Package 'SurrogateParadoxTest'

Meta-Analytic Resilience Probability using Bootstrap

Description

Calculates the meta-analytic resilience probability, estimating the standard error (SE) using the nonparametric bootstrap; used by main meta-analytic function, not intended to be called directly by the user.

Usage

bootstrap_run_procedure_parallel(data, s0.B, s1.B, degree = 3, 
n.reps = 200, 
use_spline = FALSE, 
n.boot = 200, 
n.cores = 2, 
seed = NULL, knots0, knots1, boundary_knots0, boundary_knots1)

Arguments

data	Dataset in same format as required by meta_analytic_resilience function.
s0.B	Vector of S values in Study B in control group.
s1.B	Vector of S values in Study B in treatment group.
degree	Desired polynomial degree for mean function.
n.reps	Number of Delta_B samples to generate.
use_spline	Whether to use B-spline basis.
n.boot	Number of nonparametric bootstrap samples.
n.cores	Number of cores to use in parallelization.
seed	Seed for parallelization.
knots0	Knots for B-spline in control group.
knots1	Knots for B-spline in treatment group.
boundary_knots0	Boundary knots for spline in control group.
boundary_knots1	Boundary knots for spline in treatment group.

Value

p_boot	Estimated resilience probability.
var_p	Estimated variance of resilience probability.
se_p	Estimated SE of resilience probability.

---

Calculate resilience probability.

Description

Calculates resilience probability; used by main meta-analytic function, not intended to be called directly by the user.

Usage

calculate_p_hat(data, s0.B, s1.B, degree = 3, n.reps = 200, use_spline = FALSE, 
knots0, knots1, boundary_knots0, boundary_knots1)

Arguments

data	Dataset in same format as required by meta_analytic_resilience function.
s0.B	Vector of S values in Study B in control group.
s1.B	Vector of Y values in Study B in treatment group.
degree	Degree of basis expansion.
n.reps	Number of Delta_B samples.
use_spline	Use B-spline basis.
knots0	Knots for B-spline in control group.
knots1	Knots for B-spline in treatment group.
boundary_knots0	Boundary knots for spline in control group.
boundary_knots1	Boundary knots for spline in treatment group.

Value

p	Estimated resilience probability.
theta_hat0	Estimated theta in control group.
theta_hat1	Estimated theta in treatment group.
sigma2_hat0	Estimated sigma^2 in control group.
sigma2_hat1	Estimated sigma^2 in treatment group.
v2_hat0	Estimated v^2 in control group.
v2_hat1	Estimated v^2 in treatment group.
beta0_hat	Estimated beta vector in control group.
beta1_hat	Estimated beta vector in treatment group.
par0	Estimated parameter vector for control group.
par1	Estimated parameter vector for treatment group.

---

Example dataset for meta-analytic analysis

Description

Example dataset for meta-analytic analysis; this dataset contains the surrogate and primary outcome in the treatment and control groups, measured for multiple studies.

Usage

data("dataA")

Format

A data frame with 500 observations on the following 4 variables.

S

the surrogate value

Y

the primary outcome

G

the treatment indicator

study

the Study ID

Examples

data(dataA)
names(dataA)
head(dataA)

---

Example dataset for meta-analytic analysis, new study

Description

Example dataset for meta-analytic analysis; this dataset contains the surrogate in the treatment (s1.B) and control group (s0.B) for the new study.

Usage

data("dataB")

Format

A list of 10 observations in each treatment group:

s0.B

the surrogate values in the control group

s1.B

the surrogate values in the treated group

Examples

data(dataB)
names(dataB)
head(dataB)

---

Fourier Resilience Interval

Description

Calculates the resilience probability and resilience bound, assuming that the mean function of Study B data is generated by adding a Fourier basis with random coefficients with specified parameters.

