permutation_cer: Permutation Conditional Error Rate
In floatofmath/adaperm: Permutation tests for adaptive designs

Description Usage Arguments Details Value Author(s)

Computes the conditional type I error rate of a pre-planned permutation test in a two-stage adaptive design. For a two-group design we condition on the observed first stage data and treatment assignments as well as the observed second stage data - which we assume are obtained when the experiment reaches its preplanned sample size. In a one-sample design we condition on the absolute values of the outcome variable in both stages and as well as the first stage sign arrangement.

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permutation_cer(x1, x2, g1, nt2 = floor(length(x2)/2), test_statistic,
  permutations, alpha, restricted, cer_type = c("non-randomized",
  "randomized", "uniform"), stratified = FALSE)

`x1`	vector of preplanned first stage observations
`x2`	vector of preplanned second stage observations
`g1`	vector of first stage treatment assignments
`nt2`	preplanned second stage treatment group size (irrelevant for one-sample tests)
`test_statistic`	function computing the test statistic (see Details)
`permutations`	number of permutations (rerandomizations) used to compute unconditional and conditional permutation distributions
`alpha`	pre-fixed significance level
`restricted`	should stagewise treatment group sizes be considered fixed
`cer_type`	type of preplanned test for which the CER is computed (see details)
`stratified`	should permutation be performed stratified by stage

Based on the first stage data and treatment assignments one may perform sample size reassassment - and possibly other trial modifications - as long as the (preplanned) second stage sample size is not reduced.

stat needs to be a function of the form function(x,g) returning a numeric of length one. Possible options are sumdiff, meandiff, zstat

For restricted=TRUE, we assume that observations are randomized using random allocation blocked by stages, (i.e. wewould resample the first stage using sample(g1)). restricted=FALSE does keep the treatment group sizes fixed (i.e. one would resample using sample(c(-1,1),n,replace=T). This is mainly usefull for onesample test that are invariant under sign-flip transformations.

The conditional error rate may be computed for different types of pre-planned permutation tests. "non-randomized" assumes that the pre-planned test is the usual non-randomized permutation test that has size strictly below alpha. "randomized" assumes a randomized pre-planned test which makes a randomized decision if the observed test statistic is equal to the critical value, such that the size is exactly alpha. Uniform adds the difference between alpha and the size of the non-randomized test to the conditional error rate, such that the expectation of the resulting conditional error function over all permutations of the first stage data is exactly alpha.

numeric value of the conditional error rate

Florian Klinglmueller

floatofmath/adaperm documentation built on May 16, 2019, 1:18 p.m.