rpact: Confirmatory Adaptive Clinical Trial Design and Analysis

1 The design

  • 1:1 randomized
  • Two-sided log-rank test; 80% power at the 5% significance level (or one-sided at 2.5%)
  • Target HR for primary endpoint (PFS) is 0.75
  • PFS in the control arm follows a piece-wise exponential distribution, with the hazard rate h(t) estimated using historical controls as follows:
    • h(t) = 0.025 for t between 0 and 6 months;
    • h(t) = 0.04 for t between 6 and 9 months;
    • h(t) = 0.015 for t between 9 and 15 months;
    • h(t) = 0.01 for t between 15 and 21 months;
    • h(t) = 0.007 for t beyond 21 months.
  • An annual dropout probability of 20%
  • Interim analyses at 33% and 70% of total information
  • Alpha-spending version of O’Brien-Fleming boundary for efficacy
  • No futility interim
  • 1405 subjects recruited in total
  • Staggered recruitment:
    • 15 pt/month during first 12 months;
    • subsequently, increase of # of sites and ramp up of recruitment by +6 pt/month each month until a maximum of 45 pt/month

2 Calculation with gsDesign

## Lade nötiges Paket: xtable
## Time to event group sequential design with HR= 0.75 
## Equal randomization:          ratio=1
## One-sided group sequential design with
## 80 % power and 2.5 % Type I Error.
##               
##   Analysis  N   Z   Nominal p  Spend
##          1 128 3.73    0.0001 0.0001
##          2 271 2.44    0.0074 0.0073
##          3 386 2.00    0.0227 0.0176
##      Total                    0.0250 
## 
## ++ alpha spending:
##  Lan-DeMets O'brien-Fleming approximation spending function.
## 
## Boundary crossing probabilities and expected sample size
## assume any cross stops the trial
## 
## Upper boundary (power or Type I Error)
##           Analysis
##    Theta      1      2      3 Total  E{N}
##   0.0000 0.0001 0.0073 0.0176 0.025 385.0
##   0.1437 0.0175 0.4517 0.3309 0.800 329.1
##              T         n   Events HR efficacy
## IA 1  26.78703  785.4162 127.3407       0.516
## IA 2  38.62360 1318.0620 270.1171       0.743
## Final 50.80093 1405.0000 385.8810       0.816
## Accrual rates:
##          Stratum 1
## 0-12            15
## 12-13           21
## 13-14           27
## 14-15           33
## 15-16           39
## 16-40.56        45
## Control event rates (H1):
##        Stratum 1
## 0-6        0.025
## 6-9        0.040
## 9-15       0.015
## 15-21      0.010
## 21-Inf     0.007
## Censoring rates:
##        Stratum 1
## 0-6       0.0186
## 6-9       0.0186
## 9-15      0.0186
## 15-21     0.0186
## 21-Inf    0.0186

3 Calculation with rpact

3.1 Design

## [1] '2.0.1.9003'
## Design parameters and output of group sequential design:
## 
## User defined parameters:
##   Type of design                               : asOF 
##   Information rates                            : 0.330, 0.700, 1.000 
## 
## Derived from user defined parameters:
##   Maximum number of stages                     : 3 
## 
## Default parameters:
##   Stages                                       : 1, 2, 3 
##   Significance level                           : 0.0250 
##   Type II error rate                           : 0.2 
##   Two-sided power                              : FALSE 
##   Test                                         : one-sided 
##   Tolerance                                    : 1e-08 
##   Type of beta spending                        : none 
## 
## Output:
##   Cumulative alpha spending                    : 9.549e-05, 7.384e-03, 2.500e-02 
##   Critical values                              : 3.731, 2.440, 2.000 
##   Stage levels                                 : 9.549e-05, 7.351e-03, 2.274e-02

3.2 Sample size/timing of interim

## Design plan parameters and output for survival data:
## 
## Design parameters:
##   Significance level                           : 0.0250 
##   Test                                         : one-sided 
## 
## User defined parameters:
##   Direction upper                              : FALSE 
##   Lambda (2)                                   : 0.025, 0.040, 0.015, 0.010, 0.007 
##   Hazard ratio                                 : 0.750 
##   Maximum number of subjects                   : 1405.0 
##   Maximum number of events                     : 385.9 
##   Accrual intensity                            : 15.0, 21.0, 27.0, 33.0, 39.0, 45.0 
##   Piecewise survival times                     : 0.00, 6.00, 9.00, 15.00, 21.00 
##   Drop-out rate (1)                            : 0.200 
##   Drop-out rate (2)                            : 0.200 
## 
## Default parameters:
##   Type of computation                          : Schoenfeld 
##   Theta H0                                     : 1 
##   Planned allocation ratio                     : 1 
##   Event time                                   : 12 
##   Drop-out time                                : 12.00 
## 
## Sample size and output:
##   Lambda (1)                                   : 0.01875, 0.03000, 0.01125, 0.00750, 0.00525 
##   Accrual time                                 : 12.00, 13.00, 14.00, 15.00, 16.00, 40.56 
##   Total accrual time                           : 40.56 
##   Follow up time                               : 10.25 
##   Analysis times [1]                           : 26.79 
##   Analysis times [2]                           : 38.62 
##   Analysis times [3]                           : 50.80 
##   Expected study duration                      : 44.87 
##   Maximal study duration                       : 50.80 
##   Number of events by stage [1]                : 127.3 
##   Number of events by stage [2]                : 270.1 
##   Number of events by stage [3]                : 385.9 
##   Expected number of events                    : 328.9 
##   Number of subjects [1]                       : 785.4 
##   Number of subjects [2]                       : 1318.1 
##   Number of subjects [3]                       : 1405.0 
##   Expected number of subjects                  : 1354.8 
##   Reject per stage [1]                         : 0.0175 
##   Reject per stage [2]                         : 0.4526 
##   Reject per stage [3]                         : 0.3307 
##   Overall reject                               : 0.801 
##   Early stop                                   : 0.47 
##   Critical values (effect scale) [1]           : 0.516 
##   Critical values (effect scale) [2]           : 0.743 
##   Critical values (effect scale) [3]           : 0.816 
##   Local one-sided significance levels [1]      : 9.549e-05 
##   Local one-sided significance levels [2]      : 7.351e-03 
##   Local one-sided significance levels [3]      : 2.274e-02 
## 
## Legend:
##   (i): values of treatment arm i
##   [k]: values at stage k

4 Comparison: analysis time of rpact vs. gsDesign

Absolute differences:

##         Difference analysis time
## Stage 1                    0e+00
## Stage 2                    0e+00
## Stage 3                   -1e-04

5 Remark

Obviously, there is a difference in the calculation of the necessary number of events which are, in rpact, calculated as

## [1] 385.0479

which is slightly different to the maximum number of events in gsDesign which is

## [1] 385.881

Therefore, running

##          [,1]
## [1,] 26.76183
## [2,] 38.57834
## [3,] 50.63114

is not exactly equal to getPowerSurvival from above. This, however, has absolutely no consequences in practice but explains the differences in rpact and gsDesign.


System: rpact 2.0.1.9003, R version 3.5.3 (2019-03-11), platform: x86_64-w64-mingw32

To cite package ‘rpact’ in publications use:

Gernot Wassmer and Friedrich Pahlke (2019). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. R package version 2.0.1.9003. https://www.rpact.org

 

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