20 patients per month for 12 months.

accrual(time = 3, accrualTime = 0, accrualIntensity = 20,
        accrualDuration = 12)


# Example 2: Piecewise accrual, 10 patients per month for the first
# 3 months, and 20 patients per month thereafter. Patient recruitment
# ends at 12 months for the study.

accrual(time = c(2, 9), accrualTime = c(0, 3),
        accrualIntensity = c(10, 20), accrualDuration = 12)

Description

Calculates the conditional power for specified incremental information, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks. Conversely, calculates the incremental information required to attain a specified conditional power, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks.

Usage

adaptDesign(
  betaNew = NA_real_,
  INew = NA_real_,
  L = NA_integer_,
  zL = NA_real_,
  theta = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityTheta = NULL,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  kNew = NA_integer_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  futilityStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  futilityBoundsInt = NULL,
  futilityCPInt = NULL,
  futilityThetaInt = NULL,
  typeBetaSpendingNew = "none",
  parameterBetaSpendingNew = NA_real_,
  userBetaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_,
  varianceRatio = 1
)

Arguments

Value

An adaptDesign object with three list components:

• primaryTrial: A list of selected information for the primary trial, including L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, information, alpha, conditionalAlpha, conditionalPower, predictivePower, and and MullerSchafer.

• secondaryTrial: A list of selected information for the secondary trial, including overallReject, alpha, kMax, maxInformation, informationRates, efficacyBounds, futilityBounds, cumulativeRejection, cumulativeFutility, cumulativeAlphaSpent, information, typeAlphaSpending, parameterAlphaSpending, typeBetaSpending, parameterBetaSpending, userBetaSpending, and spendingTime.

• integratedTrial: A list of selected information for the integrated trial, including L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, and information.

Author(s)

Kaifeng Lu, [email protected]

References

Lu Chi, H. M. James Hung, and Sue-Jane Wang. Modification of sample size in group sequential clinical trials. Biometrics 1999;55:853-857.

Hans-Helge Muller and Helmut Schafer. Adaptive group sequential designs for clinical trials: Combining the advantages of adaptive and of classical group sequential approaches. Biometrics 2001;57:886-891.

See Also

getDesign

Examples

# two-arm randomized clinical trial with a normally distributed endpoint
# 90% power to detect mean difference of 15 with a standard deviation of 50
# Design the Stage I Trial with 3 looks and Lan-DeMets O'Brien-Fleming type
# spending function
delta <- 15
sigma <- 50

(des1 <- getDesignMeanDiff(
  beta = 0.1, meanDiff = delta, stDev = sigma,
  kMax = 3, alpha = 0.025, typeAlphaSpending = "sfOF"
))

s1 <- des1$byStageResults$informationRates
b1 <- des1$byStageResults$efficacyBounds
n <- des1$overallResults$numberOfSubjects

# Monitoring the Stage I Trial
L <- 1
nL <- des1$byStageResults$numberOfSubjects[L]
deltahat <- 8
sigmahat <- 55
sedeltahat <- sigmahat * sqrt( 4 / nL)
zL <- deltahat / sedeltahat

# Making an Adaptive Change: Stage I to Stage II
# revised clinically meaningful difference downward to 10 power the study
# retain the standard deviation at the design stage
# Muller & Schafer (2001) method to design the secondary trial
# with 2 looks and Lan-DeMets Pocock type spending function
# re-estimate sample size to reach 90% conditional power
deltaNew <- 10

(des2 <- adaptDesign(
  betaNew = 0.1, L = L, zL = zL, theta = deltaNew,
  IMax = n / (4 * sigma^2), kMax = 3, informationRates = s1,
  alpha = 0.025, typeAlphaSpending = "sfOF",
  MullerSchafer = TRUE, kNew = 2, typeAlphaSpendingNew = "sfP"
))

INew <- des2$maxInformation
(nNew <- ceiling(INew * 4 * sigma^2))
(nTotal <- nL + nNew)

Description

Calculates the conditional power for specified incremental information, given the interim results, parameter value, data-dependent changes in treatment selection, the error spending function, and the number and spacing of interim looks. Conversely, calculates the incremental information required to attain a specified conditional power, given the interim results, parameter value, data-dependent changes in treatment selection, the error spending function, and the number and spacing of interim looks.

Usage

adaptDesign_mams(
  betaNew = NA_real_,
  INew = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  L = NA_integer_,
  zL = NA_real_,
  theta = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityTheta = NULL,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  MNew = NA_integer_,
  selected = NA_integer_,
  rNew = 1,
  kNew = NA_integer_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  futilityStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  futilityBoundsInt = NULL,
  futilityCPInt = NULL,
  futilityThetaInt = NULL,
  typeBetaSpendingNew = "none",
  parameterBetaSpendingNew = NA_real_,
  userBetaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Arguments

Value

An adaptDesign_mams object with three list components:

• primaryTrial: A list of selected information for the primary trial, including M, r, corr_known, L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, information, alpha, conditionalAlpha, conditionalPower, MullerSchafer, and byLevelBounds, where byLevelBounds is a data frame with columns level, stage, and efficacyBounds, representing the efficacy bounds for each combination of the number of active arms and the stage of analysis in the primary trial.

• secondaryTrial: A list of selected information for the secondary trial, including overallReject, alpha, M, r, selected, corr_known, kMax, maxInformation, informationRates, cumulativeRejection, cumulativeAlphaSpent, information, typeAlphaSpending, parameterAlphaSpending, typeBetaSpending, parameterBetaSpending, userBetaSpending, spendingTime, and byHypothesisBounds, where byHypothesisBounds is a data frame with columns hypothesis, stage, efficacyBounds, and futilityBounds, representing the efficacy and futility bounds for each hypothesis and each stage of analysis in the secondary trial.

