Package 'SurrogateRank'

Title: Rank-Based Test to Evaluate a Surrogate Marker
Description: Uses a novel rank-based nonparametric approach to evaluate a surrogate marker in a small sample size setting. Details are described in Parast et al (2024) <doi:10.1093/biomtc/ujad035>, in Hughes A et al (2025) <doi:10.1002/sim.70241>, and in Hughes A et al (2026) <doi:10.48550/arXiv.2605.03819>. A tutorial for this package can be found at <https://www.laylaparast.com/surrogaterank> and a Shiny App implementing the package can be found at <https://parastlab.shinyapps.io/SurrogateRankApp/>.
Authors: Layla Parast [aut, cre], Arthur Hughes [aut]
Maintainer: Layla Parast <[email protected]>
License: GPL
Version: 3.0
Built: 2026-05-20 19:36:53 UTC
Source: https://github.com/laylaparast/surrogaterank

Help Index

Calculates the rank-based test statistic for Y and S and the difference, delta

Description

Calculates the rank-based test statistic for Y and the rank-based test statistic for S and the difference, delta, along with corresponding standard error estimates

Usage

delta.calculate(full.data = NULL, yone = NULL, yzero = NULL, sone = NULL, szero = NULL)

Arguments

full.data

either full.data or yone, yzero, sone, szero must be supplied; if full data is supplied it must be in the following format: one observation per row, Y is in the first column, S is in the second column, treatment group (0 or 1) is in the third column.

yone

primary outcome, Y, in group 1

yzero

primary outcome, Y, in group 0

sone

surrogate marker, S, in group 1

szero

surrogate marker, S, in group 0

Value

u.y

rank-based test statistic for Y
u.s

rank-based test statistic for S
delta

difference, u.y-u.s
sd.u.y

standard error estimate of u.y
sd.u.s

standard error estimate of u.s
sd.delta

standard error estimate of delta

Author(s)

Layla Parast

Examples

data(example.data)
delta.calculate(yone = example.data$y1, yzero = example.data$y0, sone = example.data$s1, 
szero = example.data$s0)

Calculate Delta: Difference in Rank-based Statistics for Two Outcomes

Description

This function calculates the difference in treatment effects on a univariate marker and on a continuous primary response. This extends the delta.calculate() function from the SurrogateRank package to the case where samples may be paired instead of independent, and where a two sided test is desired.

Usage

delta.calculate.extension(
  yone,
  yzero,
  sone,
  szero,
  alpha = 0.05,
  paired = FALSE
)

Arguments

yone

numeric vector of primary response values in the treated group.
yzero

numeric vector of primary response values in the untreated group.
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of untreated samples and p the number of candidates. Sample ordering must match exactly yzero.
alpha

significance level of test, default is 0.05
paired

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero.

Details

This function estimates the difference (delta) between two rank-based statistics (e.g., Wilcoxon statistics or paired ranks) for a primary outcome and a surrogate, under either an independent or paired design.

Value

A list with the following elements:

  • u.y: Rank-based test statistic for the primary outcome

  • u.s: Rank-based test statistic for the surrogate

  • delta.estimate: Estimated difference between outcome and surrogate statistics

  • sd.u.y: Standard deviation of the outcome statistic

  • sd.u.s: Standard deviation of the surrogate statistic

  • sd.delta: Standard error of the delta estimate

Author(s)

Arthur Hughes, Layla Parast

Examples

# Load data
data("example.data")
yone <- example.data$y1
yzero <- example.data$y0
sone <- example.data$s1
szero <- example.data$s0
delta.calculate.extension.result <- delta.calculate.extension(
  yone, yzero, sone, szero,
  paired = TRUE
)

Function to perform meta-analysis of summary statistics and hypothesis testing for a single marker

Description

Function to perform meta-analysis of summary statistics and hypothesis testing for a single marker

Usage

delta.reml.meta(
  delta = NULL,
  sd.delta = NULL,
  epsilon = NULL,
  alpha = 0.05,
  alternative = "two.sided",
  tol = 1e-10,
  verbose = FALSE,
  test = "knha",
  meta.analysis.method = "RE"
)

Arguments

delta

numeric vector of delta values per study
sd.delta

numeric vector of standard error of delta values per study
epsilon

numeric non-inferiority margin for testing cross-study validity
alpha

numeric significance level of test. Note : using the two-one-sided test (alternative = "two.sided") produces a (1-2alpha)*100% confidence interval.
alternative

character giving the alternative hypothesis type for testing the summary effect. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
tol

numeric convergence tolerance for finding a root of the score equation
verbose

logical flag indicating whether messages should be printed, defaults to FALSE
test

character giving the type of test to be performed. The default is knha, corresponding to variance estimation using the more conservative Hartung-Knapp estimator and performes tests with the t-distribution, whereas setting this argument to z estimates the variance with the conventional estimator and uses a normal approximation for testing.
meta.analysis.method

character giving the meta-analysis method to be used. The default is RE, corresponding to random-effects meta-analysis, whereas setting this argument to FE uses fixed-effects meta-analysis.

Value

a list with elements

  • n.studies : numeric, number of studies considered

  • tau2 : numeric, estimated tau-squared (between-study heterogeneity)

  • mu.delta : numeric, estimated mean of distribution of delta

  • se.delta : numeric, standard error of delta summary estimate

  • ci.delta.upper : numeric, upper confidence interval for mean of delta. Note : if using the non-inferiority test (i.e. alternative = "less"), these bounds correspond to a (1-alpha)*100% confidence interval, whereas the two-one-sided test (i.e. alternative = "two.sided") corresponds to a (1-2alpha)*100% interval.

  • ci.delta.lower : numeric, lower confidence interval for mean of delta

  • p.lower : numeric, if alternative is "two.sided", gives the p-value corresponding to testing the null hypothesis that delta is less than -epsilon. Value is NULL if alternative is "less".

  • p.upper : numeric, if alternative is "two.sided", gives the p-value corresponding to testing the null hypothesis that delta is less than epsilon. Value is NULL if alternative is "less".

  • p : numeric, consensus p-value for hypothesis test for either the two-one-sided test or the non-inferiorty test.

