prepivot.ks.permtest function

Permutation Test for the two-sample goodness-of-fit problem under covariate-adaptive randomization

A permutation test of the two-sample goodness-of-fit hypothesis when the randomization scheme is covariate-adaptive. The permutation test considered here is based on prepivoting the Kolmogorov-Smirnov test statistic following Beran (1987,1988), and adapted by Olivares (2020). Current version includes the following randomization schemes: simple randomization, Efron's biased-coin design, Wei's biased-coin design, and stratified block randomization. This implementation uses a Bayesian bootstrap approximation for prepivoting.

prepivot.ks.permtest(Y1, Y0, alpha, B, n.perm)

Arguments

• Y1: Numeric. A vector containing the response variable of the treatment group.
• Y0: Numeric. A vector containing the response variable of the control group.
• alpha: Numeric. Nominal level for the test. The default is 0.05.
• B: Numeric. Number of weighted bootstrap samples.
• n.perm: Numeric. Number of permutations needed for the stochastic approximation of the p-values. The default is n.perm=999.

Returns

An object of class "prepivot.ks.permtest" containing at least the following components:

• n_populations: Number of grups.

• N: Sample Size.

• T.obs: Observed test statistic.

• cv: Critical Value. This value is used in the general construction of a randomization test.

• pvalue: P-value.

• rejectrule: Rule. Binary decision for randomization test, where 1 means "to reject"

• T.perm: Vector. Test statistic recalculated for all permutations used in the stochastic approximation.

• n.perm: Number of permutations.

• B: Bayesian bootstrap samples.

• sample_sizes: Groups size.

Examples

## Not run:

Y0 <- rnorm(100, 1, 1)
Y1 <- rbeta(100,2,2)
Tx = sample(100) <= 0.5*(100)
# Observed Outcome 
Y = ifelse( Tx, Y1, Y0 )
dta <- data.frame(Y = Y, A = as.numeric(Tx))
pKS.GoF<-prepivot.ks.permtest(dta$Y[dta$A==1],dta$Y[dta$A==0],alpha=0.05,B=1000,n.perm = 999)
summary(pKS.GoF)
## End(Not run)

References

Beran, R. (1987). Prepivoting to reduce level error of confidence sets. Biometrika, 74(3): 457–468. Beran, R. (1988). Prepivoting test statistics: a bootstrap view of asymptotic refinements. Journal of the American Statistical Association, 83(403):687–697. Olivares, M. (2020). Asymptotically Robust Permutation Test under Covariate-Adaptive Randomization. Working Paper.

Author(s)

Maurcio Olivares