Package 'surrosurv'

Title: Evaluation of Failure Time Surrogate Endpoints in Individual Patient Data Meta-Analyses
Description: Provides functions for the evaluation of surrogate endpoints when both the surrogate and the true endpoint are failure time variables. The approaches implemented are: (1) the two-step approach (Burzykowski et al, 2001) <DOI:10.1111/1467-9876.00244> with a copula model (Clayton, Plackett, Hougaard) at the first step and either a linear regression of log-hazard ratios at the second step (either adjusted or not for measurement error); (2) mixed proportional hazard models estimated via mixed Poisson GLM (Rotolo et al, 2017 <DOI:10.1177/0962280217718582>).
Authors: Federico Rotolo [aut] , Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] , Dan Chaltiel [cre]
Maintainer: Dan Chaltiel <[email protected]>
License: GPL-2
Version: 1.1.26
Built: 2024-11-12 04:56:38 UTC
Source: https://github.com/oncostat/surrosurv

Help Index

Evaluation of Failure Time Surrogate Endpoints in Individual Patient Data Meta-Analyses

Description

Provides functions for the evaluation of surrogate endpoints when both the surrogate and the true endpoint are failure time variables. The approaches implemented are: (1) the two-step approach (Burzykowski et al, 2001) <DOI:10.1111/1467-9876.00244> with a copula model (Clayton, Plackett, Hougaard) at the first step and either a linear regression of log-hazard ratios at the second step (either adjusted or not for measurement error); (2) mixed proportional hazard models estimated via mixed Poisson GLM (Rotolo et al, 2017 <DOI:10.1177/0962280217718582>).

Details

The DESCRIPTION file:

Package: surrosurv
Type: Package
Title: Evaluation of Failure Time Surrogate Endpoints in Individual Patient Data Meta-Analyses
Version: 1.1.26
Authors@R: c( person("Federico", "Rotolo", role="aut", email="[email protected]", comment = c(ORCID = "0000-0003-4837-6501")), person("Xavier", "Paoletti", role="ctb"), person("Marc", "Buyse", role="ctb"), person("Tomasz", "Burzykowski", role="ctb"), person("Stefan", "Michiels", role="ctb", email="[email protected]", comment = c(ORCID = "0000-0002-6963-2968")), person("Dan", "Chaltiel", role="cre", email="[email protected]", comment = c(ORCID = "0000-0003-3488-779X")))
Maintainer: Dan Chaltiel <[email protected]>
Description: Provides functions for the evaluation of surrogate endpoints when both the surrogate and the true endpoint are failure time variables. The approaches implemented are: (1) the two-step approach (Burzykowski et al, 2001) <DOI:10.1111/1467-9876.00244> with a copula model (Clayton, Plackett, Hougaard) at the first step and either a linear regression of log-hazard ratios at the second step (either adjusted or not for measurement error); (2) mixed proportional hazard models estimated via mixed Poisson GLM (Rotolo et al, 2017 <DOI:10.1177/0962280217718582>).
Depends: R (>= 3.5.0)
Imports: copula, eha, grDevices, lme4, MASS, Matrix, msm, mvmeta, optimx, parallel, parfm, stats, survival
License: GPL-2
URL: https://github.com/Oncostat/surrosurv
BugReports: https://github.com/Oncostat/surrosurv/issues/
VignetteBuilder: R.rsp
Suggests: R.rsp, testthat (>= 3.0.0)
Encoding: UTF-8
Config/testthat/edition: 3
Config/pak/sysreqs: cmake make libgsl0-dev
Repository: https://oncostat.r-universe.dev
RemoteUrl: https://github.com/oncostat/surrosurv
RemoteRef: HEAD
RemoteSha: 0fac54249f9f3eae82fc1dadd526e8b729389dc1
Author: Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

Index of help topics: 

convergence             Assesses the convergence of fitted models for
                        surrogacy evaluation
gastadj                 Individual data from the adjuvant GASTRIC
                        meta-analysis
gastadv                 Individual data from the advanced GASTRIC
                        meta-analysis
loocv                   Leave-one-trial-out cross-validation for
                        treatment effect prediction
poissonize              Transform survival data for fitting a Poisson
                        model
simData.re              Generate survival times for two endpoints in a
                        meta-analysis of randomized trials
ste                     Surrogate threshold effect
surrosurv               Fit and print the models for evaluating the
                        surrogacy strength of a candidate surrogate
                        endpoint
surrosurv-package       Evaluation of Failure Time Surrogate Endpoints
                        in Individual Patient Data Meta-Analyses

