This function converts between two different parameterizations of a family of conditional error functions: a (more ‘traditional’) parameter \(c\), and a (more convenient) parameter \(\alpha_2\) specifying the local level of the test after the second stage.
parconv(typ, a2 = NA, c = NA)parconv returns \(\alpha_2\) corresponding to the supplied \(c\), or \(c\) corresponding to the supplied \(\alpha_2\).
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
\(\alpha_2\), the local level of the test after the second stage (see details)
the parameter \(c\) (see details)
Marc Vandemeulebroecke
Traditionally, a family of conditional error functions is often parameterized by some parameter \(c\) that, in turn, depends on the local level \(\alpha_2\) of the test after the second stage. However, it can be convenient to parameterize the family directly by \(\alpha_2\). 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:
\(c = \exp(-\chi^2_{4,\alpha_2}/2)\) for Fisher's combination test (Bauer and Koehne, 1994)
\(c = \Phi^{-1}(1-\alpha_2)\) for the inverse normal method (Lehmacher and Wassmer, 1999)
\(\alpha_2 = {(\Gamma(1+1/r))^2}/{\Gamma(1+2/r)}\) for Vandemeulebroecke (2006)
\(c = \alpha_2\) for the family of horizontal conditional error functions
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.
adaptTest package description, getpar, CEF
## 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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