Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function converts between two different parameterizations of a family of conditional error functions: a (more ‘traditional’) parameter c, and a (more convenient) parameter alpha2 specifying the local level of the test after the second stage.
1 
typ 
type of test: 
a2 
alpha2, the local level of the test after the second stage (see details) 
c 
the parameter c (see details) 
Traditionally, a family of conditional error functions is often parameterized by some parameter c that, in turn, depends on the local level alpha2 of the test after the second stage. However, it can be convenient to parameterize the family directly by alpha2. The function parconv
converts one parameter into the other: provide one, and it returns the other.
Essentially, the relation between the two parameterizations is implemented as:
c = exp(chi2_{4,alpha2}/2) for Fisher's combination test (Bauer and Koehne, 1994)
c = Phi^{1}(1alpha2) for the inverse normal method (Lehmacher and Wassmer, 1999)
alpha2 = {(Gamma(1+1/r))^2}/{Gamma(1+2/r)} for Vandemeulebroecke (2006)
c = alpha2 for the family of horizontal conditional error functions
parconv
returns alpha2 corresponding to the supplied c, or c corresponding to the supplied alpha2.
Provide either a2
or c
, not both!
alpha2 is the local level of the test after the second stage, and it equals the integral under the corresponding conditional error function:
alpha2 = int_0^1 cef_{alpha2}(p1) d p1,
where cef_{alpha2} is the conditional error function (of a specified family) with parameter alpha2.
Note that in this implementation of adaptive twostage tests, early stopping bounds are not part of the conditional error function. Rather, they are specified separately (see also tsT
).
alpha2 can take any value in [0,1]; c can take values in
[0,1] for Fisher's combination test (Bauer and Koehne, 1994)
(infty, infty) for the inverse normal method (Lehmacher and Wassmer, 1999)
[0,infty) for Vandemeulebroecke (2006)
[0,1] for the family of horizontal conditional error functions
Marc Vandemeulebroecke
Bauer, P., Koehne, K. (1994). Evaluation of experiments with adaptive interim analyses. Biometrics 50, 10291041.
Lehmacher, W., Wassmer, G. (1999). Adaptive sample size calculations in group sequential trials. Biometrics 55, 12861290.
Vandemeulebroecke, M. (2006). An investigation of twostage tests. Statistica Sinica 16, 933951.
adaptTest
package description, getpar
, CEF
1 2  ## Obtain the parameter c for Fisher's combination test, using the local level 0.05 for the test after the second stage
parconv(typ="b", a2=0.05)

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