parconv: Function to convert between two different parameterizations...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

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.

Usage

1
parconv(typ, a2 = NA, c = NA)

Arguments

typ

type of test: "b" for Bauer and Koehne (1994), "l" for Lehmacher and Wassmer (1999), "v" for Vandemeulebroecke (2006) and "h" for the horizontal conditional error function

a2

alpha2, the local level of the test after the second stage (see details)

c

the parameter c (see details)

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:

Value

parconv returns alpha2 corresponding to the supplied c, or c corresponding to the supplied alpha2.

Note

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 two-stage 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

Author(s)

Marc Vandemeulebroecke

References

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.

See Also

adaptTest package description, getpar, CEF

Examples

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)

adaptTest documentation built on May 29, 2017, 8:29 p.m.