• integratedTrial: A list of selected information for the integrated trial, including M, r, corr_known, MNew, rNew, selected, L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, information, and byIntersectionBounds, where byIntersectionBounds is a data frame with columns intersectionHypothesis, stage, and efficacyBounds, representing the efficacy bounds for each intersection hypothesis and each stage of analysis in the integrated trial.

Author(s)

Kaifeng Lu, [email protected]

References

Ping Gao, Yingqiu Li. Adaptive multiple comparison sequential design (AMCSD) for clinical trials. Journal of Biopharmaceutical Statistics, 2024, 34(3), 424-440.

See Also

getDesign_mams

Examples

# Two active treatment arms are compared with a common control in a
# two-look time-to-event design using O'Brien–Fleming–type alpha spending.
# Suppose each active arm has a true hazard ratio of 0.75 versus control,
# and the total number of events across all three arms at the final analysis
# is 486. This corresponds to approximately 324 events for each active arm
# versus the common control. Under these assumptions, the trial has about
# 80% power to detect the treatment effect in at least one active arm.

(des1 <- getDesign_mams(
  IMax = 324 / 4, theta = c(-log(0.75), -log(0.75)),
  M = 2, r = 1, kMax = 2, informationRates = c(1/2, 1),
  alpha = 0.025, typeAlphaSpending = "OF"))

# Now assume that, at the interim analysis, the observed hazard ratios for
# the two active arms versus control are 0.91 and 0.78, respectively. Using
# the rule “drop any arm with an observed hazard ratio > 0.9”, arm 1 is
# dropped. We then aim to achieve 80% conditional power to detect a hazard
# ratio of 0.78 for the remaining arm at the final look. The analysis below
# indicates that the required total number of events for arm 2 versus control
# at the final analysis should be increased from 324 to 535.

(des2 <- adaptDesign_mams(
  betaNew = 0.2, M = 2, r = 1, corr_known = FALSE,
  L = 1, zL = c(-log(0.91), -log(0.78)) * sqrt(324 / 4 / 2),
  theta = c(-log(0.91), -log(0.78)),
  IMax = 324 / 4, kMax = 2, informationRates = c(1/2, 1),
  alpha = 0.025, typeAlphaSpending = "OF",
  MNew = 1, selected = 2, rNew = 1))

Description

Calculates the conditional power for specified incremental information, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks. Conversely, calculates the incremental information required to attain a specified conditional power, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks.

Usage

adaptDesign_seamless(
  betaNew = NA_real_,
  INew = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  L = NA_integer_,
  zL = NA_real_,
  theta = NA_real_,
  IMax = NA_real_,
  K = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityTheta = NULL,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  kNew = NA_integer_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  futilityStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  futilityBoundsInt = NULL,
  futilityCPInt = NULL,
  futilityThetaInt = NULL,
  typeBetaSpendingNew = "none",
  parameterBetaSpendingNew = NA_real_,
  userBetaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Arguments

Value

An adaptDesign_seamless object with three list components:

• primaryTrial: A list of selected information for the primary trial, including M, r, corr_known, K, L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, information, alpha, conditionalAlpha, conditionalPower, and MullerSchafer.

• secondaryTrial: A list of selected information for the seconary trial, including overallReject, alpha, kMax, maxInformation, informationRates, efficacyBounds, futilityBounds, cumulativeRejection, cumulativeFutility, cumulativeAlphaSpent, information, typeAlphaSpending, parameterAlphaSpending, typeBetaSpending, parameterBetaSpending, userBetaSpending, and spendingTime.

• integratedTrial: A list of selected information for the integrated trial, including M, r, corr_known, K, L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, and information.

Author(s)

Kaifeng Lu, [email protected]

References

Ping Gao, Yingqiu Li. Adaptive two-stage seamless sequential design for clinical trials. Journal of Biopharmaceutical Statistics, 2025, 35(4), 565-587.

See Also

getDesign_seamless

Examples

(des1 <- adaptDesign_seamless(
  betaNew = 0.1, M = 2, r = 1, corr_known = FALSE,
  L = 1, zL = -log(0.67) * sqrt(80 / 4), theta = -log(0.691),
  IMax = 120 / 4, K = 2, informationRates = c(1/3, 2/3, 1),
  alpha = 0.025, typeAlphaSpending = "OF", kNew = 1))

Description

Survival in patients with acute myelogenous leukemia.

time

Survival or censoring time

status

censoring status

x

maintenance chemotherapy given or not

Usage

aml

Format

An object of class data.frame with 23 rows and 3 columns.

Description

Obtains the standardized score processes and the simulated distribution under the null hypothesis as well as the p-values for the supremum tests.

Usage

assess_phregr(object, resample = 1000, seed = 12345)

Arguments

Details

The supremum test corresponds to the ASSESS statement with ph option of SAS PROC PHREG.

Value

A list with the following components:

• time the unique event times.

• score_t the observed standardized score process.

• score_t_list a list of simulated standardized score processes under the null hypothesis.

• max_abs_value the supremum of the absolute value of the observed standardized score process for each covariate and the supremum of the sum of absolute values of the observed standardized score processes across all covariates.

• p_value the p-values for the supremum tests for each covariate and the global test.

Author(s)

Kaifeng Lu, [email protected]

References

D. Y. Lin, L. J. Wei, and Z. Ying. Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 1993; 80:557-572.

Examples

fit <- phregr(data = liver, time = "Time", event = "Status",
              covariates = c("log(Bilirubin)", "log(Protime)",
                             "log(Albumin)", "Age", "Edema"),
              ties = "breslow")

aph <- assess_phregr(fit, resample = 1000, seed = 314159)

aph

plot(aph, nsim = 20)

Description

Performs simulation for two-endpoint two-arm group sequential trials.

