Function to specify a conditional error function
Description
This function returns a conditional error function.
Usage
1 
Arguments
typ 
type of test: 
c 
the parameter c 
a2 
alpha2, the local level of the test after the second stage 
p1 
the pvalue p1 of the test after the first stage 
p2 
the pvalue p2 of the test after the second stage, defaults to 
fun 
a conditional error function 
dis 
a distortion method for a supplied conditional error function (see details): 
Details
There are two alternative ways of specifying the desired conditional error function:
through a type
typ
, and either a parameter (eithera2
orc
) or a point(p1,p2)
, ORthrough an initial conditional error function
fun
, and possibly a distortion methoddis
together with either the parametera2
or a point(p1,p2)
Most people will only need the first of these two ways; the second leads to userdefined nonstandard tests.
If typ
is specified, a parameter a2
or c
or the point (p1,p2)
must be provided. In this case, CEF
returns the conditional error function of the chosen type with the given parameter or running through the given point.
If typ
is not specified, a conditional error function (i.e., a nonincreasing function defined on [0,1] with values in [0,1]) fun
must be provided. If no distortion method is selected (dis = NA
), fun
is returned unchanged. Otherwise, the function is distorted using the chosen distortion method, either to match a desired second stage level a2
or to run through a specified point (p1,p2)
(one of which must be provided). Currently, two distortion methods are implemented:

dis = "pl"
, Power lines: For an initial function f, define f[r](x) = (f(x^r))^(1/r), r>0. Note that if f is a conditional error function of type"b"
(Bauer and Koehne, 1994), so is f[r]. 
dis = "pl"
, Vertical translation: The initial function is shifted vertically.
See parconv
for more information on the two alternative parameterizations by alpha2 and c.
Value
These functions return a conditional error function (see details).
Note
Provide either typ
or fun
, not both! If typ
is provided, then also specify a2
, c
, or p1
(and possibly p2
). If fun
is provided, then also specify dis
and a2
, or dis
and p1
(and possibly p2
), or none of these.
Warning: Values of a2
close to 0 or 1 may not work for dis = "pl"
.
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
).
Author(s)
Marc Vandemeulebroecke
References
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.
See Also
adaptTest
package description, parconv
, plotCEF
, tsT
Examples
1 2 3 4 5 6 7 8 9 10  ## Plot two conditional error functions of the LehmacherWassmer (1999) type:
## one to the local level alpha2=0.1, and one that runs through (p1,p2)=(0.3,0.7)
foo1 < CEF(typ="l", a2=0.1)
foo2 < CEF(typ="l", p1=0.3, p2=0.7)
plot(foo1, xlim=0:1)
plot(foo2, add=TRUE)
## A different way of doing the same
plotCEF(typ="l", a2=0.1, add=FALSE)
plotCEF(typ="l", p1=0.3, p2=0.7, plt.pt=FALSE)