  • Q : numeric, Cochran's Q-statistic for heterogeneity between studies

  • I2 : numeric, Higgins-Thompson I-squared statistic representing the total percentage of variation attributable to between-study heterogeneity

  • weights.tau : numeric vector of raw study weights for the summary measure

  • weights.tau.relative : numeric vector of relative study weights for the summary measure, such that each weight is a percentage adding to 100%

  • weights.tau.sum : numeric, sum of weights.tau

Author(s)

Arthur Hughes

Estimated power to detect a valid surrogate

Description

Calculates the estimated power to detect a valid surrogate given a total sample size and specified alternative

Usage

est.power(n.total, rho = 0.8, u.y.alt, delta.alt, power.want.s = 0.7, alpha = 0.05)

Arguments

n.total

total sample size in study

rho

rank correlation between Y and S in group 0, default is 0.8

u.y.alt

specified alternative for u.y

delta.alt

specified alternative for u.s

power.want.s

desired power for u.s, default is 0.7

alpha

significance level, default is 0.05

Value

estimated power

Author(s)

Layla Parast

Examples

est.power(n.total = 50, rho = 0.8, u.y.alt=0.9, delta.alt = 0.1)

Example data

Description

Example data use to illustrate the functions

Usage

data("example.data")

Format

A list with 4 elements representing 25 observations from a treatment group (group 1) and 25 observations from a control group (group 0):

y1

the primary outcome,Y, in group 1

y0

the primary outcome, Y, in group 0

s1

the surrogate marker, S, in group 1

s0

the surrogate marker, S, in group 0

Examples

data(example.data)

High‑dimensional surrogate candidate example dataset

Description

A simulated high‑dimensional dataset for demonstrating the RISE methodology implemented in SurrogateRank. The data contains primary response and 1000 surrogate candidates from 25 treated individuals and 25 untreated individuals, where 10% of the surrogate candidates are "valid".

Usage

data("example.data.highdim", package = "SurrogateRank")

Format

A list containing :

y1

primary response in treated

y0

primary response in untreated

s1

1000 surrogate candidates in treated

s0

1000 surrogate candidates in untreated

hyp

for each surrogate, null false if the surrogate is valid

Source

Simulated for package examples.

Examples

data("example.data.highdim", package = "SurrogateRank")
head(example.data.highdim)

High-dimensional, multi-study surrogate candidate example dataset

Description

A simulated high-dimensional, multi-study dataset for demonstrating the RISE-meta methodology implemented in SurrogateRank, generated with the generate.example.data.highdim.multistudy() function. The data contains treatment effect measures on the primary endpoint and on 500 surrogate candidates, where the first 50 of these candidates are "valid" surrogates.

Usage

data("example.data.highdim.multistudy", package = "SurrogateRank")

Format

A list with the following components:

uy

Numeric vector of length M containing treatment effects on the primary endpoint across trials.

us

Numeric matrix of dimension M times J containing treatment effects on each of the J candidate markers.

hyp

Vector of length J containing the truth of surrogate validity. null false corresponds to valid surrogates, whereas null true corresponds to invalid surrogates.

epsilon

Value of epsilon used to define surrogate validity.

Source

Simulated for package examples.

Examples

data("example.data.highdim.multistudy", package = "SurrogateRank")
head(example.data.highdim.multistudy)

High‑dimensional multi-study individual participant surrogate candidate example dataset

Description

A simulated high‑dimensional dataset for demonstrating the RISE-Meta methodology implemented in SurrogateRank. The data contains primary response and 100 surrogate candidates from 25 treated individuals and 25 untreated individuals across 5 different studies, where 10% of the surrogate candidates are "valid".

Usage

data("example.data.highdim.multistudy.ipd", package = "SurrogateRank")

Format

A list containing :

y1

primary response in treated

y0

primary response in untreated

s1

1000 surrogate candidates in treated

s0

1000 surrogate candidates in untreated

study1

study names for treated

study0

study names for untreated

hyp

for each surrogate, null false if the surrogate is valid

Source

Simulated for package examples.

Examples

data("example.data.highdim.multistudy.ipd", package = "SurrogateRank")
head(example.data.highdim.multistudy.ipd)

Generate individual participant data for high-dimensional surrogate candidates and response

Description

Generates individual participant data for high-dimensional surrogate candidates using one of two data generating processes, as described in Hughes A et al (2025) https://doi.org/10.1002/sim.70241.

Usage

generate.example.data.highdim(
  n1,
  n0,
  p,
  prop_valid,
  valid_sigma = 1,
  corr = 0,
  mode = "simple",
  y0_mean = 0,
  y0_sd = 1,
  y1_mean = 3,
  y1_sd = 1,
  s0_mean = 0,
  s0_sd = 1,
  s1_mean = 0,
  s1_sd = 1,
  seed = 12345
)

Arguments

n1

positive numeric giving the sample size in the treated group
n0

positive numeric giving the sample size in the untreated group
p

positive numeric giving the number of markers to generate
prop_valid

numeric between 0 and 1 (inclusive) giving the proportion of surrogate candidates to generate as valid.
valid_sigma

non-negative numeric giving the standard deviation for valid candidates
corr

non-negative numeric giving the correlation between the surrogate candidates
mode

character taking values in c("simple", "complex"). If "simple", generates all variables with (multivariate) normal distributions. Else, uses a more complex exponential distribution.
y0_mean

numeric giving the mean of the primary endpoint in the untreated group
y0_sd

non-negative numeric giving the standard deviation of the primary endpoint in the untreated group
y1_mean

numeric giving the mean of the primary endpoint in the treated group
y1_sd

non-negative numeric giving the standard deviation of the primary endpoint in the treated group
s0_mean

numeric giving the mean of the surrogate candidates in the untreated group
s0_sd

non-negative numeric giving the standard deviation of the surrogate candidates in the untreated group
s1_mean

numeric giving the mean of the surrogate candidates in the treated group
s1_sd

non-negative numeric giving the standard deviation of the surrogate candidates in the treated group
seed

numeric giving a seed for reproducibility

Value

A list with the following components:

y1

vector containing primary endpoint values in treated group

y0

vector containing primary endpoint values in untreated group

s1

n1 times p matrix containing surrogate candidate values in treated group

s0

n0 times p matrix containing surrogate candidate values in untreated group

hyp

character vector giving the truth behind the null hypothesis for each surrogate candidate

Examples

res <- generate.example.data.highdim(n1 = 25, n0 = 25, p = 500, prop_valid = 1)
dim(res$s1)       # 25 x 500

Generate high-dimensional multi-study surrogate marker trial-level effects

Description

Generates simulated trial-level treatment effects for multiple surrogate markers across multiple studies, including both valid and invalid surrogates. This function implements a hierarchical random-effects model: true trial-level effects are drawn from marker-specific means with between-trial heterogeneity, and observed trial-level effects include additional within-study sampling error.

