getDesign_seamless: Power and Sample Size for Phase 2/3 Seamless Design

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Power and Sample Size for Phase 2/3 Seamless Design

Description

Computes either the maximum information and stopping boundaries for a phase 2/3 seamless design, or the achieved power when the maximum information and stopping boundaries are provided. Both efficacy and futility stopping can be incorporated.

Usage

getDesign_seamless(
  beta = NA_real_,
  IMax = NA_real_,
  theta = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  K = 1L,
  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,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = NA_real_,
  spendingTime = NA_real_
)

Arguments

beta	Type II error rate. Provide either beta or IMax; the other should be missing.
IMax	Maximum information for any active arm versus the common control. Provide either IMax or beta; the other should be missing.
theta	A vector of length M representing the true treatment effects for each active arm versus the common control. The global null is \theta_i = 0 for all i, and alternatives are one-sided: \theta_i > 0 for at least one i = 1, \ldots, M.
M	Number of active treatment arms in Phase 2.
r	Randomization ratio of each active arm to the common control in Phase 2.
corr_known	Logical. If TRUE, the correlation between Wald statistics in Phase 2 is derived from the randomization ratio r as r / (r + 1). If FALSE, a conservative correlation of 0 is used.
K	Number of sequential looks in Phase 3.
informationRates	A numeric vector of information rates fixed before the trial. If unspecified, defaults to (1:(K+1)) / (K+1).
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage. Defaults to TRUE if left unspecified.
futilityStopping	Indicators of whether futility stopping is allowed at each stage. Defaults to TRUE if left unspecified.
criticalValues	The upper boundaries on the max-Z statistic scale for Phase 2 and the Z statistics for the selected arm in Phase 3. If missing, boundaries will be computed based on the specified alpha spending function.
alpha	The significance level. Defaults to 0.025.
typeAlphaSpending	The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpending	The parameter value for the alpha spending. Corresponds to \Delta for "WT", \rho for "sfKD", and \gamma for "sfHSD".
userAlphaSpending	The user defined alpha spending. Cumulative alpha spent up to each stage.
futilityBounds	A numeric vector of length K specifying futility boundaries on the max-Z scale at the end of Phase 2 and on the Z scale for the K - 1 analyses in Phase 3. The final analysis uses the efficacy boundary as the futility boundary.
futilityCP	A numeric vector of length K specifying futility boundaries on the conditional power scale.
futilityTheta	A numeric vector of length K specifying futility boundaries on the parameter scale.
typeBetaSpending	The type of beta spending. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early futility stopping. Defaults to "none".
parameterBetaSpending	The parameter value for the beta spending. Corresponds to \rho for "sfKD", and \gamma for "sfHSD".
userBetaSpending	The user defined beta spending. Cumulative beta spent up to each stage.
spendingTime	A numeric vector of length K+1 specifying the error spending time at each analysis. Values must be strictly increasing and end at 1. If omitted, defaults to informationRates.

Details

If corr_known is FALSE, critical boundaries are computed assuming independence among the Phase-2 Wald statistics (a conservative assumption). Power calculations, however, use the correlation implied by the randomization ratio r.

Futility boundaries may be supplied directly on the Z scale, derived from conditional power, derived from parameter values, or computed from a beta spending function.

Value

An S3 object of class seamless with the following components:

• overallResults: A data frame containing:

  • overallReject: Overall probability of rejecting the null hypothesis.

  • alpha: Overall significance level.

  • attainedAlpha: The attained significance level, which may differ from alpha in the presence of futility stopping.

  • M: Number of active arms in Phase 2.

  • r: Randomization ratio per active arm versus control in Phase 2.

  • corr_known: Whether the phase-2 correlation was assumed known.

  • K: Number of looks in Phase 3.

  • information: Maximum information for any active arm versus control.

  • expectedInformationH1: Expected information under the alternative.

  • expectedInformationH0: Expected information under the null.

  • informationOverall: Maximum information for the overall study.

  • expectedInformationH1: Expected information under the alternative for the overall study.

  • expectedInformationH0: Expected information under the null for the overall study.

• byStageResults: A data frame containing:

  • informationRates: Information rates at each analysis.

  • efficacyBounds: Efficacy boundaries on the Z scale.

  • futilityBounds: Futility boundaries on the Z scale.

  • rejectPerStage: Probability of efficacy stopping at each stage.

  • futilityPerStage: Probability of futility stopping at each stage.

  • cumulativeRejection: Cumulative probability of efficacy stopping.

  • cumulativeFutility: Cumulative probability of futility stopping.

  • cumulativeAlphaSpent: Cumulative alpha spent.

  • efficacyTheta: Efficacy boundaries on the parameter scale.

  • futilityTheta: Futility boundaries on the parameter scale.

  • efficacyP: Efficacy boundaries on the p-value scale.

  • futilityP: Futility boundaries on the p-value scale.

  • information: Cumulative information at each analysis.

  • informationOverall: Cumulative information for the overall study at each analysis.

  • efficacyStopping: Indicator of whether efficacy stopping is permitted.

  • futilityStopping: Indicator of whether futility stopping is permitted.

  • rejectPerStageH0: Probability of efficacy stopping under the global null.

  • futilityPerStageH0: Probability of futility stopping under the global null.

  • cumulativeRejectionH0: Cumulative probability of efficacy stopping under the global null.

  • cumulativeFutilityH0: Cumulative probability of futility stopping under the global null.

• byArmResults: A data frame containing:

  • theta: Parameter values for the active arms.

  • selectAsBest: Probability an arm is selected as best at the end of Phase 2.

  • powerByArm: Probability of rejecting the null for each arm by trial end.

  • condPowerByArm: Conditional power for each arm given it was selected as the best at the end of Phase 2.

• settings: A list of input settings:

  • typeAlphaSpending: Type of alpha spending function.

  • parameterAlphaSpending: Parameter value for the chosen alpha spending function.

  • userAlphaSpending: User-specified alpha spending values.

  • typeBetaSpending: Type of beta spending function.

  • parameterBetaSpending: Parameter value for the chosen beta spending function.

  • userBetaSpending: User-specified beta spending values.

  • spendingTime: Error-spending times at each analysis.

Author(s)

Kaifeng Lu, [e-mail]

References

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

Examples

# Example 1: obtain the maximum information given power with no futility
(design1 <- getDesign_seamless(
  beta = 0.1, theta = c(0.3, 0.5), M = 2, r = 1.0,
  K = 2, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "OF"))

# Example 2: obtain power given the maximum information and a futility rule
(design2 <- getDesign_seamless(
  IMax = 110/(2*1^2), theta = c(0.3, 0.5), M = 2, r = 1.0,
  K = 2, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "OF",
  futilityBounds = c(0.0, 0.5)))

# Example 3: derive futility boundaries using beta spending
(design3 <- getDesign_seamless(
  beta = 0.1, theta = c(-log(0.5), -log(0.7)),
  M = 2, r = 1.0, corr_known = FALSE,
  K = 2, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "sfOF",
  typeBetaSpending = "sfHSD", parameterBetaSpending = -2))

lrstat documentation built on May 13, 2026, 9:06 a.m.