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

Maintainer: Dan Chaltiel <[email protected]>

References

Rotolo F, Paoletti X, Burzykowski T, Buyse M, Michiels S. A Poisson approach for the validation of failure time surrogate endpoints in individual patient data meta-analyses. Statistical Methods in Medical Research 2017; In Press. doi:10.1177/0962280217718582

Burzykowski T, Molenberghs G, Buyse M et al. Validation of surrogate end points in multiple randomized clinical trials with failure time end points. Journal of the Royal Statistical Society C 2001; 50:405–422. doi:10.1111/1467-9876.00244

Gasparrini A, Armstrong B, Kenward MG. Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine 2012; 31:3821–39. doi:10.1002/sim.5471

Burzykowski T, Molenberghs G, Buyse M (2005). The Evaluation of Surrogate Endpoints. Springer, New York. https://rd.springer.com/book/10.1007/b138566

See Also

Surrogate, mvmeta

Assesses the convergence of fitted models for surrogacy evaluation

Description

This function evaluates whether the fitted models for evaluating the surrogacy of a candidate endpoint have converged. Convergence is assessed by checking whether the maximum gradient is small enough, and whether the Hessian matrix and the variance-covariance matrix of random treatment effects are positive definite.

Usage

## S3 method for class 'surrosurv'
convals(x, ...)
  ## S3 method for class 'surrosurv'
convergence(x, kkttol = 1e-2, kkt2tol = 1e-8, ...)

Arguments

x

The fitted models, an object of class surrosurv.

kkttol

The tolerance threshold for the assessing whether the maximum (absolute) scaled gradient is small enough.

kkt2tol

The tolerance threshold for checking whether the Hessian matrix and the variance-covariance matrix of random treatment effects are positive definite. The threshold is for the minimum of the eigenvalues.

...

Further parameters (not implemented)

Value

The function convals() returns a matrix with one row per model and three columns, reporting the values of the maximum scaled gradient (maxSgrad), of the minimum eigenvalue of the Hessian matrix (minHev), and of the minimum eigenvalue of the estimated variance-covariance matrix of random treatment effects (minREev). The function convergence() returns a matrix with the same structure as convals(), with TRUE/FALSE values for the test of the results of convals() against the given thresholds kkttol and kkt2tol.

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

Individual data from the adjuvant GASTRIC meta-analysis

Description

The gastadj dataset contains individual data (overall and disease-free survival) of 3288 patients with resectable gastric cancer from 14 randomized trials of adjuvant chemotherapy.

Usage

data(gastadj)

Format

A dataframe with variables:

timeT:

Overall survival time (days).

statusT:

Overall survival indicator (0=censored, 1=death).

timeS:

Disease-free survival time (days).

statusS:

Disease-free survival indicator (0=censored, 1=progression on death).

trialref:

Trial indicator

trt:

Treatment arm (-0.5 = control, 0.5=chemotherapy).

id:

Patient identifier.

Source

The authors thank the GASTRIC (Global Advanced/Adjuvant Stomach Tumor Research International Collaboration) Group for permission to use their data. The investigators who contributed to GASTRIC are listed in Oba et al (2013) and GASTRIC (2010). The GASTRIC Group data are available within the surrosurv package for research purposes, under the conditions that (1) the research be scientifically appropriate, (2) the confidentiality of individual patient data be protected, (3) the results of the analyses be shared with the GASTRIC Group prior to public communication, (4) the source of data be fully acknowledged as above, and (5) resulting data and results be further shared with the research community.

References

Paoletti X, Oba K, Bang Y-J, et al. Disease-free survival as a surrogate for overall survival in adjuvant trials of gastric cancer: a meta-analysis. J Ntl Cancer Inst, 105(21):1600-7, 2013. doi:10.1093/jnci/djt270.

The GASTRIC group. Benefit of adjuvant chemotherapy for resectable gastric cancer: a meta-analysis. JAMA, 303(17):1729-37, 2010. doi:10.1001/jama.2010.534.