Usage

generate.example.data.highdim.multistudy(
  epsilon = 0.2,
  M = 5,
  sample_sizes = c(25, 50, 100, 150, 250),
  J = 500,
  prop_valid = 0.1,
  u_tau_min = 0.01,
  u_tau_max = 0.1,
  u_nu_min = 0.01,
  u_nu_max = 0.1,
  prop_invalid_under = 0.5,
  invalid_at_boundary = FALSE,
  invalid_mean_discrete = NULL,
  valid_mean_discrete = NULL,
  seed = 12345
)

Arguments

epsilon

Numeric in (0,1). Defines the region of validity for the surrogate marker means. Markers with mean discrepancy within [-epsilon, epsilon] are valid; others are invalid.
M

Integer. Number of trials (studies) to simulate. Must be > 1.
sample_sizes

Numeric vector of length M. Sample size for each trial. Used to compute within-study variances.
J

Integer. Total number of markers to simulate (valid + invalid).
prop_valid

Numeric, between 0 and 1. Proportion of markers that are valid.
u_tau_min

Numeric >= 0. Lower bound of marker-specific between-trial heterogeneity variance (τj2\tau_j^2).
u_tau_max

Numeric >= u_tau_min. Upper bound of marker-specific between-trial heterogeneity variance (τj2\tau_j^2).
u_nu_min

Numeric > 0. Lower bound of marker-specific variance component (νj\nu_j) used to scale within-study sampling error.
u_nu_max

Numeric >= u_nu_min. Upper bound of marker-specific variance component (νj\nu_j) used to scale within-study sampling error.
prop_invalid_under

Numeric, between 0 and 1. Probability that an invalid marker underestimates the treatment effect on Y.
invalid_at_boundary

default FALSE, meaning invalid surrogates are generated uniformly across the entire invalid region. If TRUE, generates invalid surrogates at the boundary values defined by epsilon. This is the worst-case scenario for invalid surrogates and thus is useful for checking the calibration of the method.
invalid_mean_discrete

vector of discrete numeric values to sample true means of valid surrogates at. These values must be greater or equal in absolute value than epsilon.
valid_mean_discrete

vector of discrete numeric values to sample true means of valid surrogates at. These values must be smaller in absolute value than epsilon.
seed

numeric giving a seed for reproducibility

Details

The function first draws marker-level parameters: μδ,j\mu_{\delta,j} from the validity or invalidity region, τj2\tau_j^2 from a uniform distribution, and νj\nu_j from a uniform distribution. Then, for each trial, true trial-level effects are drawn as δm,jtrue∼N(μδ,j,τj2)\delta_{m,j}^{true} \sim N(\mu_{\delta,j}, \tau_j^2), and observed effects include independent within-study sampling error δ^m,j∼N(δm,jtrue,νj/nm)\hat{\delta}_{m,j} \sim N(\delta_{m,j}^{true}, \nu_j / n_m).

Value

A list with the following components:

delta

M x J matrix of observed trial-level discrepancies (δ^m,j\hat{\delta}_{m,j}) including sampling error.

sd.delta

M x J matrix of within-study standard deviations (σm,j\sigma_{m,j}).

n

Numeric vector of sample sizes for each trial.

hyp

Character vector of length J, "null true" for valid markers and "null false" for invalid markers.

mu.true

Numeric vector of true marker-level mean discrepancies (μδ,j\mu_{\delta,j}).

tau2.true

Numeric vector of marker-specific between-trial heterogeneity variances (τj2\tau_j^2).

Examples

res <- generate.example.data.highdim.multistudy(
  epsilon = 0.2,
  M = 5,
  sample_sizes = c(25, 50, 100, 150, 250),
  J = 500,
  prop_valid = 0.1
)
dim(res$delta)       # 5 x 500
head(res$mu.true)

Generate multi-study individual participant data for high-dimensional surrogate candidates and response

Description

Generates individual participant data for high-dimensional surrogate candidates using one of two data generating processes, as described in Hughes A et al (2025) https://doi.org/10.1002/sim.70241.

Usage

generate.example.data.highdim.multistudy.ipd(
  M,
  n1,
  n0,
  p,
  prop_valid,
  valid_sigma = 1,
  corr = 0,
  mode = "simple",
  y0_mean = 0,
  y0_sd = 1,
  y1_mean = 3,
  y1_sd = 1,
  s0_mean = 0,
  s0_sd = 1,
  s1_mean = 0,
  s1_sd = 1,
  seed = 12345
)