• Endpoint 1: Binary endpoint, analyzed using the Mantel-Haenszel test for risk difference.

• Endpoint 2: Time-to-event endpoint, analyzed using the log-rank test for treatment effect.

The analysis times for the binary endpoint are based on calendar times, while the time-to-event analyses are triggered by reaching the pre-specified number of events. The binary endpoint is assessed at the first post-treatment follow-up visit (PTFU1).

Usage

binary_tte_sim(
  kMax1 = 1,
  kMax2 = 1,
  riskDiffH0 = 0,
  hazardRatioH0 = 1,
  allocation1 = 1,
  allocation2 = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  globalOddsRatio = NA,
  pi1 = NA,
  pi2 = NA,
  lambda1 = NA,
  lambda2 = NA,
  gamma1 = NA,
  gamma2 = NA,
  delta1 = NA,
  delta2 = NA,
  upper1 = NA,
  upper2 = NA,
  n = NA,
  plannedTime = NA,
  plannedEvents = NA,
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 0,
  seed = 0,
  nthreads = 0
)

Arguments

Details

We consider dual primary endpoints with endpoint 1 being a binary endpoint and endpoint 2 being a time-to-event endpoint. The analyses of endpoint 1 will be based on calendar times, while the analyses of endpoint 2 will be based on the number of events. Therefore, the analyses of the two endpoints are not at the same time points. The correlation between the two endpoints is characterized by the global odds ratio of the Plackett copula. In addition, the time-to-event endpoint will render the binary endpoint as a non-responder, and so does the dropout. In addition, the treatment discontinuation will impact the number of available subjects for analysis. The administrative censoring will exclude subjects from the analysis of the binary endpoint.

Value

A list with 4 components:

• sumdataBIN: A data frame of summary data by iteration and stage for the binary endpoint:

  • iterationNumber: The iteration number.

  • stageNumber: The stage number, covering all stages even if the trial stops at an interim look.

  • analysisTime: The time for the stage since trial start.

  • accruals1: The number of subjects enrolled at the stage for the treatment group.

  • accruals2: The number of subjects enrolled at the stage for the control group.

  • totalAccruals: The total number of subjects enrolled at the stage.

  • source1: The total number of subjects with response status determined by the underlying latent response variable.

  • source2: The total number of subjects with response status (non-responder) determined by experiencing the event for the time-to-event endpoint.

  • source3: The total number of subjects with response status (non-responder) determined by dropping out prior to the PTFU1 visit.

  • n1: The number of subjects included in the analysis of the binary endpoint for the treatment group.

  • n2: The number of subjects included in the analysis of the binary endpoint for the control group.

  • n: The total number of subjects included in the analysis of the binary endpoint at the stage.

  • y1: The number of responders for the binary endpoint in the treatment group.

  • y2: The number of responders for the binary endpoint in the control group.

  • y: The total number of responders for the binary endpoint at the stage.

  • riskDiff: The estimated risk difference for the binary endpoint.

  • seRiskDiff: The standard error for risk difference based on the Sato approximation.

  • mhStatistic: The Mantel-Haenszel test Z-statistic for the binary endpoint.

• sumdataTTE: A data frame of summary data by iteration and stage for the time-to-event endpoint:

  • iterationNumber: The iteration number.

  • eventsNotAchieved: Whether the target number of events is not achieved for the iteration.

  • stageNumber: The stage number, covering all stages even if the trial stops at an interim look.

  • analysisTime: The time for the stage since trial start.

  • accruals1: The number of subjects enrolled at the stage for the treatment group.

  • accruals2: The number of subjects enrolled at the stage for the control group.

  • totalAccruals: The total number of subjects enrolled at the stage.

  • events1: The number of events at the stage for the treatment group.

  • events2: The number of events at the stage for the control group.

  • totalEvents: The total number of events at the stage.

  • dropouts1: The number of dropouts at the stage for the treatment group.

  • dropouts2: The number of dropouts at the stage for the control group.

  • totalDropouts: The total number of dropouts at the stage.

  • uscore: The numerator of the log-rank test statistic for the time-to-event endpoint.

  • vscore: The variance of the log-rank test statistic for the time-to-event endpoint.

  • logRankStatistic: The log-rank test Z-statistic for the time-to-event endpoint.

• rawdataBIN (exists if maxNumberOfRawDatasetsPerStage is a positive integer): A data frame for subject-level data for the binary endpoint for selected replications, containing the following variables:

  • iterationNumber: The iteration number.

  • stageNumber: The stage under consideration.

  • analysisTime: The time for the stage since trial start.

  • subjectId: The subject ID.

  • arrivalTime: The enrollment time for the subject.

  • stratum: The stratum for the subject.

  • treatmentGroup: The treatment group (1 or 2) for the subject.

  • survivalTime: The underlying survival time for the time-to-event endpoint for the subject.

  • dropoutTime: The underlying dropout time for the time-to-event endpoint for the subject.

  • trtDiscTime: The underlying treatment discontinuation time for the binary endpoint for the subject.

  • trtDurUpperLimit: The maximum protocol-specified treatment duration for the subject based on the treatment group assignment.

  • ptfu1Time:The underlying assessment time for the binary endpoint for the subject.

  • timeUnderObservation: The time under observation since randomization for the binary endpoint for the subject.

  • latentResponse: The underlying latent response variable for the binary endpoint for the subject, which determines the response status for the binary endpoint at PTFU1 visit.

  • responder: Whether the subject is a responder for the binary endpoint.