Buyse M, Molenberghs G, Paoletti Xavier et al. Statistical evaluation of surrogate endpoints with examples from cancer clinical trials. Biom J, 58(1):104-32, 2016. doi:10.1002/bimj.201400049

Examples

## Not run: 
    data('gastadj')
    allSurroRes <- surrosurv(gastadj, c('Clayton', 'PoissonTIa'), verbose = TRUE)
    convergence(allSurroRes)
    allSurroRes
    predict(allSurroRes)
    plot(allSurroRes)
  
## End(Not run)

Individual data from the advanced GASTRIC meta-analysis

Description

The gastadv dataset contains individual data (overall and progression-free survival) of 4069 patients with advanced/recurrent gastric cancer from 20 randomized trials of chemotherapy.

Usage

data(gastadv)

Format

A dataframe with variables:

timeT:

Overall survival time (days).

statusT:

Overall survival indicator (0=censored, 1=death).

timeS:

Progression-free survival time (days).

statusS:

Progression-free survival indicator (0=censored, 1=progression on death).

trialref:

Trial indicator

trt:

Treatment arm (-0.5 = control, 0.5=chemotherapy).

id:

Patient identifier.

Source

The authors thank the GASTRIC (Global Advanced/Adjuvant Stomach Tumor Research International Collaboration) Group for permission to use their data. The investigators who contributed to GASTRIC are listed in Paoletti et al (2013) and GASTRIC (2013). The GASTRIC Group data are available within the surrosurv package for research purposes, under the conditions that (1) the research be scientifically appropriate, (2) the confidentiality of individual patient data be protected, (3) the results of the analyses be shared with the GASTRIC Group prior to public communication, (4) the source of data be fully acknowledged as above, and (5) resulting data and results be further shared with the research community.

References

Paoletti X, Oba K, Bang Y-J, et al. Progression-free survival as a surrogate for overall survival in advanced/recurrent gastric cancer trials: a meta-analysis. J Ntl Cancer Inst, 105(21):1667-70, 2013. doi:10.1093/jnci/djt269.

The GASTRIC group. Role of chemotherapy for advanced/recurrent gastric cancer: An individual-patient-data meta-analysis. Eur J Cancer, 49(7):1565-77, 2013. doi:10.1016/j.ejca.2012.12.016.

Buyse M, Molenberghs G, Paoletti Xavier et al. Statistical evaluation of surrogate endpoints with examples from cancer clinical trials. Biom J, 58(1):104-32, 2016. doi:10.1002/bimj.201400049

Examples

## Not run: 
    data('gastadv')
    allSurroRes <- surrosurv(gastadv, c('Clayton', 'PoissonTIa'), verbose = TRUE)
    convergence(allSurroRes)
    allSurroRes
    predict(allSurroRes)
    plot(allSurroRes)
  
## End(Not run)

Leave-one-trial-out cross-validation for treatment effect prediction

Description

The function loocv() computed leave-one-out prediction of the treatment effect on the true endpoint for each trial, based on the observed effect on the surrogate endpoint in the trial itself and based on the meta-analytic model fitted on the remaining trials (Michiels et al, 2009).

Usage

## S3 method for class 'surrosurv'
loocv(object, models, nCores, parallel = TRUE, ...)

## S3 method for class 'loocvSurrosurv'
print(x, n = min(length(x), 6), silent = FALSE, ...)
          
## S3 method for class 'loocvSurrosurv'
plot(x, models, exact.models, 
                                plot.type = c('classic', 'regression'),
                                main, ylab, xlab, ...)

Arguments

object

Either an object of class surrosurv with an attribute data of class data.frame or a data.frame with columns

  • trialref, the trial reference

  • trt, the treatment arm (-0.5 or 0.5)

  • id, the patient id

  • timeT, the value of the true endpoint T

  • statusT, the censoring/event (0/1) indicator of the true endpoint T

  • timeS, the value of the surrogate endpoint S

  • statusS, the censoring/event (0/1) indicator of the surrogate endpoint S

nCores

The number of cores for parallel computing

parallel

Should results be computed using parallelization?

models, exact.models

Which models should be fitted (see surrosurv()). By default, the same models fitted in object (or x).

x

The fitted models, an object of class surrosurv

n

the number of rows to print

silent

Should the results be return for storing without printing them?

plot.type

The type ox x-scale for the loocv plot: either the trial number (classic) or the log-HR on the surrogate endpoint (regression).

main, ylab, xlab, ...