Arguments

M

number of studies
n1

positive numeric giving the sample size in the treated groups
n0

positive numeric giving the sample size in the untreated groups
p

positive numeric giving the number of markers to generate
prop_valid

numeric between 0 and 1 (inclusive) giving the proportion of surrogate candidates to generate as valid.
valid_sigma

non-negative numeric giving the standard deviation for valid candidates
corr

non-negative numeric giving the correlation between the surrogate candidates
mode

character taking values in c("simple", "complex"). If "simple", generates all variables with (multivariate) normal distributions. Else, uses a more complex exponential distribution.
y0_mean

numeric giving the mean of the primary endpoint in the untreated group
y0_sd

non-negative numeric giving the standard deviation of the primary endpoint in the untreated group
y1_mean

numeric giving the mean of the primary endpoint in the treated group
y1_sd

non-negative numeric giving the standard deviation of the primary endpoint in the treated group
s0_mean

numeric giving the mean of the surrogate candidates in the untreated group
s0_sd

non-negative numeric giving the standard deviation of the surrogate candidates in the untreated group
s1_mean

numeric giving the mean of the surrogate candidates in the treated group
s1_sd

non-negative numeric giving the standard deviation of the surrogate candidates in the treated group
seed

numeric giving a seed for reproducibility

Value

A list with the following components:

y1

vector containing primary endpoint values in treated group

y0

vector containing primary endpoint values in untreated group

s1

n1 times p matrix containing surrogate candidate values in treated group

s0

n0 times p matrix containing surrogate candidate values in untreated group

study1

study names for treated samples

study0

study names for untreated samples

hyp

character vector giving the truth behind the null hypothesis for each surrogate candidate

Examples

res <- generate.example.data.highdim.multistudy.ipd(
M = 5,
n1 = 25,
n0 = 25,
p = 500,
prop_valid = 1
)
dim(res$s1)       # (5 studies x 25 individuals = 125) x 500

Function to perform the evaluation stage of RISE : Two-Stage Rank-Based Identification of High-Dimensional Surrogate Markers

Description

A set of high-dimensional surrogate candidates are evaluated jointly. Strength of surrogacy is assessed through a rank-based measure of the similarity in treatment effects on a candidate surrogate and the primary response.

Usage

rise.evaluate(
  yone,
  yzero,
  sone,
  szero,
  alpha = 0.05,
  power.want.s = NULL,
  epsilon = NULL,
  u.y.hyp = NULL,
  p.correction = "BH",
  n.cores = 1,
  alternative = "two.sided",
  paired = FALSE,
  return.all.evaluate = TRUE,
  return.plot.evaluate = TRUE,
  evaluate.weights = TRUE,
  screening.weights = NULL,
  markers = NULL
)

Arguments

yone

numeric vector of primary response values in the treated group.
yzero

numeric vector of primary response values in the untreated group.
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of untreated samples and p the number of candidates. Sample ordering must match exactly yzero.
alpha

significance level for determining surrogate candidates. Default is 0.05.
power.want.s

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. Either this or epsilon argument must be specified.
epsilon

numeric in (0,1) - non-inferiority margin for determining surrogate validity. Either this or power.want.s argument must be specified.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
p.correction

character. Method for p-value adjustment (see p.adjust() function). Defaults to the Benjamini-Hochberg method ("BH").
n.cores

numeric giving the number of cores to commit to parallel computation in order to improve computational time through the pbmcapply() function. Defaults to 1.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
paired

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero.
return.all.evaluate

logical flag. If TRUE (default), a dataframe will be returned giving the evaluation of each individual marker passed to the evaluation stage.
return.plot.evaluate

logical flag. If TRUE (default), a ggplot2 object will be returned allowing the user to visualise the association between the composite surrogate on the individual-scale.
evaluate.weights

logical flag. If TRUE (default), the composite surrogate is constructed with weights such that surrogates which are predicted to be stronger receive more weight.
screening.weights

dataframe with columns marker and weight giving the weight in for the evaluation. Typically this is taken directly from the screening stage as the output from the rise.screen() function. Must be given if evaluate.weights is TRUE.
markers

a vector of marker names (column names of szero and sone) to evaluate. If not given, will default to evaluating all markers in the dataframes.

Value

a list with

  • individual.metrics if return.all.evaluate=TRUE, a dataframe of evaluation results for each significant marker.

  • gamma.s a list with elements gamma.s.one and gamma.s.zero, giving the combined surrogate marker in the treated and untreated groups, respectively.

  • gamma.s.evaluate : a dataframe giving the evaluation of gamma.s

  • gamma.s.plot : a ggplot2 plot showing gamma.s against the primary response on the rank-scale.

Author(s)

Arthur Hughes

Examples

# Load high-dimensional example data

Function to perform the evaluation stage of RISE-meta : Meta-Analysis of High-Dimensional Surrogate Markers

Description

Function to perform the evaluation stage of RISE-meta : Meta-Analysis of High-Dimensional Surrogate Markers

Usage

rise.evaluate.meta(
  yone,
  yzero,
  sone,
  szero,
  studyone,
  studyzero,
  alpha = 0.05,
  power.want.s.study = NULL,
  epsilon.study = NULL,
  epsilon.meta.mode = "user",
  epsilon.meta = NULL,
  u.y.hyp = NULL,
  p.correction = "BH",
  n.cores = 1,
  alternative = "two.sided",
  test = "knha",
  paired.all = FALSE,
  paired.studies = NULL,
  evaluate.weights = TRUE,
  screening.weights = NULL,
  weight.mode = "diff.epsilon",
  markers = NULL,
  return.all.evaluate = FALSE,
  return.forest.plot = TRUE,
  return.fit.plot = TRUE,
  show.pooled.effect = TRUE,
  meta.analysis.method = "RE"
)

Arguments

yone

numeric vector of primary response values in the treated participants
yzero

numeric vector of primary response values in the untreated participants
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yzero.
studyone

character vector of length n1 indicating the study corresponding to each treated sample. Ordering much match yone.
studyzero

character vector of length n0 indicating the study corresponding to each untreated sample. Ordering much match yzero.
alpha

significance level for determining valid surrogates. Default is 0.05.
power.want.s.study

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. If return.all.evaluate = TRUE, either this or epsilon.study argument must be specified.
epsilon.study

numeric in (0,1) - non-inferiority margin for determining surrogate validity in the within-study screening phase. If return.all.evaluate = TRUE, either this or power.want.s.study argument must be specified.
epsilon.meta.mode

character string specifying the mode to choose the value of the acceptable margin defined by epsilon. By default, this is set to "user", where the value of epsilon is fixed by the user, defined by the value of the argument epsilon.meta. The alternative is to set this as "mean.power", which corresponds to taking the mean value of epsilon across studies such that the power to detect departures from the null within each study is defined by the power.want.s.study argument.
epsilon.meta

numeric in (0,1) - non-inferiority margin for determining surrogate validity in the meta-analysis stage. Must be specified.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
p.correction

character. Method for p-value adjustment (see p.adjust() function). Defaults to the Benjamini-Hochberg method ("BH").
n.cores

numeric giving the number of cores to commit to parallel computation in order to improve computational time through the pbmcapply() function. Defaults to 1.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
test

character giving the type of test to be performed. The default is knha, corresponding to variance estimation using the more conservative Hartung-Knapp estimator and performes tests with the t-distribution, whereas setting this argument to z estimates the variance with the conventional estimator and uses a normal approximation for testing.
paired.all

