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  • 1.  power calculation for futility analysis

    Posted 05-29-2015 17:14

    I'm trying to determine the loss of power from an interim analysis for futility (binary outcome). 

    I'm planning a study with 200 subjects randomized (1 placebo):(3 verum) and would like to stop early if there isn't at least some benefit in the verum group.  H0: p1=p2=.5; H1: p1=2*p2=.5  (no continuity "correction"). 

      p1 p2 d alpha power n1 n2  
      .50 .25 -.25 .05 .90 50 150  

    How much more subjects do I need to compensate for loss of power when stopping for futility if p2>=.45 (e.g.) after 20+60=80 subjects? My gut feeling is that 60+180=240 would be more than enough, but I'd like to be a bit more precise.

    Thanks
    Knut

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    Knut Wittkowski
    Head, Dept. Biostatistics, Epidemiology, and Research Design
    The Rockefeller University
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  • 2.  RE: power calculation for futility analysis

    Posted 06-01-2015 02:06

    Knut,

    To answer your problem you need to specify

    1. Will the interim analysis be only for futility or also for efficacy?

    2. Will there be one look or more?

    3. When will you be doing the interim analyses? After how many accrued?

    Also, why are you choosing the criterion of p2>.45 as futility boundary? That does not seem right.

    As far as I know, futility boundaries are computed formally on the test statistic via methods analogous to interim analyses for efficacy (error spending functions). Alternatively, you can do futility assessment based on conditional power.



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    Constantine Daskalakis
    Thomas Jefferson University, Philadelphia, PA
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    Original Message


  • 3.  RE: power calculation for futility analysis

    Posted 06-01-2015 03:50

    Hi Knut and Constantine

    Knut's proposal might not be the most efficient one, but it can be realized. I understand that stopping only for futility is planned and the (only) interim takes place after 80 subjects (20+60) have reached the endpoint.

    If H1 is true and thus p2=0.25 then the probability to see an event rate of .45 or higher  among the 60 subjects is negligible (p=0.0005925201888). This small probability would hardly influence the power. Things would of course be different if the futility bound decreases.

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    Joachim Roehmel

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    Original Message


  • 4.  RE: power calculation for futility analysis

    Posted 06-01-2015 06:44

    It looks like asymptotic approximations for group sequential design should be sufficient.

    Take a look at https://gsdesign.shinyapps.io/prod/ (I would recommend Chrome, but any HTML5 compatible browser should work).

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    Keaven Anderson
    Exexutive Director
    Merck & Company, Inc.
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    Original Message


  • 5.  RE: power calculation for futility analysis

    Posted 06-01-2015 14:31
      |   view attached



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    Anthiyur Kannappan
    Cytel Inc.
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    Two 2- look designs, one for Efficacy only and another for Efficacy & Futility were created using East software. The details of the assumptions and results are shown in the attached Knut.docx file, as screenshots from the software.

    The results show that adding futility boundary could increase the total sample size from 200 to 220.

    Anthiyur Kannappan


    Attachment(s)

    docx
    Knut.docx   236 KB 1 version
    Original Message


  • 6.  RE: power calculation for futility analysis

    Posted 06-01-2015 21:52


    All,

    thanks a lot!

    Joachim,

    I agree with your interpretation and thanks for running the simulations. As I understand, no adjustment is necessary as long as the interim analysis is for futility only and the futility cut-off is not lower than .40

    Anthiyur,

    Thanks for considering the scenario where the first look is also for efficacy. Is the reason for the sample size to increase that the futility boundary "Interp. (NB)" is below .40 ?

    Keaven,

    thanks for pointing me to the gsDesign Explorer. I may have to find some documentation to be able to set the Boundaries parameters to match the problem.

    Knut



  • 7.  RE: power calculation for futility analysis

    Posted 06-02-2015 15:26

    Knut,

    The reason for sample size increase is the width of the futility boundary at the first look. The assumption I made using your information, was that the futility boundaries in the õ scale to be ±0.05. The corresponding Type-2 error at this look is 0.041. If the boundaries are taken to be smaller, like ±0.004, then the corresponding type-2 error would have been 0.0035. In this latter case, a sample size of 200 would have been sufficient. But in the former case, a larger type-2 error leads to lower power without increase in the sample size and keeping same type-1 error. So the sample size had to increase to 220 as computed by the algorithm. This is somewhat a rough explanation.

    Anthiyur



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    Anthiyur Kannappan
    Cytel Inc.
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    Original Message


  • 8.  RE: power calculation for futility analysis

    Posted 06-02-2015 17:02

    Knut,

    Regarding the reason for the sample size increase, I refer you to my paper on this topic in Journal of Bioppharmaceutical Statistics, "The type II error probability of a group sequential test of efficacy and futility, and considerations for power and sample size," JBS 23:378-393, 2013.

    In this paper I derive the full probability model for the type II error probability of GSD, partitioning the total type II error probability of GSD into the sum of its component type II error probabilities of efficacy and futility.  This partitioning is used to show, in particular, that sample size is increased to maintain the total type II error probability when adding tests of futility to GSD; however, this increase actually lowers the type II error probability of the tests of efficacy, i.e., it overpowers tests of efficacy, and is therefore unnecessary and inefficient.  

    Tom


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    Thomas Dobbins
    Executive Director, Clinical Development
    Merck & Co., Inc.
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    Original Message


  • 9.  RE: power calculation for futility analysis

    Posted 06-03-2015 16:48

    All, thanks, again, for your help!

    Knut



  • 10.  RE: power calculation for futility analysis

    Posted 06-04-2015 13:51

    My package seqmon on CRAN can perform this calculation, for any sequential design.

      



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    David Schoenfeld
    Professor of Medicine
    Massachusetts General Hospital
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    Original Message