Further parameters to be passed to surrosurv (for loocv()) or to the generics print() and plot()

Value

An object of class loocvSurrosurv containing, for each trial:

margPars

the observed treatment effects on the surrogate ednpoint (alpha) and on the true endpoint (beta)

...

for each method in models the predicted value and prediction interval for beta.

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

References

Michiels S, Le Maitre A, Buyse M, et al. Surrogate endpoints for overall survival in locally advanced head and neck cancer: meta-analyses of individual patient data. Lancet Oncol. 2009;10(4):341-50. doi:10.1016/S1470-2045(09)70023-3

Examples

## Not run: 
  # Possibly long computation time!
  data('gastadv')
  cvRes <- loocv(gastadv)
  cvRes
  plot(cvRes)
  
## End(Not run)

Transform survival data for fitting a Poisson model

Description

This function transform survival data into a format compatible with the glm() function for fitting an auxiliary Poisson model, providing the parameter estimates of the associated proportional hazard model.

Usage

poissonize(data,
           all.breaks = NULL, interval.width = NULL, nInts = 8,
           factors = NULL, compress = TRUE)
plotsson(x, type = c('survival', 'hazard'),
         add = FALSE, xscale = 1, by, col, ...)

Arguments

data

a data frame with columns:

  • id : the patient identifier

  • time : the event/censoring time

  • status : the event(1) or censoring(0) indicator

  • ... : other factors such like the covariables needed in the regression model

all.breaks

the breakpoints between time intervals

interval.width

the width of the time intervals on which the risks will be assumed constant, in case of intervals of the same length. This parameter is ignored if all.breaks is specified

nInts

the number of intervals containing the same expected number of events (used only if is.null(interval.width), see Details). This parameter is ignored if either all.breaks or interval.width is specified

factors

a vector of characters, containing the names of the factors to be kept in the transformed data set

compress

a logical, indicating whether the record with the same factor profile should be summarized into one record, i.e. whether the data should be expressed in a short form

x

The fitted Poisson model on the poissonized data

type

the type of plot, either 'haz' for the hazard function or 'Surv', for the survival curve

add

should the plot added to the active device?

xscale

scaling factor for the time (x) axis

by

covariate for which a different curve per level has to be plotted

col, ...

other graphical parameters

Details

If interval.width is not null, the study period is divided into equal-length intervals of length interval.width. Otherwise, nInts intervals are used, and the location of their bounds is computed based on the empirical quantiles of the survival function.

Note

This code is hugely inspired by original code made publicly available by Stephanie Kovalchik.

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

References

Whitehead, J. Fitting Cox's regression model to survival data using GLIM. J Roy Stat Soc C Appl Stat 1980; 29(3):268-275. https://www.jstor.org/stable/2346901.

Crowther MJ, Riley RD, Staessen JA, Wang J, Gueyffier F, Lambert PC. Individual patient data meta-analysis of survival data using Poisson regression models. BMC Medical Research Methodology 2012; 12:34. doi:10.1186/1471-2288-12-34.

Examples

################################################################################
# Example 1 - KIDNEY data                                                      #
################################################################################
library(survival)
data(kidney)
kidney <- kidney[1:(nrow(kidney)/2)*2,]
head(kidney) 

par(mfrow=c(1, 3))
for (int in c(50, 20, 10)) {
    head(wdata1 <- poissonize(kidney, interval.width = int, 
                              factors = c('disease'), compress = FALSE))
    head(wdata2 <- poissonize(kidney, interval.width = int, 
                              factors = c('disease'), compress = TRUE))
    