Usage

fourier_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, var_vec, period, 
  n.iter = 500, M = 100, q_quant = 0.1,      plot = FALSE, intervals 
  = TRUE, get_var = TRUE)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
var_vec	Length-4 vector governing the variance of the random coefficients of the mean function for Study B.
period	Length-3 vector dictating the period of the Fourier basis for Study B. Each item represents a proportion of the range of the surrogate values of Study A.
n.iter	Number of $\Delta_B$ samples to generate; should be large.
M	Number of bootstrap iterations to estimate the SE of $\hat{p}_0$ and $\hat{q}_\alpha$.
q_quant	Desired quantile for the resilience bound. Default is 0.10.
plot	TRUE or FALSE; include plots of randomly generated functions in results. Default is FALSE.
intervals	TRUE or FALSE; return the inner 95% of $\Delta_B$ samples. Default is TRUE.
get_var	TRUE or FALSE; return an estimated variance of the $\hat{p}_0$ and $\hat{q}_\alpha$ parameters. Default is TRUE.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Delta_hats	Vector of samples of $\Delta_B$.
Delta_estimate	Mean of samples of $\Delta_B$.
p_hat	Estimated value $\hat{p}_0$, the probability of the surrogate paradox.
q_hat	Estimated value $\hat{q}_\alpha$

, the resilience bound.

p_se	Estimated variance of $\hat{p}_0$; only returned if get_var = TRUE.
q_se	Estimated variance of $\hat{q}_\alpha$; only returned if get_var = TRUE.
control_plot	Plot including data points of control group of Study A and functions generated for Study B; only returned if plot = TRUE.
treatment_plot	Plot including data points of treatment group of Study A and functions generated for Study B; only returned if plot = TRUE.

Author(s)

Emily Hsiao

Examples

n.example = 200
  s0.A <- rnorm(n.example, 3, sqrt(3))
  y0.A <- sapply(s0.A, function(x) 2 * x - 1)
  s1.A <- rnorm(n.example, 4, sqrt(3))
  y1.A <- sapply(s1.A, function(x) x + 3)
  s0.B <- rnorm(n.example, 4.75, sqrt(1))
  s1.B <- rnorm(n.example, 5.25, sqrt(1))
  result <- fourier_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, 
  var_vec = c(0.25, 0.25, 0.1, 0.1), period = c(0.5, 0.25, 0.1), n.iter = 100, M = 20)
  result$p_hat

---

Fourier Resilience Set

Description

Creates a plot of the resilience set i.e., the possible variance parameters of the coefficients of the Fourier terms of the mean function of Study B such that the probability of the surrogate paradox is below a threshold $\alpha$. Note that this function assumes that the covariance matrix of the random coefficients takes the form $\Sigma = diag(\sigma_{11}^2, \sigma_{11}^2, \sigma_{22}^2, \sigma_{22}^2)$.

Usage

fourier_resilience_set(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, 
  sig1_values, sig2_values, alpha = 0.10)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
sig1_values	Vector of values of $\sigma_{11}^2$ for which the probability of surrogate paradox should be calculated with the given data.
sig2_values	Vector of values of $\sigma_{22}^2$ for which the probability of surrogate paradox should be calculated with the given data.
alpha	Threshold value of the surrogate paradox. Default is 0.10.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Returns a ggplot object with values of $\sigma_{11}^2$ on the x-axis and $\sigma_{22}^2$ on the y-axis, and regions where $P(\Delta_B) < \alpha$ with given data and parameters highlighted in blue.

Author(s)

Emily Hsiao

Examples

n_A=200
n_B=200
s0.A <- rnorm(n_A, mean = 10, sd = 2)
y0.A <- 5 + 0.5 * s0.A + rnorm(n_A, mean = 0, sd = 0.5)

s1.A <- rnorm(n_A, mean = 12, sd = 2.5)
y1.A <- 5.5 + 0.6 * s1.A + rnorm(n_A, mean = 0, sd = 0.6)

 s0.B <- rnorm(n_B, 10, 2)
 s1.B <- rnorm(n_B, 11, 3)
 sig1_vals_example <- seq(0.1, 1, length.out = 30) # Sigma squared values
 sig2_vals_example <- seq(0.1, .5, length.out = 30)

 # Run the function with the generated example data
 
 fourier_resilience_set(
   s0.A, y0.A, s1.A, y1.A, s0.B, s1.B,
   sig1_values = sig1_vals_example,
   sig2_values = sig2_vals_example,
   alpha = 0.05
 )

---

Gaussian Process Resilience Interval

Description

Calculates the resilience probability and resilience bound, assuming that the mean function of Study B data is generated according to a Gaussian Process with specified parameters.