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, all samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero, and all studies must be paired. If only some studies are paired and others have independent samples, one may specify the paired.studies argument instead.
paired.studies

character vector specifying the names of the studies in studyone or studyzero which are paired, in the case where some have paired designs and others do not. By default, this is NULL, indicating that study designs are all specified by the paired.all argument.
evaluate.weights

logical flag. If TRUE (default), the composite surrogate is constructed with weights such that surrogates which are predicted to be stronger receive more weight.
screening.weights

dataframe with columns marker and weight giving the weight in for the evaluation. Typically this is taken directly from the screening stage as the output from the rise.screen.meta() function. Must be given if evaluate.weights is TRUE.
weight.mode

character giving the type of weighting to return to be used in case return.all.evaluate = TRUE. See rise.screen.meta() for detail.
markers

a vector of marker names (column names of szero and sone) to evaluate. If not given, will default to evaluating all markers in the dataframes.
return.all.evaluate

logical flag. If TRUE, a dataframe will be returned giving the meta-analysis evaluation of each individual marker passed to the evaluation stage. Defaults to FALSE for computational time.
return.forest.plot

logical flag. If TRUE (default), a forest plot of the effect sizes for the combined signature across studies, with its meta-analysis summary measure, will be included in the output.
return.fit.plot

logical flag. If TRUE (default), a plot of the effects on the primary response versus the effects on the combined surrogate signature for each study will be included in the output.
show.pooled.effect

logical flag. If TRUE (default), the forest plot will show the pooled effect estimate. Otherwise, it will just show the individual trial estimates.
meta.analysis.method

character giving the meta-analysis method to be used. The default is RE, corresponding to random-effects meta-analysis, whereas setting this argument to FE uses fixed-effects meta-analysis.

Value

a list with elements

  • individual.metrics : if return.all.evaluate=TRUE, a list containing dataframes individual.metrics.study (per-study results for individual markers) and individual.metrics.meta (meta-analysis results for individual markers).

  • evaluation.metrics.study : study-level results for the combined marker, gamma.

  • evaluation.metrics.meta : meta-analysis results for the combined marker, gamma.

  • gamma.s : a list with elements gamma.s.one and gamma.s.zero, giving the values of the combined surrogate marker gamma in the treated and untreated groups, respectively.

  • gamma.s.plot : if return.forest.plot and/or return.fit.plot are TRUE, returns evaluation plots as a list

Author(s)

Arthur Hughes

Examples

data("example.data.highdim.multistudy.ipd")
yone <- example.data.highdim.multistudy.ipd$y1
yzero <- example.data.highdim.multistudy.ipd$y0
sone <- example.data.highdim.multistudy.ipd$s1
szero <- example.data.highdim.multistudy.ipd$s0
studyone <- example.data.highdim.multistudy.ipd$study1
studyzero <- example.data.highdim.multistudy.ipd$study0
rise.meta.screen.result <- rise.screen.meta(
yone, yzero, 
sone, szero, 
studyone, studyzero, 
epsilon.study = 0.2, epsilon.meta = 0.2
)
markers = rise.meta.screen.result[["significant.markers"]]
screening.weights = rise.meta.screen.result[["screening.weights"]]
rise.meta.evaluate.result <- rise.evaluate.meta(
yone, yzero, 
sone, szero, 
studyone, studyzero, 
epsilon.meta = 0.2, 
markers = markers, 
screening.weights = screening.weights, 
epsilon.study = 0.2
)

Function to perform the screening stage of RISE : Two-Stage Rank-Based Identification of High-Dimensional Surrogate Markers

Description

A set of high-dimensional surrogate candidates are screened one-by-one to identify strong candidates. Strength of surrogacy is assessed through a rank-based measure of the similarity in treatment effects on a candidate surrogate and the primary response. P-values corresponding to hypothesis testing on this measure are corrected for the high number of statistical tests performed.

Usage

rise.screen(
  yone,
  yzero,
  sone,
  szero,
  alpha = 0.05,
  power.want.s = NULL,
  epsilon = NULL,
  u.y.hyp = NULL,
  p.correction = "BH",
  n.cores = 1,
  alternative = "two.sided",
  paired = FALSE,
  return.all.screen = TRUE,
  return.all.weights = FALSE,
  weight.mode = "inverse.delta",
  normalise.weights = TRUE,
  verbose = T
)

Arguments

yone

numeric vector of primary response values in the treated group.
yzero

numeric vector of primary response values in the untreated group.
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of untreated samples and p the number of candidates. Sample ordering must match exactly yzero.
alpha

significance level for determining surrogate candidates. Default is 0.05.
power.want.s

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. Either this or epsilon argument must be specified.
epsilon

numeric in (0,1) - non-inferiority margin for determining surrogate validity. Either this or power.want.s argument must be specified.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
p.correction

character. Method for p-value adjustment (see p.adjust() function). Defaults to the Benjamini-Hochberg method ("BH").
n.cores

numeric giving the number of cores to commit to parallel computation in order to improve computational time through the pbmcapply() function. Defaults to 1.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
paired

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero.
return.all.screen

logical flag. If TRUE (default), a dataframe will be returned giving the screening results for all candidates. Else, only the significant candidates will be returned.
return.all.weights

logical flag. If FALSE (default), a dataframe will be returned giving weights for significant markers screened. If TRUE, weights for all markers will be returned. Note that, if normalised weights are required, these will only be returned for significant markers, and raw weights will be returned in a second column.
weight.mode

character giving the type of weighting to return. One of c("inverse.delta","diff.epsilon", or "none"). The default is "inverse.delta", which means the weights are determined by taking the inverse of the absolute values of delta. If delta is exactly 0, this is uncomputable and the weight defaults to the inverse of the next closest absolute delta value. If delta is very close to 0, these estimates can be unstable and extreme. The "diff.epsilon" option seeks to aid this by calculating weights as the proportion of the interval between 0 and epsilon cut by the absolute value of delta, therefore giving delta = 0 a weight of 1 and delta = epsilon a weight of 0. When "none", the weights are set to 1 for every marker.
normalise.weights

logical flag. If TRUE (default), the weights are normalised by the sum of all the weights such that the maximum weight is 1, which can help with interpretability.
verbose

logical flag. If TRUE, prints warning messages.

