Combined p-value for quantile treatment effects in CRE

Tests the null hypothesis \(H_0: \tau_{(k)} \leq c\), where \(\tau_{(k)}\) denotes the individual treatment effect at rank k. The test combines multiple rank sum statistics to improve power.

Usage

comb_p_val_cre(
  Z,
  Y,
  k,
  c,
  methods.list,
  Z.perm = NULL,
  nperm,
  stat.null.mult = NULL
)

Arguments

Z

An n-dimensional binary treatment assignment vector (1 = treated, 0 = control).

Y

An n-dimensional observed outcome vector.

k

An integer between 1 and n specifying which quantile of individual effect is of interest.

c

A numeric value specifying the threshold for the null hypothesis.

methods.list

A list of method specifications for the rank sum statistics. Each element should be a list with:

• name: "Wilcoxon", "Stephenson", or "Polynomial"

• s: (for Stephenson) parameter s

• r: (for Polynomial) power parameter

• std: (for Polynomial) logical, use Puri normalization

• scale: logical, standardize scores

Z.perm

An n x nperm matrix of permuted treatment assignments for approximating the null distribution. If NULL, generated automatically.

nperm

Number of permutations for approximating the null distribution.

stat.null.mult

A matrix whose empirical distribution approximates the randomization distribution of multiple rank statistics. If NULL, computed from Z.perm.

Value

A numeric p-value for testing the specified null hypothesis.

Details

Calculate a valid p-value, based on multiple rank sum statistics, for testing the null hypothesis about quantiles of individual treatment effects in completely randomized experiments (CRE).

See also

pval_comb_block for stratified experiments

Examples

# Simple example with Wilcoxon and Stephenson statistics
set.seed(123)
n <- 30
Z <- sample(c(rep(1, 15), rep(0, 15)))
Y <- rnorm(n) + 0.5 * Z  # Treatment effect of 0.5

# Define methods: Wilcoxon and Stephenson with s=3
methods.list <- list(
  list(name = "Wilcoxon", scale = FALSE),
  list(name = "Stephenson", s = 3, scale = FALSE)
)

# Test if the 80th percentile effect is <= 0
k <- floor(0.8 * n)
pval <- comb_p_val_cre(Z, Y, k, c = 0, methods.list, nperm = 1000)