Usage

gaussian_process_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sigma2, theta, 
  n.iter = 500, M = 100, q_quant = 0.1, plot = FALSE, intervals = TRUE, get_var = TRUE)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
sigma2	Variance parameter of the Gaussian Process.
theta	Smoothness parameter of the Gaussian Process.
n.iter	Number of $\Delta_B$ samples to generate; should be large.
M	Number of bootstrap iterations to estimate the SE of $\hat{p}_0$ and $\hat{q}_\alpha$.
q_quant	Desired quantile for the resilience bound. Default is 0.10.
plot	TRUE or FALSE; include plots of randomly generated functions in results. Default is FALSE.
intervals	TRUE or FALSE; return the inner 95% of $\Delta_B$ samples. Default is TRUE.
get_var	TRUE or FALSE; return an estimated variance of the $\hat{p}_0$ and $\hat{q}_\alpha$ parameters. Default is TRUE.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Delta_hats	Vector of samples of $\Delta_B$.
Delta_estimate	Mean of samples of $\Delta_B$.
p_hat	Estimated value $\hat{p}_0$, the probability of the surrogate paradox.
q_hat	Estimated value $\hat{q}_\alpha$

, the resilience bound.

p_se	Estimated variance of $\hat{p}_0$; only returned if get_var = TRUE.
q_se	Estimated variance of $\hat{q}_\alpha$; only returned if get_var = TRUE.
control_plot	Plot including data points of control group of Study A and functions generated for Study B; only returned if plot = TRUE.
treatment_plot	Plot including data points of treatment group of Study A and functions generated for Study B; only returned if plot = TRUE.
p_interval	Inner 95% of $\hat{p}_0$ samples from bootstrap; only returned if intervals = TRUE.
q_interval	Inner 95% of $\hat{q}_\alpha$ samples from bootstrap; only returned if intervals = TRUE.

Author(s)

Emily Hsiao

Examples

n.example = 200
  s0.A <- rnorm(n.example, 3, sqrt(3))
  y0.A <- sapply(s0.A, function(x) 2 * x - 1)
  s1.A <- rnorm(n.example, 4, sqrt(3))
  y1.A <- sapply(s1.A, function(x) x + 3)
  s0.B <- rnorm(n.example, 4.75, sqrt(1))
  s1.B <- rnorm(n.example, 5.25, sqrt(1))
  result <- gaussian_process_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sigma2 = 0.25, 
    theta = 2, n.iter = 100, M = 20)
  result$p_hat

---

Gaussian Process Resilience Set

Description

Creates a plot of the resilience set i.e., the possible parameters of the Gaussian Process such that the probability of the surrogate paradox is below a threshold $\alpha$.

Usage

gp_resilience_set(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sigma2_vals, theta_vals, 
  alpha = 0.10)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
sigma2_vals	Vector of values of $\sigma^2$ for which the probability of surrogate paradox should be calculated with the given data.
theta_vals	Vector of values of $\theta$ for which the probability of surrogate paradox should be calculated with the given data.
alpha	Threshold value of the surrogate paradox. Default is 0.10.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Returns a ggplot object with values of $\theta$ on the x-axis and $\sigma^2$ on the y-axis, and regions where $P(\Delta_B) < \alpha$ with given data and parameters highlighted in blue.

Author(s)

Emily Hsiao

Examples

n_A=200
n_B=200
s0.A <- rnorm(n_A, mean = 10, sd = 2)
y0.A <- 5 + 0.5 * s0.A + rnorm(n_A, mean = 0, sd = 0.5)

s1.A <- rnorm(n_A, mean = 12, sd = 2.5)
y1.A <- 5.5 + 0.6 * s1.A + rnorm(n_A, mean = 0, sd = 0.6)

 s0.B <- rnorm(n_B, 10, 2)
 s1.B <- rnorm(n_B, 11, 3)

  
  sigma2_values <- seq(0.01, 10, length.out = 30)
  theta_values <- seq(0.01, 10, length.out = 30)
  
  gp_resilience_set(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sigma2_values, theta_values, 
  alpha = 0.05)

---

Basis

Description

Make basis matrix; used by main meta-analytic function, not intended to be called directly by the user.

Usage

make_basis(x, degree = 3, use_spline = FALSE, knots = NULL, boundary_knots = NULL)

Arguments

x	Vector of values.
degree	Polynomial Degree.
use_spline	Use B-spline or monomial.
knots	Knots.
boundary_knots	Boundary knots.

Value

Basis matrix.

---

Meta-Analytic Resilience Probability

Description

This function calculates the resilience probability for the meta-analytic setting.