Value

a list with elements

  • screening.metrics : dataframe of screening results (for each candidate marker - number of observations n, u.y, u.s, delta, CI, sd, epsilon, p-values).

  • significant.markers: character vector of markers with p_adjusted < alpha

  • screening.weights: dataframe giving marker names and the inverse absolute value of the associated deltas.

Author(s)

Arthur Hughes

Examples

# Load high-dimensional example data

Function to perform the screening stage of RISE-meta : Meta-Analysis of High-Dimensional Surrogate Markers

Description

The RISE screening algorithm is applied to each study using a rank-based measure of treatment effect similarity. In the second stage, these effect estimates are combined using a random-effects meta-analysis and the retained markers are those for which there is strong evidence of surrogacy across many studies.

Usage

rise.screen.meta(
  yone,
  yzero,
  sone,
  szero,
  studyone,
  studyzero,
  alpha = 0.05,
  power.want.s.study = NULL,
  epsilon.study = NULL,
  epsilon.meta.mode = "user",
  epsilon.meta = NULL,
  u.y.hyp = NULL,
  p.correction = "BH",
  n.cores = 1,
  alternative = "two.sided",
  test = "knha",
  paired.all = FALSE,
  paired.studies = NULL,
  return.all.screen = TRUE,
  return.all.weights = FALSE,
  weight.mode = "diff.epsilon",
  return.screen.plot = TRUE,
  screen.plot.topN = 15,
  screen.plot.point.estimate = FALSE,
  normalise.weights = TRUE,
  return.forest.plot = TRUE,
  return.fit.plot = TRUE,
  show.pooled.effect = TRUE,
  return.study.similarity.plot = TRUE,
  return.evaluate.results = TRUE,
  meta.analysis.method = "RE"
)

Arguments

yone

numeric vector of primary response values in the treated participants
yzero

numeric vector of primary response values in the untreated participants
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yzero.
studyone

character vector of length n1 indicating the study corresponding to each treated sample. Ordering much match yone.
studyzero

character vector of length n0 indicating the study corresponding to each untreated sample. Ordering much match yzero.
alpha

significance level for determining surrogate candidates in both stages. Default is 0.05.
power.want.s.study

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. Either this or epsilon.study argument must be specified.
epsilon.study

numeric in (0,1) - non-inferiority margin for determining surrogate validity in the within-study screening phase. Either this or power.want.s.study argument must be specified.
epsilon.meta.mode

character string specifying the mode to choose the value of the acceptable margin defined by epsilon. By default, this is set to "user", where the value of epsilon is fixed by the user, defined by the value of the argument epsilon.meta. The alternative is to set this as "mean.power", which corresponds to taking the mean value of epsilon across studies such that the power to detect departures from the null within each study is defined by the power.want.s.study argument.
epsilon.meta

numeric in (0,1) - fixed non-inferiority margin for determining surrogate validity in the meta-analysis stage.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
p.correction

character. Method for p-value adjustment (see p.adjust() function). Defaults to the Benjamini-Hochberg method ("BH").
n.cores

numeric giving the number of cores to commit to parallel computation in order to improve computational time through the pbmcapply() function. Defaults to 1.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
test

character giving the type of test to be performed. The default is knha, corresponding to variance estimation using the more conservative Hartung-Knapp estimator and performes tests with the t-distribution, whereas setting this argument to z estimates the variance with the conventional estimator and uses a normal approximation for testing.
paired.all

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, all samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero, and all studies must be paired. If only some studies are paired and others have independent samples, one may specify the paired.studies argument instead.
paired.studies

character vector specifying the names of the studies in studyone or studyzero which are paired, in the case where some have paired designs and others do not. By default, this is NULL, indicating that study designs are all specified by the paired.all argument.
return.all.screen

logical flag. If TRUE (default), a dataframe will be returned giving the screening results for all candidates. Else, only the significant candidates will be returned.
return.all.weights

logical flag. If FALSE (default), a dataframe will be returned giving weights for significant markers screened. If TRUE, weights for all markers will be returned. Note that, if normalised weights are required, these will only be returned for significant markers, and raw weights will be returned in a second column.
weight.mode

character giving the type of weighting to return. One of c("diff.epsilon", "inverse.delta", or "none"). The default is "diff.epsilon", which calculates weights as the proportion of the interval between 0 and epsilon.study cut by the absolute value of delta, therefore giving delta = 0 a weight of 1 and delta = epsilon.study a weight of 0. Another option is "inverse.delta" where the weights are determined by taking the inverse of the absolute values of delta. When "none", the weights are set to 1 for every marker.
return.screen.plot

logical flag. If TRUE (default), returns a forest plot of the top predictors, sorted by p-value, from the screening stage. The number of predictors to display is given by the screen.plot.topN argument, which has default value 15.
screen.plot.topN

number of predictors to display in the screening results figure, default value is 15.
screen.plot.point.estimate

logical flag. If FALSE (default), uses the screen.plot.topN argument to determine how many markers to display on the screen plot. Otherwise, plots all the markers with a point estimate within the equivalence region.
normalise.weights

logical flag. If TRUE (default), the weights are normalised by the sum of all the weights such that the maximum weight is 1, which can help with interpretability.
return.forest.plot

logical flag. If TRUE (default), a forest plot of the effect sizes for the combined signature across studies, with its meta-analysis summary measure and prediction interval, will be included in the output.
return.fit.plot

logical flag. If TRUE (default), a plot of the effects on the primary response versus the effects on the combined surrogate signature for each study will be included in the output.
show.pooled.effect

logical flag. If TRUE (default), the forest plot will show the pooled effect estimate. Otherwise, it will just show the individual trial estimates.
return.study.similarity.plot

logical flag. If TRUE (default), will return two plots showing the similarity between study-wise marker signatures (i.e., the application of RISE to each study individually, with p-value correction within-study).
return.evaluate.results

logical flag. If TRUE (default), returns results for combined marker gamma, evaluated on the same data. Can be useful to set this as FALSE to save computational time if this is not of interest.
meta.analysis.method

character giving the meta-analysis method to be used. The default is RE, corresponding to random-effects meta-analysis, whereas setting this argument to FE uses fixed-effects meta-analysis.

