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Risk Difference Simulation for Phase 2/3 Seamless Design

Source: R/rdsim_seamless.R
rdsim_seamless.Rd

Simulate phase 2/3 seamless design testing for risk difference.

Usage

rdsim_seamless(
  M = 2,
  K = 1,
  rankp0 = 1,
  criticalValues = NA,
  futilityBounds = NULL,
  riskDiffH0s = 0,
  allocations = 1,
  pis = NULL,
  nullVariance = TRUE,
  n = NA,
  plannedSubjects = NA,
  maxNumberOfIterations = 1000,
  seed = 0,
  nthreads = 0
)

Arguments

M

Number of active treatment arms in Phase 2.

K

Number of sequential looks in Phase 3.

rankp0

Integer rank in phase 2 used to select the active arm. rankp0 = 1 selects the most efficacious arm by risk-difference statistic, rankp0 = 2 selects the second most efficacious arm, and so on.

criticalValues

Numeric vector of length \(K + 1\) giving the critical value for the Wald statistic at each look (Look 1 through Look \(K + 1\)). Decision rule:

  • At Look 1, compute the Wald statistic for each active arm versus the common control. If the rankp0-th largest test statistic exceeds the Look 1 critical value, stop for efficacy.

  • If the Look 1 stopping rule is not met, select the active arm with the rankp0-th largest Wald statistic and continue with that arm only versus control at subsequent looks.

  • For each look \(j = 2,\ldots,K+1\), compare the selected arm to control; if its Wald statistic exceeds the Look \(j\) critical value, stop for efficacy; otherwise continue.

  • If no critical value is exceeded by Look \(K + 1\), the procedure ends without rejection.

futilityBounds

Numeric vector of length \(K\) giving the futility boundaries for Phase 2 and the first \(K-1\) looks in Phase 3. The study stops for futility:

  • in Phase 2 if the selected treatment arm crosses the phase-2 futility boundary;

  • in Phase 3 if the selected arm crosses the futility boundary at an interim look; If omitted, no interim futility stopping is applied.

riskDiffH0s

Numeric vector of length \(M\). Risk differences under \(H_0\) for each active arm versus the common control. Defaults to 0 for superiority tests.

allocations

Integer or integer vector of length \(M + 1\). Number of subjects per arm within a randomization block. A single value implies equal allocation; defaults to 1. The first \(M\) elements refer to the active arms and the last element refers to the common control.

pis

Numeric vector of length \(M + 1\). Each element corresponds to the response rate for a treatment arm. The first \(M\) elements refer to the active arms and the last element refers to the common control.

nullVariance

Whether to use the variance under the null or the empirical variance under the alternative.

n

Planned total sample size across all active arms and control.

plannedSubjects

Numeric vector of length \(K + 1\) giving the planned cumulative sample size at each look. Each entry refers to the combined number of patients for the first active arm and the common control.

maxNumberOfIterations

Number of Monte Carlo replications. Defaults to 1000.

seed

Random seed for reproducibility.

nthreads

Number of threads for parallel simulation. Use 0 to accept the default RcppParallel behavior.

Value

An S3 object of class "rdsim_seamless" with these components:

  • overview: A list summarizing trial-level results and settings:

    • selectionProb: Probability of selecting each active arm at the prespecified rank at the end of phase 2.

    • selectToStage2: Probability of selecting each active arm to enter stage 2.

    • selectAnyToStage2: Probability of selecting any active arm to enter stage 2.

    • rejectPerStage: Probability of rejecting the null for each active arm at each stage.

    • futilityPerStage: Probability of futility stopping for each active arm at each stage.

    • cumulativeRejection: Cumulative probability of rejection by stage.

    • cumulativeFutility: Cumulative futility stopping probabilities by stage.

    • numberOfEvents: Cumulative event counts by stage, including events from all arms in stage 1 and events from the selected arm and control in later stages.

    • numberOfSubjects: Cumulative enrollments by stage. replications that reached that stage.