Usage

meta_analytic_resilience(data, s0.B, s1.B, degree = 3, use_spline = FALSE, 
n.reps = 200, calculate_se = TRUE, try_analytic = TRUE, n_mc = 200, n_bootstrap = 200)

Arguments

data	Data from Study A. Needs to be in the specific format of a table with the columns: S, Y, G (treatment indicator), study (study index).
s0.B	Vector of surrogate values in Study B in control group.
s1.B	Vector of surrogate values in Study B in treatment group.
degree	The degree of polynomial desired for the basis expansion.
use_spline	TRUE or FALSE: whether to use a B-spline basis expansion for mean function.
n.reps	How many samples of Delta_K+1 are desired.
calculate_se	TRUE or FALSE: return SE of estimated p.
try_analytic	TRUE or FALSE: run PAB method or default to fully nonparametric bootstrap.
n_mc	Number of samples in PAB method.
n_bootstrap	Number of samples in nonparametric bootstrap.

Details

More details can be found in Hsiao, Parast. "A Functional-Class Meta-Analytic Framework for Quantifying Surrogate Resilience" (2026).

Value

p_hat	Estimated resilience probability.
se_p	Estimated SE of resilience probability; only if calculate_se = TRUE.
conf_p	95% confidence interval for resilience probability; only if calculate_se = TRUE.
var_method	Method used to estimate SE, bootstrap or analytic; only if calculate_se = TRUE.

Examples

#use example datasets
data(dataA)
names(dataA)
head(dataA)

data(dataB)
names(dataB)
head(dataB)


#apply function, no uncertainty quantification
set.seed(1)
result = meta_analytic_resilience(data=dataA, s0.B = dataB$s0.B, s1.B = dataB$s1.B, 
degree = 1, use_spline = FALSE, calculate_se = FALSE)
result

#apply function, uncertainty quantification, analytic SE
set.seed(1)
result = meta_analytic_resilience(data=dataA, s0.B = dataB$s0.B, s1.B = dataB$s1.B, 
degree = 1, use_spline = FALSE, calculate_se = TRUE, try_analytic = TRUE)
result

#apply function, uncertainty quantification, bootstrap SE
set.seed(1)
result = meta_analytic_resilience(data=dataA, s0.B = dataB$s0.B, s1.B = dataB$s1.B, 
degree = 1, use_spline = FALSE, calculate_se = TRUE, try_analytic = FALSE)
result

---

Polynomial Resilience Interval

Description

Calculates the resilience probability and resilience bound, assuming that the mean function of Study B data is generated by adding a polynomial basis with random coefficients with specified parameters.

Usage

polynomial_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, var_vec, n.iter = 500, 
  M = 100, q_quant = 0.1, plot =    FALSE, intervals = TRUE, get_var = TRUE)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
var_vec	Length-4 vector governing the variance of the random coefficients of the mean function for Study B.
n.iter	Number of $\Delta_B$ samples to generate; should be large.
M	Number of bootstrap iterations to estimate the SE of $\hat{p}_0$ and $\hat{q}_\alpha$.
q_quant	Desired quantile for the resilience bound. Default is 0.10.
plot	TRUE or FALSE; include plots of randomly generated functions in results. Default is FALSE.
intervals	TRUE or FALSE; return the inner 95% of $\Delta_B$ samples. Default is TRUE.
get_var	TRUE or FALSE; return an estimated variance of the $\hat{p}_0$ and $\hat{q}_\alpha$ parameters. Defaults to TRUE.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Delta_hats	Vector of samples of $\Delta_B$.
Delta_estimate	Mean of samples of $\Delta_B$.
p_hat	Estimated value $\hat{p}_0$, the probability of the surrogate paradox.
q_hat	Estimated value $\hat{q}_\alpha$

, the resilience bound.

p_se	Estimated variance of $\hat{p}_0$; only returned if get_var = TRUE.
q_se	Estimated variance of $\hat{q}_\alpha$; only returned if get_var = TRUE.
control_plot	Plot including data points of control group of Study A and functions generated for Study B; only returned if plot = TRUE.
treatment_plot	Plot including data points of treatment group of Study A and functions generated for Study B; only returned if plot = TRUE.