Value

a list with elements

  • screening.metrics.study : dataframe of per-study results from RISE screening. For each candidate marker - study name, study sample size, estimate of delta, standard error of delta.

  • screening.metrics.meta : dataframe of meta-analysis screening results. For each candidate marker - number of studies n.studies, estimate of mean delta value mu.delta, its standard error se.delta, confidence interval and prediction interval, estimate of tau-squared tau2, Cochran's Q-statistic and Higgins-Thompson I-Squared, unadjusted and adjusted meta-analysis p-values, and standardised weights. Note : if using the non-inferiority test (i.e. alternative = "less"), the intervals have width (1-alpha)*100%, whereas the two-one-sided test (i.e. alternative = "two.sided") corresponds to a (1-2alpha)*100% width.

  • significant.markers: character vector of markers with meta-analysis p-values < alpha

  • screening.weights: dataframe giving marker names and the standardised meta-analysis weights

  • evaluation.metrics.study : dataframe of per-study results for the combined marker gamma, evaluated on the same data

  • evaluation.metrics.meta : dataframe of meta-analysis results for the combined marker gamma, evaluated on the same data

  • gamma.s.plot: if return.forest.plot, return.fit.plot, and/or return.study.similarity.plot are TRUE, returns fitted evaluation plots on training data as a list.

Author(s)

Arthur Hughes

Examples

data("example.data.highdim.multistudy.ipd")
yone <- example.data.highdim.multistudy.ipd$y1
yzero <- example.data.highdim.multistudy.ipd$y0
sone <- example.data.highdim.multistudy.ipd$s1
szero <- example.data.highdim.multistudy.ipd$s0
studyone <- example.data.highdim.multistudy.ipd$study1
studyzero <- example.data.highdim.multistudy.ipd$study0
rise.meta.screen.result <- rise.screen.meta(
yone, yzero, 
sone, szero, 
studyone, studyzero, 
epsilon.study = 0.2, epsilon.meta = 0.2
)

Tests whether the surrogate is valid

Description

Calculates the rank-based test statistic for Y and the rank-based test statistic for S and the difference, delta, along with corresponding standard error estimates, then tests whether the surrogate is valid

Usage

test.surrogate(full.data = NULL, yone = NULL, yzero = NULL, sone = NULL, 
szero = NULL, epsilon = NULL, power.want.s = 0.7, u.y.hyp = NULL, alpha = 0.05)

Arguments

full.data

either full.data or yone, yzero, sone, szero must be supplied; if full data is supplied it must be in the following format: one observation per row, Y is in the first column, S is in the second column, treatment group (0 or 1) is in the third column.

yone

primary outcome, Y, in group 1

yzero

primary outcome, Y, in group 0

sone

surrogate marker, S, in group 1

szero

surrogate marker, S, in group 0

epsilon

threshold to use for delta, default calculates epsilon as a function of desired power for S

power.want.s

desired power for S, default is 0.7

u.y.hyp

hypothesized value of u.y used in the calculation of epsilon, default uses estimated valued of u.y

alpha

significance level, default is 0.05

Value

u.y

rank-based test statistic for Y
u.s

rank-based test statistic for S
delta

difference, u.y-u.s
sd.u.y

standard error estimate of u.y
sd.u.s

standard error estimate of u.s
sd.delta

standard error estimate of delta
ci.delta

1-sided confidence interval for delta
epsilon.used

the epsilon value used for the test
is.surrogate

logical, TRUE if test indicates S is a good surrogate, FALSE otherwise

Author(s)

Layla Parast

Examples

data(example.data)
test.surrogate(yone = example.data$y1, yzero = example.data$y0, sone = example.data$s1, 
szero = example.data$s0)

Function to test for trial-level surrogacy of a single marker extended to the paired, two sided test setting

Description

This function tests for surrogacy of a univariate marker with respect to a continuous primary response. This extends the test.surrogate() function from the SurrogateRank package to the case where samples may be paired instead of independent, and where a two sided test is desired.

Usage

test.surrogate.extension(
  yone,
  yzero,
  sone,
  szero,
  alpha = 0.05,
  power.want.s = NULL,
  epsilon = NULL,
  u.y.hyp = NULL,
  alternative = "two.sided",
  paired = FALSE
)

Arguments

yone

numeric vector of primary response values in the treated group.
yzero

numeric vector of primary response values in the untreated group.
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of untreated samples and p the number of candidates. Sample ordering must match exactly yzero.
alpha

significance level for determining surrogate candidates. Default is 0.05.
power.want.s

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. Either this or epsilon argument must be specified.
epsilon

numeric in (0,1) - non-inferiority margin for determining surrogate validity. Either this or power.want.s argument must be specified.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
paired

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero.

Value

A list containing:

  • u.y: Estimated rank-based treatment effect on the outcome.

  • u.s: Estimated rank-based treatment effect on the surrogate.

  • delta.estimate: Estimated difference in treatment effects: u.y - u.s.

  • sd.u.y: Standard deviation of u.y.

  • sd.u.s: Standard deviation of u.s.

  • sd.delta: Standard deviation of delta.estimate.

  • ci.delta: One-sided confidence interval upper bound for delta.estimate.

  • p.delta: p-value for validity of trial-level surrogacy.

