The Wang-Tsiatis Power Alpha Spending Function

Description

Stipulates alpha spending according to the Wang-Tsiatis Power function in the Lan-Demets boundary construction method. Its intended purpose is in constructing calls to GrpSeqBnds and PwrGSD.

Usage

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Pow(rho)

Arguments

rho

The exponent for the Wang-Tsiatis power spending function

Details

Larger rho results in more conservative boundaries. rho=3 is roughly equivalent to Obrien-Fleming spending. rho=1 spends alpha linearly in the information fraction

Value

An object of class spending.function which is really a list with the following components. The print method displays the original call.

type

Gives the spending function type, which is the character string "Pow"

rho

the numeric value passed to the single argument, rho

call

returns the call

Note

The print method returns the call by default

Author(s)

Grant Izmirlian

References

see references under PwrGSD

See Also

LanDemets, ObrienFleming, Pocock, GrpSeqBnds, PwrGSD

Examples

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## example 1: what is the result of calling a spending function
    ## A call to 'Pow' just returns the call
    Pow(rho=2)

    ## It does argument checking...the following results in an error:
    ## Not run: 
      Pow()
    
## End(Not run)
    
    ## it doesn't matter whether the argument is named or not,
    ## either produces the same result
    Pow(2)

    ## but really its value is a list with a component named
    ## 'type' equal to "Pow", a component named 'rho' equal
    ## to the numeric value passed to the single argument 'rho'
    ## and a component  named 'call' equal to the call.
    names(Pow(rho=2))
    
    names(Pow(2))
    
    Pow(rho=2)$type
    Pow(rho=2)$rho
    Pow(rho=2)$call    

## example 2: ...But the intended purpose of the spending functions its
    ## intended purpose is in constructing calls to 'GrpSeqBnds' and to 'PwrGSD':
     

    frac <- c(0.07614902,0.1135391,0.168252,0.2336901,0.3186155,
              0.4164776,0.5352199,0.670739,0.8246061,1)
    drift <- c(0.3836636,0.5117394,0.6918584,0.8657705,1.091984,
               1.311094,1.538582,1.818346,2.081775,2.345386)

    test <- GrpSeqBnds(frac=frac, EfficacyBoundary=LanDemets(alpha=0.05, spending=Pow(2)),
                       FutilityBoundary=LanDemets(alpha=0.10, spending=ObrienFleming),
                       drift=drift)

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