    fitcox <- (coxph(Surv(time, status) ~ disease, data = kidney))
    fitpoi1 <- glm(event ~ -1 + interval + disease + offset(log(time)),
                   data = wdata1, family = 'poisson')
    fitpoi2 <- glm(m ~ -1 + interval + offset(log(Rt)) + disease,
                   data = wdata2, family = 'poisson')
    cox.base <- basehaz(fitcox, centered = FALSE)
    plot(stepfun(cox.base$time[-nrow(cox.base)], exp(-cox.base$hazard)),
         ylim = 0:1, xlim = c(0, max(cox.base$time)),
         do.points = FALSE, verticals = FALSE, xaxs = 'i',
         main = paste0('KIDNEY data set\nInterval width = ', int),
         xlab = 'Time', ylab = 'Survival probability')
    plotsson(fitpoi1, 'Surv', add = TRUE, col = 2, lty = 2)
    plotsson(fitpoi2, 'Surv', add = TRUE, col = 3, lty = 3) 
    legend('topright', col = 1:3, lty = 1:3,
           legend = c('Breslow (Cox)', 'Poisson',
                      'Poisson (compressed dataset)'))
}
print(cbind(Cox                = coef(fitcox),
            Poisson            = rev(rev(coef(fitpoi1))[1:3]),
            Poisson_Compressed = rev(rev(coef(fitpoi2))[1:3])), digits = 2)



################################################################################
#  Example 2 - COLON data                                                      #
################################################################################
library(survival)
data(colon)
head(wdata1 <- poissonize(subset(colon, etype == 1), interval.width = 365.25, 
                          factors=c('surg', 'sex', 'age'), compress = FALSE))
head(wdata2 <- poissonize(subset(colon, etype == 1), interval.width = 365.25, 
                          factors=c('surg', 'sex', 'age'), compress = TRUE))

fitcox <- coxph(Surv(time, status) ~ surg + sex + age, 
                data = subset(colon, etype == 1))

system.time({
    fitpoi1 <- glm(event ~ -1 + interval + surg + sex + age + offset(log(time)),
                   data = wdata1, fam = 'poisson')
})
system.time({
    fitpoi2 <- glm(m ~ -1 + interval + offset(log(Rt)) + surg + sex + age,
                   data = wdata2, family = 'poisson')
})
{
    cox.base <- basehaz(fitcox, centered = FALSE)
    par(mfrow = c(1, 1))
    plot(stepfun(cox.base$time[-nrow(cox.base)], exp(-cox.base$hazard)),
         ylim = 0:1, xlim = c(0, max(cox.base$time)),
         do.points = FALSE, verticals = FALSE, xaxs = 'i',
         main = 'COLON data set', xlab = 'Time', ylab = 'Survival probability')
    plotsson(fitpoi1, 'Surv', add = TRUE, col = 2, lty = 2) 
    plotsson(fitpoi2, 'Surv', add = TRUE, col = 3, lty = 3) 
    legend('topright', col = 1:3, lty = 1:3,
           legend = c('Cox', 'Poisson', 'Poisson (compressed dataset)'))
}
print(cbind(Cox                = coef(fitcox),
            Poisson            = rev(rev(coef(fitpoi1))[1:3]),
            Poisson_Compressed = rev(rev(coef(fitpoi2))[1:3])), digits = 2)



################################################################################
#  Example 3 - LUNG data                                                       #
################################################################################
library(survival)
data(lung)
lung$status <- lung$status - 1
lung$id <- 1:nrow(lung)
head(wdata1 <- poissonize(lung, interval.width = 365.25/12, 
                          factors = c('pat.karno', 'sex', 'age'), 
                          compress = FALSE))
head(wdata2 <- poissonize(lung, interval.width = 365.25/12,
                          factors = c('pat.karno', 'sex', 'age'),
                          compress = TRUE))

fitcox <- coxph(Surv(time, status) ~ pat.karno + sex + age, data = lung)

system.time({
    fitpoi1 <- glm(event ~ -1 + interval + pat.karno + sex + age + 
                              offset(log(time)),
                   data = wdata1, family = 'poisson')
})
system.time({
    fitpoi2 <- glm(m ~ -1 + interval + pat.karno + sex + age + offset(log(Rt)),
                   data = wdata2, family = 'poisson')
})
{
    cox.base <- basehaz(fitcox, centered = FALSE)
    plot(stepfun(cox.base$time[-nrow(cox.base)], exp(-cox.base$hazard)),
         ylim = 0:1, xlim = c(0, max(cox.base$time)),
         do.points = FALSE, verticals = FALSE, xaxs = 'i',
         main = 'LUNG data set', xlab = 'Time', ylab = 'Survival probability')
    plotsson(fitpoi1, 'Surv', add = TRUE, col = 2, lty = 2) 
    plotsson(fitpoi2, 'Surv', add = TRUE, col = 3, lty = 3) 
    legend('topright', col = 1:3, lty = 1:3,
           legend = c('Cox', 'Poisson', 'Poisson (compressed dataset)'))
}
print(cbind(Cox                = coef(fitcox),
            Poisson            = rev(rev(coef(fitpoi1))[1:3]),
            Poisson_Compressed = rev(rev(coef(fitpoi2))[1:3])), digits = 2)

