riskRegression (version 2023.12.21)

transformCIBP: Compute Confidence Intervals/Bands and P-values After a Transformation

Description

Compute confidence intervals/bands and p-values after a transformation

Usage

transformCIBP(
  estimate,
  se,
  iid,
  null,
  conf.level,
  alternative,
  ci,
  type,
  min.value,
  max.value,
  band,
  method.band,
  n.sim,
  seed,
  p.value,
  df = NULL
)

Arguments

estimate

[numeric matrix] the estimate value before transformation.

se

[numeric matrix] the standard error before transformation.

iid

[numeric array] the iid decomposition before transformation.

null

[numeric] the value of the estimate (before transformation) under the null hypothesis.

conf.level

[numeric, 0-1] Level of confidence.

alternative

[character] a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".

ci

[logical] should confidence intervals be computed.

type

[character] the transforamtion. Can be "log", "loglog", "cloglog", or "atanh" (Fisher transform), or "atanh2" (modified Fisher transform for [0-1] variable).

min.value

[numeric] if not NULL and the lower bound of the confidence interval is below min, it will be set at min.

max.value

[numeric] if not NULL and the lower bound of the confidence interval is below max, it will be set at max.

band

[integer 0,1,2] When non-0, the confidence bands are computed for each contrasts (band=1) or over all contrasts (band=2).

method.band

[character] method used to adjust for multiple comparisons. Can be any element of p.adjust.methods (e.g. "holm"), "maxT-integration", or "maxT-simulation".

n.sim

[integer, >0] the number of simulations used to compute the quantiles for the confidence bands.

seed

[integer, >0] seed number set before performing simulations for the confidence bands.

p.value

[logical] should p-values and adjusted p-values be computed. Only active if ci=TRUE or band>0.

df

[integer, >0] optional. Degrees of freedom used for the student distribution of the test statistic. If not specified, use a normal distribution instead.

Details

The iid decomposition must have dimensions [n.obs,time,n.prediction] while estimate and se must have dimensions [n.prediction,time].

Single step max adjustment for multiple comparisons, i.e. accounting for the correlation between the test statistics but not for the ordering of the tests, can be performed setting the arguemnt method.band to "maxT-integration" or "maxT-simulation". The former uses numerical integration (pmvnorm and qmvnorm to perform the adjustment while the latter using simulation. Both assume that the test statistics are jointly normally distributed.

Examples

set.seed(10)
n <- 100
X <- rnorm(n)

res2sided <- transformCIBP(estimate = mean(X), se = cbind(sd(X)/sqrt(n)), null = 0,
              type = "none", ci = TRUE, conf.level = 0.95, alternative = "two.sided",
              min.value = NULL, max.value = NULL, band = FALSE,
              p.value = TRUE, seed = 10, df = n-1)

resLess <- transformCIBP(estimate = mean(X), se = cbind(sd(X)/sqrt(n)), null = 0,
              type = "none", ci = TRUE, conf.level = 0.95, alternative = "less",
              min.value = NULL, max.value = NULL, band = FALSE,
              p.value = TRUE, seed = 10, df = n-1)

resGreater <- transformCIBP(estimate = mean(X), se = cbind(sd(X)/sqrt(n)), null = 0,
              type = "none", ci = TRUE, conf.level = 0.95, alternative = "greater",
              min.value = NULL, max.value = NULL, band = FALSE,
              p.value = TRUE, seed = 10, df = n-1)


## comparison with t-test
GS <- t.test(X, alternative = "two.sided")
res2sided$p.value - GS$p.value
unlist(res2sided[c("lower","upper")]) - GS$conf.int

GS <- t.test(X, alternative = "less")
resLess$p.value - GS$p.value
unlist(resLess[c("lower","upper")]) - GS$conf.int

GS <- t.test(X, alternative = "greater")
resGreater$p.value - GS$p.value
unlist(resGreater[c("lower","upper")]) - GS$conf.int