  • source: The source of the determination of responder status for the binary endpoint: = 1 based on the underlying latent response variable, = 2 based on the occurrence of the time-to-event endpoint before the assessment time of the binary endpoint (imputed as a non-responder), = 3 based on the dropout before the assessment time of the binary endpoint (imputed as a non-responder), = 4 excluded from analysis due to administrative censoring.

• rawdataTTE (exists if maxNumberOfRawDatasetsPerStage is a positive integer): A data frame for subject-level data for the time-to-event endpoint for selected replications, containing the following variables:

  • iterationNumber: The iteration number.

  • stageNumber: The stage under consideration.

  • analysisTime: The time for the stage since trial start.

  • subjectId: The subject ID.

  • arrivalTime: The enrollment time for the subject.

  • stratum: The stratum for the subject.

  • treatmentGroup: The treatment group (1 or 2) for the subject.

  • survivalTime: The underlying survival time for the time-to-event endpoint for the subject.

  • dropoutTime: The underlying dropout time for the time-to-event endpoint for the subject.

  • timeUnderObservation: The time under observation since randomization for the time-to-event endpoint for the subject.

  • event: Whether the subject experienced the event for the time-to-event endpoint.

  • dropoutEvent: Whether the subject dropped out for the time-to-event endpoint.

Author(s)

Kaifeng Lu, [email protected]

Examples

tcut <- c(0, 12, 36, 48)
surv <- c(1, 0.95, 0.82, 0.74)
lambda2 <- (log(surv[1:3]) - log(surv[2:4]))/(tcut[2:4] - tcut[1:3])

sim1 <- binary_tte_sim(
  kMax1 = 1,
  kMax2 = 2,
  accrualTime = seq(0, 8),
  accrualIntensity = 40/9 * seq(1, 9),
  piecewiseSurvivalTime = c(0, 12, 36),
  globalOddsRatio = 1,
  pi1 = 0.80,
  pi2 = 0.65,
  lambda1 = 0.65*lambda2,
  lambda2 = lambda2,
  gamma1 = -log(1-0.04)/12,
  gamma2 = -log(1-0.04)/12,
  delta1 = -log(1-0.02)/12,
  delta2 = -log(1-0.02)/12,
  upper1 = 15*28/30.4,
  upper2 = 12*28/30.4,
  n = 640,
  plannedTime = 20 + 15*28/30.4,
  plannedEvents = c(130, 173),
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 1,
  seed = 314159,
  nthreads = 1)

Description

Generates the decision table for the Bayesian Optimal Interval (BOIN) design, a widely used approach for dose-escalation trials that guides dose-finding decisions based on observed toxicity rates.

Usage

BOINTable(
  nMax = NA_integer_,
  pT = 0.3,
  phi1 = 0.6 * pT,
  phi2 = 1.4 * pT,
  a = 1,
  b = 1,
  pExcessTox = 0.95
)

Arguments

Value

An S3 class BOINTable object with the following components:

• settings: The input settings data frame with the following variables:

  • nMax: The maximum number of subjects in a dose cohort.

  • pT: The target toxicity probability.

  • phi1: The lower equivalence limit for target toxicity probability.

  • phi2: The upper equivalence limit for target toxicity probability.

  • lambda1: The lower decision boundary for observed toxicity probability.

  • lambda2: The upper decision boundary for observed toxicity probability.

  • a: The prior toxicity parameter for the beta prior.

  • b: The prior non-toxicity parameter for the beta prior.

  • pExcessTox: The threshold for excessive toxicity.

• decisionDataFrame: A data frame listing dose-finding decisions for each combination of sample size (n) and number of observed toxicities (y):

  • n: Cohort size.

  • y: Number of observed toxicities.

  • decision: Recommended action: escalate, de-escalate, or stay at the current dose.

• decisionMatrix: A matrix version of the decision table showing the recommended action based on the number of toxicities for each possible cohort size.

Author(s)

Kaifeng Lu, [email protected]

References

Liu, S., & Yuan, Y. (2015). Bayesian optimal interval designs for phase I clinical trials. Journal of the Royal Statistical Society: Series C (Applied Statistics), 64(3), 507-523.

Examples

BOINTable(nMax = 18, pT = 0.3, phi = 0.6*0.3, phi2 = 1.4*0.3)

Description

Obtains the calendar times needed to reach the target number of subjects experiencing an event.

Usage

caltime(
  nevents = NA_real_,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  followupTime = NA_real_,
  fixedFollowup = FALSE
)

Arguments

Value

A vector of calendar times expected to yield the target number of events.

Author(s)

Kaifeng Lu, [email protected]

Examples

# Piecewise accrual, piecewise exponential survivals, and 5% dropout by
# the end of 1 year.

caltime(nevents = c(24, 80), allocationRatioPlanned = 1,
        accrualTime = seq(0, 8),
        accrualIntensity = 26/9*seq(1, 9),
        piecewiseSurvivalTime = c(0, 6),
        lambda1 = c(0.0533, 0.0309),
        lambda2 = c(0.0533, 0.0533),
        gamma1 = -log(1-0.05)/12,
        gamma2 = -log(1-0.05)/12,
        accrualDuration = 22,
        followupTime = 18, fixedFollowup = FALSE)

Description

Obtains the Clopper-Pearson exact confidence interval for a one-sample proportion.

Usage

ClopperPearsonCI(n, y, cilevel = 0.95)

Arguments

Value

A data frame with the following variables:

• n: The sample size.

• y: The number of responses.

• phat: The observed proportion of responses.

• lower: The lower limit of the confidence interval.

• upper: The upper limit of the confidence interval.

• cilevel: The confidence interval level.

Author(s)

Kaifeng Lu, [email protected]

References

Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4), 404-413.

Examples

ClopperPearsonCI(20, 3)

Description

Computes the correlation between PFS and OS given the correlation between PD and OS.

