TIE depends on CVwR (and n) [RSABE / ABEL]

posted by Helmut Homepage – Vienna, Austria, 2017-04-26 14:17 (1684 d 12:08 ago) – Posting: # 17267
Views: 10,191

Hi Yura,

can you please explain what you mean by the abbreviations you used?

» Correction of alpha is carried out by CVWR and CVWT-R (nR and nT-R, GRMR and
» GRMT-R, respectively, for TRR / RTR / RRT) or only by CVWR? Since it is necessary to calculate CIT-R.

The inflation of the Type I Error depends on CVwR (and to a minor extent on the sample size). CVwT – which is indeed nice to know – is not accessible in the partial replicate design.
Examples of the TIE and adjusting α for an assumed true ratio of 0.9:
  1. n = 48, balanced sequences
    library(PowerTOST)
    scABEL.ad(CV=0.35, n=48, design="2x3x3")

    +++++++++++ scaled (widened) ABEL ++++++++++++
             iteratively adjusted alpha
       (simulations based on ANOVA evaluation)
    ----------------------------------------------
    Study design: 2x3x3 (TRR|RTR|RRT)
    log-transformed data (multiplicative model)
    1,000,000 studies in each iteration simulated.

    CVwR 0.35, n(i) 16|16|16 (N 48)
    Nominal alpha                 : 0.05
    True ratio                    : 0.9000
    Regulatory settings           : EMA (ABEL)
    Switching CVwR                : 0.3
    Regulatory constant           : 0.76
    Expanded limits               : 0.7723 ... 1.2948
    Upper scaling cap             : CVwR > 0.5
    PE constraints                : 0.8000 ... 1.2500
    Empiric TIE for alpha 0.0500  : 0.05663
    Power for theta0 0.9000       : 0.801
    Iteratively adjusted alpha    : 0.04405
    Empiric TIE for adjusted alpha: 0.05000
    Power for theta0 0.9000       : 0.785


  2. Three dropouts
    scABEL.ad(CV=0.35, n=c(16, 14, 15), design="2x3x3")

    +++++++++++ scaled (widened) ABEL ++++++++++++
             iteratively adjusted alpha
       (simulations based on ANOVA evaluation)
    ----------------------------------------------
    Study design: 2x3x3 (TRR|RTR|RRT)
    log-transformed data (multiplicative model)
    1,000,000 studies in each iteration simulated.

    CVwR 0.35, n(i) 16|14|15 (N 45)
    Nominal alpha                 : 0.05
    True ratio                    : 0.9000
    Regulatory settings           : EMA (ABEL)
    Switching CVwR                : 0.3
    Regulatory constant           : 0.76
    Expanded limits               : 0.7723 ... 1.2948
    Upper scaling cap             : CVwR > 0.5
    PE constraints                : 0.8000 ... 1.2500
    Empiric TIE for alpha 0.0500  : 0.05634
    Power for theta0 0.9000       : 0.779
    Iteratively adjusted alpha    : 0.04420
    Empiric TIE for adjusted alpha: 0.05000
    Power for theta0 0.9000       : 0.762

Due to the smaller sample size in #2 the TIE is less inflated (0.05634 < 0.05663) and less adjustment is required (0.04420 > 0.4405) to preserve the patient’s risk. On the other hand the narrower CI (91.16% < 91.19%) cannot outweigh the loss in power (76.2% < 78.5%).

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Helmut Schütz
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