This function returns a conditional error function.
type of test:
the parameter c
alpha2, the local level of the test after the second stage
the p-value p1 of the test after the first stage
the p-value p2 of the test after the second stage, defaults to
a conditional error function
a distortion method for a supplied conditional error function (see details):
There are two alternative ways of specifying the desired conditional error function:
through a type
typ, and either a parameter (either
c) or a point
through an initial conditional error function
fun, and possibly a distortion method
dis together with either the parameter
a2 or a point
Most people will only need the first of these two ways; the second leads to user-defined non-standard tests.
typ is specified, a parameter
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.
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.
parconv for more information on the two alternative parameterizations by alpha2 and c.
These functions return a conditional error function (see details).
fun, not both! If
typ is provided, then also specify
p1 (and possibly
fun is provided, then also specify
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 two-stage tests, early stopping bounds are not part of the conditional error function. Rather, they are specified separately (see also
Bauer, P., Koehne, K. (1994). Evaluation of experiments with adaptive interim analyses. Biometrics 50, 1029-1041.
Lehmacher, W., Wassmer, G. (1999). Adaptive sample size calculations in group sequential trials. Biometrics 55, 1286-1290.
Vandemeulebroecke, M. (2006). An investigation of two-stage tests. Statistica Sinica 16, 933-951.
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## Plot two conditional error functions of the Lehmacher-Wassmer (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)