    • overallReject: Overall probability of rejecting the null by trial end.

    • overallFutility: Overall probability of stopping for futility by trial end.

    • expectedNumberOfEvents: Expected cumulative events at trial end.

    • expectedNumberOfSubjects: Expected cumulative enrollments at trial end.

    • criticalValues: The input critical values for each stage.

    • futilityBounds: The input futility boundaries for each stage.

    • riskDiffH0s: The input risk differences under \(H_0\).

    • nullVariance: Whether to use variance under \(H_0\).

    • numberOfIterations: Number of simulation iterations performed.

    • n: Planned total sample size.

    • allocations: The input allocation ratios.

    • responseRates: The input response rates for each arm.

    • plannedSubjects: The input planned cumulative sample size at each look for the first active arm and the common control combined.

    • M: Number of active arms in Phase 2.

    • K: Number of sequential looks in Phase 3.

    • rankp0: Prespecified rank used for phase-2 arm selection.

  • sumdata1: Data frame summarizing each iteration, stage, and treatment group:

    • iterationNumber, stopStage, stageNumber, treatmentGroup, accruals, events, phat.

    • For each stage the final row summarizes the overall study (all arms combined).

  • summdata2: Data frame summarizing test statistics by iteration, stage, and active arm:

    • iterationNumber, selectedArm, stopStage, stageNumber, activeArm, totalAccruals, totalEvents, riskDiff, vriskDiff, riskDiffZ, reject, futility.

    • For each active arm, total accruals and events refer to the combined counts for that arm and the common control at that stage.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

(sim1 <- rdsim_seamless(
  M = 3,
  K = 1,
  criticalValues = c(8, 2.349),
  futilityBounds = 1.036,
  pis = c(0.22, 0.25, 0.35, 0.20),
  n = 1120,
  plannedSubjects = c(280, 560),
  maxNumberOfIterations = 10000,
  seed = 314159,
  nthreads = 0))
#>                                                                
#> Phase 2/3 seamless group-sequential design for risk difference 
#> Empirical power: 0.9192                                        
#> Number of active arms in phase 2: 3                            
#> Number of looks in phase 3: 1                                  
#> Selected rank in phase 2: 1                                    
#> Expected # events: 216.9                                       
#> Expected # subjects: 832.3                                     
#> n: 1120                                                        
#> Variance under H0: TRUE                                        
#> Number of simulations: 10000                                   
#>                                                                
#>                           Stage 1 Stage 2
#> Efficacy bounds (z-scale) 8.000   2.349  
#> Futility bounds (z-scale) 1.036   2.349  
#> 
#>                                           Arm 1  Arm 2  Arm 3
#> Selected at prespecified rank in phase 2 0.0081 0.0412 0.9507
#> 
#>                            Arm 1  Arm 2  Arm 3
#> Selected to enter stage 2 0.0074 0.0368 0.9284
#> 
#>                                          Probability
#> Any active arm selected to enter stage 2      0.9726
#> 
#>         Reject Active 1 Reject Active 2 Reject Active 3 Overall Rejection
#> Stage 1          0.0000          0.0000          0.0000            0.0000
#> Stage 2          0.0022          0.0177          0.8993            0.9192
#> Total            0.0022          0.0177          0.8993            0.9192
#>         Futility Continue
#> Stage 1   0.0274   0.9726
#> Stage 2   0.0534   0.0000
#> Total     0.0808       NA
#> 
#>  activeArm stage cumReject cumFutility nEvents nSubjects
#>          1     1    0.0000      0.0274   142.8     560.0
#>          1     2    0.0022      0.0326   200.9     840.0
#>          2     1    0.0000      0.0274   142.9     560.0
#>          2     2    0.0177      0.0465   205.9     840.0
#>          3     1    0.0000      0.0274   142.7     560.0
#>          3     2    0.8993      0.0565   219.7     840.0
#>    Overall     1    0.0000      0.0274   142.7     560.0
#>    Overall     2    0.9192      0.0808   219.0     840.0