Usage

corr_pfs_os(
  piecewiseSurvivalTime = 0L,
  hazard_pfs = NA_real_,
  hazard_os = NA_real_,
  rho_pd_os = NA_real_
)

Arguments

Details

This function first determines the piecewise exponential distribution for PD such that the implied survival function for PFS time, $T_{\text{pfs}} = \min(T_{\text{pd}}, T_{\text{os}})$, closely matches the specified piecewise exponential distribution for PFS with hazard vector $\lambda_{\text{pfs}}$. Then, it calculates the correlation between PFS and OS times based on the derived piecewise exponential distribution for PD and the given piecewise exponential distribution for OS.

Value

The estimated correlation between PFS and OS.

Author(s)

Kaifeng Lu ([email protected])

Examples

u <- c(0, 1, 3, 4)
lambda1 <- c(0.0151, 0.0403, 0.0501, 0.0558)
lambda2 <- 0.0145
rho_pd_os <- 0.5
corr_pfs_os(u, lambda1, lambda2, rho_pd_os)

Description

Obtains the covariance between restricted mean survival times at two different time points.

Usage

covrmst(
  t2 = NA_real_,
  tau1 = NA_real_,
  tau2 = NA_real_,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  maxFollowupTime = NA_real_
)

Arguments

Value

The covariance between the restricted mean survival times for each treatment group.

Author(s)

Kaifeng Lu, [email protected]

Examples

covrmst(t2 = 25, tau1 = 16, tau2 = 18, allocationRatioPlanned = 1,
        accrualTime = c(0, 3), accrualIntensity = c(10, 20),
        piecewiseSurvivalTime = c(0, 6),
        lambda1 = c(0.0533, 0.0309), lambda2 = c(0.0533, 0.0533),
        gamma1 = -log(1-0.05)/12, gamma2 = -log(1-0.05)/12,
        accrualDuration = 12, maxFollowupTime = 30)

Description

Obtains the density of a truncated piecewise exponential distribution.

Usage

dtpwexp(
  q,
  piecewiseSurvivalTime = 0,
  lambda = 0.0578,
  lowerBound = 0,
  log.d = FALSE
)

Arguments

Value

The density d such that d = lambda(q) * P(X > q | X > lowerBound).

Author(s)

Kaifeng Lu, [email protected]

Examples

dtpwexp(q = c(8, 18), piecewiseSurvivalTime = c(0, 6, 9, 15),
        lambda = c(0.025, 0.04, 0.015, 0.007))

Description

Obtains the error spent at given spending times for the specified error spending function.

Usage

errorSpent(t, error = 0.025, sf = "sfOF", sfpar = NA_real_)

Arguments

Details

This function implements a variety of error spending functions commonly used in group sequential designs, assuming one-sided hypothesis testing.

O'Brien-Fleming-Type Spending Function

This spending function allocates very little alpha early on and more alpha later in the trial. It is defined as:

$\alpha(t) = 2 - 2\Phi\left(\frac{z_{\alpha/2}}{\sqrt{t}}\right),$

where $\Phi$ is the standard normal cumulative distribution function, $z_{\alpha/2}$ is the critical value from the standard normal distribution, and $t \in [0, 1]$ denotes the information fraction.

Pocock-Type Spending Function

This function spends alpha more evenly throughout the study:

$\alpha(t) = \alpha \log(1 + (e - 1)t),$

where $e$ is Euler's number (approximately 2.718).

Kim and DeMets Power-Type Spending Function

This family of spending functions is defined as:

$\alpha(t) = \alpha t^{\rho}, \quad \rho > 0.$

• When $\rho = 1$, the function mimics Pocock-type boundaries.

• When $\rho = 3$, it approximates O’Brien-Fleming-type boundaries.

Hwang, Shih, and DeCani Spending Function

This flexible family of functions is given by:

$\alpha(t) = \begin{cases} \alpha \frac{1 - e^{-\gamma t}}{1 - e^{-\gamma}}, & \text{if } \gamma \ne 0 \\ \alpha t, & \text{if } \gamma = 0. \end{cases}$

• When $\gamma = -4$, the spending function resembles O’Brien-Fleming boundaries.

• When $\gamma = 1$, it resembles Pocock boundaries.

Value

A vector of errors spent up to the interim look.

Author(s)

Kaifeng Lu, [email protected]

Examples

errorSpent(t = 0.5, error = 0.025, sf = "sfOF")

errorSpent(t = c(0.5, 0.75, 1), error = 0.025, sf = "sfHSD", sfpar = -4)

Description

Obtains the stagewise exit probabilities for both efficacy and futility stopping.

Usage

exitprob(b, a = NA_real_, theta = 0L, I = NA_real_)

Arguments

Value

A list of stagewise exit probabilities:

• exitProbUpper: The vector of efficacy stopping probabilities

• exitProbLower: The vector of futility stopping probabilities.

Author(s)

Kaifeng Lu, [email protected]

Examples

exitprob(b = c(3.471, 2.454, 2.004), theta = -log(0.6),
         I = c(50, 100, 150)/4)

exitprob(b = c(2.963, 2.359, 2.014),
         a = c(-0.264, 0.599, 2.014),
         theta = c(0.141, 0.204, 0.289),
         I = c(81, 121, 160))

Description

Computes the exit (rejection) probabilities for a multi-arm multi-stage design.

Usage

exitprob_mams(
  M = NA_integer_,
  r = 1,
  theta = NA_real_,
  corr_known = TRUE,
  kMax = NA_integer_,
  b = NULL,
  a = NULL,
  I = NULL
)

Arguments

Details

The function assumes a multivariate normal distribution for the Wald statistics and all active arms share the same information level.

Value

A vector exitProb of length kMax containing the probability of rejection at each look.

