double_rank {ivdesign}

Two-sided double-rank test for Fisher's sharp null hypothesis in a cluster-level proportional treatment effect model

Description

double_rank returns the two-sided p-value testing Fisher's sharp null hypothesis in a cluster-level proportional treatment effect model.

Usage

double_rank(beta_0, R_t, R_c, d_t, d_c, Z_t, Z_c, psi = NULL)

Arguments

beta_0

The magnitude of the proportional treatment effect to be tested.

R_t

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level outcomes in the encouraged cluster of the kth matched pair of two clusters.

R_c

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level outcomes in the control cluster of the kth matched pair of two clusters.

d_t

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level treatment received in the encouraged cluster of the kth matched pair of two clusters.

d_c

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level treatment received in the control cluster of the kth matched pair of two clusters.

Z_t

A length-K vector where K is equal to the number of clusters and the kth entry equal to the encoruagement dose, i.e., the magnitude of the instrumental variable, of the encouraged cluster in the kth matched pair of two clusters.

Z_c

A length-K vector where K is equal to the number of clusters and the kth entry equal to the encoruagement dose, i.e., the magnitude of the instrumental variable, of the control cluster in the kth matched pair of two clusters.

psi

A function specifying the score used in the test statistic. See Details.

Details

Double-rank test statistics is a flexible family of nonparametric test statistics. Function psi is a function that specifies the relationship between d_k, the normalized rank of the absolute treated-minus-control dose difference in the instrumental variable, and q_k, the normalized rank of the absoluve treated-minus-control dose difference in the observed outcome. For instance, psi(d_k, q_k) = 1 yields the sign test, psi(d_k, q_k) = q_k yields the Wilcoxon signed rank test. The default setting, psi(d_k, q_k) = d_k * q_k, yields the dose-weighted signed rank test.

Value

A list of five elements: two-sided p-value, deviate, test statistics, expectation of the test statistic under the null hypothesis, and variance of the test statistic under the null hypothesis.

Examples

R_t = encouraged_clusters$aggregated_outcome
R_c = control_clusters$aggregated_outcome
d_t = encouraged_clusters$aggregated_treatment
d_c = control_clusters$aggregated_treatment
Z_t = encouraged_clusters$IV
Z_c = control_clusters$IV


# Test beta = 0 in the proportional treatment effect
# model with the help of the double rank test using
# default psi(d_k, q_k) = d_k * q_k:
res = double_rank(0, R_t, R_c, d_t, d_c, Z_t, Z_c)

# Define a new psi function: psi(d_k, q_k) = q_k
psi_2 <- function(x, y) y

# Using psi_2 and the double rank test is reduced to the
#Wilcoxon signed rank test.
res_2 = double_rank(0, R_t, R_c, d_t, d_c,
     Z_t, Z_c, psi = psi_2)