SurrogateParadoxTest (version 2.0)

test_assumptions: Test assumptions to prevent surrogate paradox

Description

Tests the assumptions necessary to prevent the surrogate paradox: stochastic dominance of surrogate values in the treatment group over control group, monotonicity of the relationship between surrogate and primary endpoint in both treatment and control group, and non-negative residual treatment effect of the treatment group over the control group. For computational efficiency, Version 2.0 of this package uses the monotonicity_test function from the MonotonicityTest package.

Usage

test_assumptions(s0 = NULL, y0 = NULL, s1 = NULL, y1 = NULL, trim = 0.95, 
alpha = 0.05, type = "all", all_results = TRUE, direction = "positive",  
monotonicity_bootstrap_n = 100, nnr_bootstrap_n = 200)

Value

result

Table or string of results of the tests

sd_result

Detailed results of stochastic dominance test; only returned if all_results is TRUE

monotonicity0_result

Detailed results of monotonicity test in control group; only returned if all_results is TRUE

monotonicity1_result

Detailed results of monotonicity test in treatment group; only returned if all_results is TRUE

nnr_result

Detailed results of nnr test; only returned if all_results is TRUE

Arguments

s0

Vector of surrogate values in control group.

y0

Vector of primary endpoint values in control group.

s1

Vector of surrogate values in treatment group.

y1

Vector of primary endpoint values in treatment group.

trim

Proportion of data to keep after trimming the outliers. Defaults to 95%. Trims data by sorting by surrogate value and removing (1 - trim)/2 % of the lowest and highest surrogate values with their corresponding primary endpoint values.

alpha

Desired alpha level of tests.

type

Type of test to run. Defaults to "all"; possible inputs are "sd" (stochastic dominance), "monotonicity" (monotonicity), and "nnr" (non-negative residual treatment effect).

all_results

TRUE or FALSE; return all outputs from hypothesis tests. Defaults to TRUE.

direction

Direction of the test. Defaults to "positive", which tests that the treatment group stochastically dominates the control group, that \(\mu_0\) and \(\mu_1\) are monotonically increasing, and that \(\mu_0 \leq \mu_1 \forall s\). Parameter "negative" tests that the control group stochastically dominates the treatment group, that \(\mu_0\) and \(\mu_1\) are monotonically decreasing, and that \(\mu_1 \leq \mu_0 \forall s\).

monotonicity_bootstrap_n

Number of bootstrap samples for monotonicity test.

nnr_bootstrap_n

Number of bootstrap samples for nnr test.

Author

Emily Hsiao

References

Barrett, Garry F., and Stephen G. Donald. "Consistent tests for stochastic dominance." Econometrica 71.1 (2003): 71-104.

Hall, Peter, and Nancy E. Heckman. "Testing for monotonicity of a regression mean by calibrating for linear functions." Annals of Statistics (2000): 20-39.

Hsiao, Tian, Parast. "Avoiding the Surrogate Paradox: An Empirical Framework for Assessing Assumptions." 2025 (Under Review)

Examples

m_c <- function(s) 1 + 2 * s
m_t <- function(s) 1 + 2 * s
    
s_c <- rnorm(100, 3, 1)
y_c <- sapply(s_c, function(s) rnorm(1, m_c(s), 1))
s_t <- rnorm(100, 3, 1)
y_t <- sapply(s_t, function(s) rnorm(1, m_t(s), 1))

test_assumptions(
s0 = s_c, y0 = y_t, s1 = s_t, y1 = y_t, type = "sd"
)

# \donttest{
test_assumptions(
s0 = s_c, y0 = y_t, s1 = s_t, y1 = y_t, type = "all")
# }