Author(s)

Kaifeng Lu, [email protected]

References

Ping Gao, Yingqiu Li. Adaptive multiple comparison sequential design (AMCSD) for clinical trials. Journal of Biopharmaceutical Statistics, 2024, 34(3), 424-440.

Examples

# Setup: 2 active arms vs control and 3 sequential looks.

# Information levels: equal spacing over 3 looks based on a maximum of
# 95 patients per arm, SD = 1.0
I <- 95 / (2 * 1.0^2) * seq(1, 3)/3

# O'Brien-Fleming critical values
b <- c(3.886562, 2.748214, 2.243907)

# Type I error under the global null hypothesis
p0 <- exitprob_mams(M = 2, theta = c(0, 0), kMax = 3, b = b, I = I)
cumsum(p0$exitProbUpper)

# Power under alternative: Treatment effects of 0.3 and 0.5
p1 <- exitprob_mams(M = 2, theta = c(0.3, 0.5), kMax = 3, b = b, I = I)
cumsum(p1$exitProbUpper)

Description

Computes the upper and lower exit probabilities for a phase 2/3 seamless design. In Phase 2, multiple active arms are compared against a common control arm. If the phase-2 max-Z statistic crosses the efficacy boundary, the trial stops early for efficacy; if it falls below the futility boundary, the trial stops early for futility. Otherwise, the best-performing arm is selected to proceed to Phase 3, where it is tested against the common control over multiple looks with upper and optional lower stopping boundaries.

Usage

exitprob_seamless(
  M = NA_integer_,
  r = 1,
  theta = NA_real_,
  corr_known = TRUE,
  K = NA_integer_,
  b = NULL,
  a = NULL,
  I = NULL
)

Arguments

Details

The function assumes a multivariate normal distribution for the Wald statistics. The "best" arm is defined as the active arm with the largest Z-statistic at the end of Phase 2 among designs that continue beyond the phase-2 analysis.

Decision Rules:

• Phase 2 efficacy stop: reject if the phase-2 max-Z statistic satisfies $\max_m Z_m(I_0) \ge b_0$.

• Phase 2 futility stop: stop for futility if the phase-2 max-Z statistic satisfies $\max_m Z_m(I_0) \le a_0$.

• Continue to Phase 3: if $a_0 < \max_m Z_m(I_0) < b_0$, select the arm with the largest phase-2 Z-statistic and continue with that arm only.

• Phase 3 efficacy stop: at look $k$, reject if the selected arm's Z-statistic exceeds the efficacy boundary and no earlier stop has occurred.

• Phase 3 futility stop: at look $k$, stop for futility if the selected arm's Z-statistic is below the futility boundary and no earlier stop has occurred.

Design Assumptions:

• All active arms share the same information level in Phase 2.

• Exactly one active arm is selected at the end of Phase 2 based on the largest observed Z-statistic when the trial continues to Phase 3.

Value

A list containing the following components:

• exitProbUpper: A vector of length $K + 1$. The first element is the probability of stopping for efficacy in Phase 2; the remaining elements are the probabilities of stopping for efficacy at each look in Phase 3.

• exitProbLower: A vector of length $K + 1$. The first element is the probability of stopping for futility in Phase 2; the remaining elements are the probabilities of stopping for futility at each look in Phase 3.

• exitProbByArmUpper: A $(K+1) \times M$ matrix. The $(k, m)$-th entry gives the probability of stopping for efficacy at look $k$ given that arm $m$ is selected as best.

• exitProbByArmLower: A $(K+1) \times M$ matrix. The $(k, m)$-th entry gives the probability of stopping for futility at look $k$ given that arm $m$ is selected as best.

• selectAsBest: A vector of length $M$ containing the probability that each active arm is selected to move on to Phase 3.

Author(s)

Kaifeng Lu, [email protected]

References

Ping Gao, Yingqiu Li. Adaptive two-stage seamless sequential design for clinical trials. Journal of Biopharmaceutical Statistics, 2025, 35(4), 565-587.

Examples

# Setup: 2 active arms vs control in Phase 2; 1 selected arm vs control
# in Phase 3. Phase 3 has 2 sequential looks.

# Information levels: equal spacing over 3 looks based on a maximum of
# 110 patients per arm, SD = 1.0
I <- c(110 / (2 * 1.0^2) * seq(1, 3)/3)

# O'Brien-Fleming efficacy boundaries
b <- c(3.776605, 2.670463, 2.180424)

# No futility stopping
p0 <- exitprob_seamless(M = 2, theta = c(0, 0), K = 2, b = b, I = I)
cumsum(p0$exitProbUpper)

# Add futility stopping
a <- c(0, 0.5, b[3])
p1 <- exitprob_seamless(M = 2, theta = c(0.3, 0.5), K = 2, b = b, a = a, I = I)
cbind(
  cumulativeEfficacy = cumsum(p1$exitProbUpper),
  cumulativeFutility = cumsum(p1$exitProbLower)
)

Description

Obtains the adjusted p-values for graphical approaches using weighted Bonferroni tests.

Usage

fadjpbon(w, G, p)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Frank Bretz, Willi Maurer, Werner Brannath and Martin Posch. A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine. 2009; 28:586-604.

Examples

pvalues <- matrix(c(0.01,0.005,0.015,0.022, 0.02,0.015,0.010,0.023),
                  nrow=2, ncol=4, byrow=TRUE)
w <- c(0.5,0.5,0,0)
g <- matrix(c(0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0),
            nrow=4, ncol=4, byrow=TRUE)
fadjpbon(w, g, pvalues)

Description

Obtains the adjusted p-values for graphical approaches using weighted Dunnett tests.