Author(s)

Emily Hsiao

Examples

n.example = 200
  s0.A <- rnorm(n.example, 3, sqrt(3))
  y0.A <- sapply(s0.A, function(x) 2 * x - 1)
  s1.A <- rnorm(n.example, 4, sqrt(3))
  y1.A <- sapply(s1.A, function(x) x + 3)
  s0.B <- rnorm(n.example, 4.75, sqrt(1))
  s1.B <- rnorm(n.example, 5.25, sqrt(1))
  result <- polynomial_interval(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, 
  var_vec = c(0.25, 0.25, 0.1, 0.1),n.iter = 100, M = 20)
  result$p_hat

---

Polynomial Resilience Set

Description

Creates a plot of the resilience set i.e., the possible variance parameters of the coefficients of the polynomial terms of the mean function of Study B such that the probability of the surrogate paradox is below a threshold $\alpha$. Note that this function assumes that the covariance matrix of the random coefficients takes the form $\Sigma = diag(\sigma_{11}^2, \sigma_{11}^2, \sigma_{22}^2, \sigma_{22}^2)$.

Usage

polynomial_resilience_set(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sig1_values, 
  sig2_values, alpha = 0.10)

Arguments

s0.A	Vector of surrogate values in the control group of Study A.
y0.A	Vector of primary outcome values in the control group of Study A.
s1.A	Vector of surrogate values in the treatment group of Study A.
y1.A	Vector of primary outcome values in the treatment group of Study A.
s0.B	Vector of surrogate values in the control group of Study B.
s1.B	Vector of surrogate values in the treatment group of Study B.
sig1_values	Vector of values of $\sigma_{11}^2$ for which the probability of surrogate paradox should be calculated with the given data.
sig2_values	Vector of values of $\sigma_{22}^2$ for which the probability of surrogate paradox should be calculated with the given data.
alpha	Threshold value of the surrogate paradox. Default is 0.10.

Details

More details can be found in Hsiao, Tian, Parast. "Resilience Measures for the Surrogate Paradox." (2025) Under Review.

Value

Returns a ggplot object with values of $\sigma_{11}^2$ on the x-axis and $\sigma_{22}^2$ on the y-axis, and regions where $P(\Delta_B) < \alpha$ with given data and parameters highlighted in blue.

Author(s)

Emily Hsiao

Examples

n_A=200
n_B=200
s0.A <- rnorm(n_A, mean = 10, sd = 2)
 y0.A <- 5 + 0.5 * s0.A + rnorm(n_A, mean = 0, sd = 0.5)

s1.A <- rnorm(n_A, mean = 12, sd = 2.5)
 y1.A <- 5.5 + 0.6 * s1.A + rnorm(n_A, mean = 0, sd = 0.6)

s0.B <- rnorm(n_B, 10, 2)
s1.B <- rnorm(n_B, 11, 3)

  
sigma1_values <- seq(0.01, 1.2, length.out = 30)
sigma2_values <- seq(0.01, .4, length.out = 30)
  
  polynomial_resilience_set(s0.A, y0.A, s1.A, y1.A, s0.B, s1.B, sigma1_values, 
  sigma2_values, alpha = 0.05)

---

Meta-Analytic Resilience Probability using PAB

Description

Calculates the meta-analytic resilience probability, estimating SE using partially analytic bootstrap; used by main meta-analytic function, not intended to be called directly by the user.

Usage

run_procedure_pab(data, s0.B, s1.B, degree = 3, use_spline = FALSE, n_mc = 200, 
knots0, knots1, boundary_knots0, boundary_knots1)

Arguments

data	Study A data.
s0.B	Vector of S values in Study B in control group.
s1.B	Vector of S values in Study B in treatment group.
degree	Desired polynomial degree for mean function.
use_spline	Whether to use B-spline basis.
n_mc	Number of Monte-Carlo iterations.
knots0	Knots for B-spline in control group.
knots1	Knots for B-spline in treatment group.
boundary_knots0	Boundary knots for spline in control group.
boundary_knots1	Boundary knots for spline in treatment group.

Value

p_boot	Estimated resilience probability.
se_p	Estimated SE of resilience probability.
var_delta	Estimated component of SE from Delta method.
var_sb	Estimated component of SE from resampling S.
mDelta	Mean for Delta method.
vDelta	Variance for Delta method.
par0	MLE parameters for control group.
par1	MLE parameters for treatment group.

---

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)

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.

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

Author(s)

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.

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_c, s1 = s_t, y1 = y_t, type = "sd"
)


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

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