  • epsilon.used: Non-inferiority threshold used in the test.

  • is.surrogate: TRUE if the surrogate passes the test, else FALSE.

Author(s)

Arthur Hughes, Layla Parast

Examples

# Load data
data("example.data")
yone <- example.data$y1
yzero <- example.data$y0
sone <- example.data$s1
szero <- example.data$s0
test.surrogate.extension.result <- test.surrogate.extension(
  yone, yzero, sone, szero,
  power.want.s = 0.8, paired = TRUE, alternative = "two.sided"
)

Function to perform RISE : Two-Stage Rank-Based Identification of High-Dimensional Surrogate Markers

Description

RISE (Rank-Based Identification of High-Dimensional Surrogate Markers) is a two-stage method to identify and evaluate high-dimensional surrogate candidates of a continuous response.

In the first stage (called screening), the high-dimensional candidates are screened one-by-one to identify strong candidates. Strength of surrogacy is assessed through a rank-based measure of the similarity in treatment effects on a candidate surrogate and the primary response. P-values corresponding to hypothesis testing on this measure are corrected for the high number of statistical tests performed.

In the second stage (called evaluation), candidates with an adjusted p-value below a given significance level are evaluated by combining them into a single synthetic marker. The surrogacy of this marker is then assessed with the univariate test as described before.

To avoid overfitting, the two stages are performed on separate data.

Usage

test.surrogate.rise(
  yone,
  yzero,
  sone,
  szero,
  alpha = 0.05,
  power.want.s = NULL,
  epsilon = NULL,
  u.y.hyp = NULL,
  p.correction = "BH",
  n.cores = 1,
  alternative = "two.sided",
  paired = FALSE,
  screen.proportion = 0.66,
  return.all.screen = TRUE,
  return.all.evaluate = TRUE,
  return.plot.evaluate = TRUE,
  evaluate.weights = TRUE,
  return.all.weights = FALSE,
  weight.mode = "inverse.delta",
  normalise.weights = TRUE
)

Arguments

yone

numeric vector of primary response values in the treated group.
yzero

numeric vector of primary response values in the untreated group.
sone

matrix or dataframe of surrogate candidates in the treated group with dimension n1 x p where n1 is the number of treated samples and p the number of candidates. Sample ordering must match exactly yone.
szero

matrix or dataframe of surrogate candidates in the untreated group with dimension n0 x p where n0 is the number of untreated samples and p the number of candidates. Sample ordering must match exactly yzero.
alpha

significance level for determining surrogate candidates. Default is 0.05.
power.want.s

numeric in (0,1) - power desired for a test of treatment effect based on the surrogate candidate. Either this or epsilon argument must be specified.
epsilon

numeric in (0,1) - non-inferiority margin for determining surrogate validity. Either this or power.want.s argument must be specified.
u.y.hyp

hypothesised value of the treatment effect on the primary response on the probability scale. If not given, it will be estimated based on the observations.
p.correction

character. Method for p-value adjustment (see p.adjust() function). Defaults to the Benjamini-Hochberg method ("BH").
n.cores

numeric giving the number of cores to commit to parallel computation in order to improve computational time through the pbmcapply() function. Defaults to 1.
alternative

character giving the alternative hypothesis type. One of c("less","two.sided"), where "less" corresponds to a non-inferiority test and "two.sided" corresponds to a two one-sided test procedure. Default is "two.sided".
paired

logical flag giving if the data is independent or paired. If FALSE (default), samples are assumed independent. If TRUE, samples are assumed to be from a paired design. The pairs are specified by matching the rows of yone and sone to the rows of yzero and szero.
screen.proportion

numeric in (0,1) - proportion of data to be used for the screening stage. The default is 2/3. If 1 is given, screening and evaluation will be performed on the same data.
return.all.screen

logical flag. If TRUE (default), a dataframe will be returned giving the screening results for all candidates. Else, only the significant candidates will be returned.
return.all.evaluate

logical flag. If TRUE (default), a dataframe will be returned giving the evaluation of each individual marker passed to the evaluation stage.
return.plot.evaluate

logical flag. If TRUE (default), a ggplot2 object will be returned allowing the user to visualise the association between the composite surrogate on the individual-scale.
evaluate.weights

logical flag. If TRUE (default), the composite surrogate is constructed with weights such that surrogates which are predicted to be stronger receive more weight.
return.all.weights

logical flag. If FALSE (default), a dataframe will be returned giving weights for significant markers screened. If TRUE, weights for all markers will be returned. Note that, if normalised weights are required, these will only be returned for significant markers, and raw weights will be returned in a second column.
weight.mode

character giving the type of weighting to return. One of c("inverse.delta","diff.epsilon", or "none"). The default is "inverse.delta", which means the weights are determined by taking the inverse of the absolute values of delta. If delta is exactly 0, this is uncomputable and the weight defaults to the inverse of the next closest absolute delta value. If delta is very close to 0, these estimates can be unstable and extreme. The "diff.epsilon" option seeks to aid this by calculating weights as the proportion of the interval between 0 and epsilon cut by the absolute value of delta, therefore giving delta = 0 a weight of 1 and delta = epsilon a weight of 0. When "none", the weights are set to 1 for every marker.
normalise.weights

logical flag. If TRUE (default), the weights are normalised by the sum of all the weights such that the maximum weight is 1, which can help with interpretability.

Value

a list with

  • screening.results: a list with

    • screening.metrics : dataframe of screening results (for each candidate marker - number of observations n, u.y, u.s, delta, CI, sd, epsilon, p-values)

    • significant_markers: character vector of markers with p_adjusted < alpha.

  • evaluate.results: a list with

    • individual.metrics if return.all.evaluate=TRUE, a dataframe of evaluation results for each significant marker.

    • gamma.s a list with elements gamma.s.one and gamma.s.zero, giving the combined surrogate marker in the treated and untreated groups, respectively.

    • gamma.s.evaluate : a dataframe giving the evaluation of gamma.s

    • gamma.s.plot : a ggplot2 plot showing gamma.s against the primary response on the rank-scale.

Author(s)

Arthur Hughes

Examples

# Load high-dimensional example data