Usage

fadjpdun(wgtmat, p, family = NULL, corr = NULL)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Frank Bretz, Martin Posch, Ekkehard Glimm, Florian Klinglmueller, Willi Maurer, and Kornelius Rohmeyer. Graphical approach for multiple comparison procedures using weighted Bonferroni, Simes, or parameter tests. Biometrical Journal. 2011; 53:894-913.

Examples

pvalues <- matrix(c(0.01,0.005,0.015,0.022, 0.02,0.015,0.010,0.023),
                  nrow=2, ncol=4, byrow=TRUE)
w <- c(0.5,0.5,0,0)
g <- matrix(c(0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0),
            nrow=4, ncol=4, byrow=TRUE)
wgtmat <- fwgtmat(w,g)

family <- matrix(c(1,1,0,0,0,0,1,1), nrow=2, ncol=4, byrow=TRUE)
corr <- matrix(c(1,0.5,NA,NA, 0.5,1,NA,NA,
                NA,NA,1,0.5, NA,NA,0.5,1),
              nrow = 4, byrow = TRUE)
fadjpdun(wgtmat, pvalues, family, corr)

Description

Obtains the adjusted p-values for graphical approaches using weighted Simes tests.

Usage

fadjpsim(wgtmat, p, family = NULL)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Frank Bretz, Martin Posch, Ekkehard Glimm, Florian Klinglmueller, Willi Maurer, and Kornelius Rohmeyer. Graphical approach for multiple comparison procedures using weighted Bonferroni, Simes, or parameter tests. Biometrical Journal. 2011; 53:894-913.

Kaifeng Lu. Graphical approaches using a Bonferroni mixture of weighted Simes tests. Statistics in Medicine. 2016; 35:4041-4055.

Examples

pvalues <- matrix(c(0.01,0.005,0.015,0.022, 0.02,0.015,0.010,0.023),
                  nrow=2, ncol=4, byrow=TRUE)
w <- c(0.5,0.5,0,0)
g <- matrix(c(0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0),
            nrow=4, ncol=4, byrow=TRUE)
wgtmat <- fwgtmat(w,g)

family <- matrix(c(1,1,0,0,0,0,1,1), nrow=2, ncol=4, byrow=TRUE)
fadjpsim(wgtmat, pvalues, family)

Description

Converts a decimal to a fraction based on the algorithm from http://stackoverflow.com/a/5128558/221955.

Usage

float_to_fraction(x, tol = 1e-06)

Arguments

Author(s)

Kaifeng Lu, [email protected]

Examples

float_to_fraction(5/3)

Description

Obtains the adjusted p-values for the modified gatekeeping procedures for multiplicity problems involving serial and parallel logical restrictions.

Usage

fmodmix(
  p,
  family = NULL,
  serial,
  parallel = NULL,
  gamma,
  test = "hommel",
  exhaust = TRUE
)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Alex Dmitrienko, George Kordzakhia, and Thomas Brechenmacher. Mixture-based gatekeeping procedures for multiplicity problems with multiple sequences of hypotheses. Journal of Biopharmaceutical Statistics. 2016; 26(4):758–780.

George Kordzakhia, Thomas Brechenmacher, Eiji Ishida, Alex Dmitrienko, Winston Wenxiang Zheng, and David Fuyuan Li. An enhanced mixture method for constructing gatekeeping procedures in clinical trials. Journal of Biopharmaceutical Statistics. 2018; 28(1):113–128.

Examples

p <- c(0.0194, 0.0068, 0.0271, 0.0088, 0.0370, 0.0018, 0.0814, 0.0066)
family <- matrix(c(1, 1, 0, 0, 0, 0, 0, 0,
                   0, 0, 1, 1, 0, 0, 0, 0,
                   0, 0, 0, 0, 1, 1, 0, 0,
                   0, 0, 0, 0, 0, 0, 1, 1),
                 nrow=4, byrow=TRUE)

serial <- matrix(c(0, 0, 0, 0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0, 0, 0, 0,
                   1, 0, 0, 0, 0, 0, 0, 0,
                   0, 1, 0, 0, 0, 0, 0, 0,
                   0, 0, 1, 0, 0, 0, 0, 0,
                   0, 0, 0, 1, 0, 0, 0, 0,
                   0, 0, 0, 0, 1, 0, 0, 0,
                   0, 0, 0, 0, 0, 1, 0, 0),
                 nrow=8, byrow=TRUE)

parallel <- matrix(0, 8, 8)
gamma <- c(0.6, 0.6, 0.6, 1)
fmodmix(p, family, serial, parallel, gamma, test = "hommel", exhaust = TRUE)

Description

Obtains the quantiles of a survival distribution.

Usage

fquantile(S, probs, ...)

Arguments

Value

A vector of length(probs) for the quantiles.

Author(s)

Kaifeng Lu, [email protected]

Examples

fquantile(pweibull, probs = c(0.25, 0.5, 0.75),
          shape = 1.37, scale = 1/0.818, lower.tail = FALSE)

Description

Obtains the test results for group sequential trials using graphical approaches based on weighted Bonferroni tests.

Usage

fseqbon(
  w,
  G,
  alpha = 0.025,
  kMax,
  typeAlphaSpending = NULL,
  parameterAlphaSpending = NULL,
  maxInformation = NULL,
  incidenceMatrix = NULL,
  k1,
  p,
  information,
  spendingTime = NULL,
  lookback = TRUE,
  nthreads = 0
)

Arguments

Details

When lookback = TRUE, the procedure allows the user to retest an unrejected hypothesis at earlier looks if its weight increased after rejection of other hypotheses. The procedure will return the first look at which the specific hypothesis is rejected. If the hypothesis is not rejected at any look, it will return 0.

