Get the Conditional Error Rate for a intersection of hypotheses

Gives the CER (condtional error rate) for a given set of hypotheses, with arbitrary weights and correlation between the hypotheses. This is an upper bound on the probabilty of rejecting all the hypotheses with weight greater 0 under the null hypothesis conditional on the stage one data, assuming we reject whenever a final p-value is smaller than cJ2 * weight

Usage

get_cer(p_values, weights, cJ2, correlation, t)

Arguments

p_values: vector of stage 1 p-values for the hypothesis
weights: weight to give to each hypothesis, ignoring all with weight 0
cJ2: factor used for deciding if the hypothesis should be rejected
correlation: matrix describing a potential known correlation structure between some hypotheses. Use NA for unkown correlations
t: information time fraction at which the interim test is performed

Value

a single number greater than 0, the CER

Details

Note that if the correlation between some values is unkown, the result may be greater than 1, see also the examples

Examples

#the CER is high (even >1) if the p_values of the first stage are already low
get_cer(
 c(0.01, 0.01, 0.9, 0.9),
 c(1, 1, 0, 0),
 0.05,
 matrix(rep(NA, 16), nrow = 4),
 0.5
)
#> [1] 1.000138

#and lower otherwise
get_cer(
 c(0.01, 0.01, 0.9, 0.9),
 c(0, 0, 1, 1),
 0.05,
 matrix(rep(NA, 16), nrow = 4),
 0.5
)
#> [1] 0.0003088926