Value

A vector to indicate the first look the specific hypothesis is rejected (0 if the hypothesis is not rejected).

Author(s)

Kaifeng Lu, [email protected]

References

Willi Maurer and Frank Bretz. Multiple testing in group sequential trials using graphical approaches. Statistics in Biopharmaceutical Research. 2013; 5:311-320.

Examples

# Case study from Maurer & Bretz (2013)

fseqbon(
  w = c(0.5, 0.5, 0, 0),
  G = matrix(c(0, 0.5, 0.5, 0,  0.5, 0, 0, 0.5,
               0, 1, 0, 0,  1, 0, 0, 0),
             nrow=4, ncol=4, byrow=TRUE),
  alpha = 0.025,
  kMax = 3,
  typeAlphaSpending = rep("sfOF", 4),
  maxInformation = rep(1, 4),
  k1 = 2,
  p = matrix(c(0.0062, 0.017, 0.009, 0.13,
               0.0002, 0.0035, 0.002, 0.06),
             nrow=2, ncol=4, byrow=TRUE),
  information = matrix(c(rep(1/3, 4), rep(2/3, 4)),
                       nrow=2, ncol=4, byrow=TRUE),
  nthreads = 1)

Description

Obtains the adjusted p-values for the standard gatekeeping procedures for multiplicity problems involving serial and parallel logical restrictions.

Usage

fstdmix(
  p,
  family = NULL,
  serial,
  parallel = NULL,
  gamma,
  test = "hommel",
  exhaust = TRUE
)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Alex Dmitrienko and Ajit C Tamhane. Mixtures of multiple testing procedures for gatekeeping applications in clinical trials. Statistics in Medicine. 2011; 30(13):1473–1488.

Examples

p <- c(0.0194, 0.0068, 0.0271, 0.0088, 0.0370, 0.0018, 0.0814, 0.0066)
family <- matrix(c(1, 1, 0, 0, 0, 0, 0, 0,
                   0, 0, 1, 1, 0, 0, 0, 0,
                   0, 0, 0, 0, 1, 1, 0, 0,
                   0, 0, 0, 0, 0, 0, 1, 1),
                 nrow=4, byrow=TRUE)

serial <- matrix(c(0, 0, 0, 0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0, 0, 0, 0,
                   1, 0, 0, 0, 0, 0, 0, 0,
                   0, 1, 0, 0, 0, 0, 0, 0,
                   0, 0, 1, 0, 0, 0, 0, 0,
                   0, 0, 0, 1, 0, 0, 0, 0,
                   0, 0, 0, 0, 1, 0, 0, 0,
                   0, 0, 0, 0, 0, 1, 0, 0),
                 nrow=8, byrow=TRUE)

parallel <- matrix(0, 8, 8)
gamma <- c(0.6, 0.6, 0.6, 1)
fstdmix(p, family, serial, parallel, gamma, test = "hommel",
        exhaust = FALSE)

Description

Obtains the adjusted p-values for the stepwise gatekeeping procedures for multiplicity problems involving two sequences of hypotheses.

Usage

fstp2seq(p, gamma, test = "hochberg", retest = TRUE)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

Examples

p <- c(0.0194, 0.0068, 0.0271, 0.0088, 0.0370, 0.0018, 0.0814, 0.0066)
gamma <- c(0.6, 0.6, 0.6, 1)
fstp2seq(p, gamma, test="hochberg", retest=1)

Description

Obtains the adjusted p-values for possibly truncated Holm, Hochberg, and Hommel procedures.

Usage

ftrunc(p, test = "hommel", gamma = 1)

Arguments

Value

A matrix of adjusted p-values.

Author(s)

Kaifeng Lu, [email protected]

References

Alex Dmitrienko, Ajit C. Tamhane, and Brian L. Wiens. General multistage gatekeeping procedures. Biometrical Journal. 2008; 5:667-677.

Examples

pvalues <- matrix(c(0.01,0.005,0.015,0.022, 0.02,0.015,0.010,0.023),
                  nrow=2, ncol=4, byrow=TRUE)
ftrunc(pvalues, "hochberg")

Description

Obtains the weight matrix for all intersection hypotheses.

Usage

fwgtmat(w, G)

Arguments

Value

The weight matrix starting with the global null hypothesis.

Author(s)

Kaifeng Lu, [email protected]

Examples

w <- c(0.5,0.5,0,0)
g <- matrix(c(0,0,1,0, 0,0,0,1, 0,1,0,0, 1,0,0,0),
            nrow=4, ncol=4, byrow=TRUE)
(wgtmat <- fwgtmat(w,g))

Description

Obtains the accrual duration to enroll the target number of subjects.

Usage

getAccrualDurationFromN(nsubjects, accrualTime, accrualIntensity)

Arguments

Value

A vector of accrual durations.

Author(s)

Kaifeng Lu, [email protected]

Examples

getAccrualDurationFromN(nsubjects = c(20, 150), accrualTime = c(0, 3),
                        accrualIntensity = c(10, 20))

Description

Obtains the p-value, median unbiased point estimate, and confidence interval after the end of an adaptive trial.

Usage

getADCI(
  L = NA_integer_,
  zL = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.25,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  Lc = NA_integer_,
  zLc = NA_real_,
  INew = NA_real_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Arguments

Details

If typeAlphaSpendingNew is "OF", "P", "WT", or "none", then informationRatesNew, efficacyStoppingNew, and spendingTimeNew must be of full length kNew, and informationRatesNew and spendingTimeNew must end with 1.

Value

A data frame with the following variables:

• pvalue: p-value for rejecting the null hypothesis.

• thetahat: Median unbiased point estimate of the parameter.

• cilevel: Confidence interval level.

• lower: Lower bound of confidence interval.

• upper: Upper bound of confidence interval.