Generate survival times for two endpoints in a meta-analysis of randomized trials

Description

Data are generated from a mixed proportional hazard model, a Clayton copula model (Burzykowski and Cortinas Abrahantes, 2005), a Gumbel-Hougaard copula model, or a mixture of half-normal and exponential random variables (Shi et al., 2011).

Usage

simData.re(R2 = 0.6, N = 30, ni = 200,
           nifix = TRUE, gammaWei = c(1, 1), censorT, censorA, 
           kTau= 0.6, baseCorr = 0.5, baseVars = c(0.2, 0.2),
           alpha = 0, beta = 0,
           alphaVar = 0.1, betaVar = 0.1,
           mstS = 4 * 365.25, mstT = 8 * 365.25)
           
simData.cc(R2 = 0.6, N = 30, ni = 200,
           nifix = TRUE, gammaWei = c(1, 1), censorT, censorA,
           kTau= 0.6, baseCorr = 0.5, baseVars = c(0.2, 0.2),
           alpha = 0, beta = 0,
           alphaVar = 0.1, betaVar = 0.1,
           mstS = 4 * 365.25, mstT = 8 * 365.25)
           
simData.gh(R2 = 0.6, N = 30, ni = 200,
           nifix = TRUE, gammaWei = c(1, 1), censorT, censorA,
           kTau= 0.6, baseCorr = 0.5, baseVars = c(0.2, 0.2),
           alpha = 0, beta = 0,
           alphaVar = 0.1, betaVar = 0.1,
           mstS = 4 * 365.25, mstT = 8 * 365.25)
           
simData.mx(R2 = 0.6, N = 30, ni = 200,
           nifix = TRUE, gammaWei = c(1, 1), censorT, censorA,
           indCorr = TRUE, baseCorr = 0.5, baseVars = c(0.2, 0.2),
           alpha = 0, beta = 0,
           alphaVar = 0.1, betaVar = 0.1,
           mstS = 4 * 365.25, mstT = 8 * 365.25)

Arguments

R2

The desired trial-level surrogacy R2R^2

N

The number of trials

ni

The (fixed or average) number of patients per trial

nifix

Should all trials have the same size (if nifix = TRUE) of should the N * ni patients be randomly assigned to trials with random probabilities (if nifix = FALSE)?

gammaWei

The shape parameter(s) of the Weibull distributions. Either one or two values. If one value is provided, it is used for both endpoints

censorT

censoring rate for the true endpoint T (before adding administrative censoring)

censorA

administrative censoring at time censorA

kTau

The desired individual-level dependence between S and T (Kendall's tau)

indCorr

Should S and T be correlated or not? (for .mx method)

baseCorr

correlation between baseline hazards (ρbasehaz\rho_{basehaz})

baseVars

variances of baseline random effects (S and T)

alpha

average treatment effect on S

beta

average treatment effect on T

alphaVar

variance of aia_i (θa2\theta_a^2)

betaVar

variance of bib_i (θb2\theta_b^2)

mstS

median survival time for S in the control arm

mstT

median survival time for T in the control arm

Details

The function simData.re generates data from a proportional hazard model with random effects at individual level and random effects and random treatment effects at trial level. Individual dependence can be tuned in terms of Kendall's tautau (kTau).

The function simData.cc generates data from a Copula function as shown by Burzykowski and Cortinas Abrahantes (2005). Individual dependence can be tuned in terms of Kendall's tautau (kTau).

The function simData.mx implements the simulation method by Shi et al. (2011). This model is based on a mixture of half-normal and exponential random variables. Under this model, individual dependence can be induced by using the same half-normal random variable for S and T. This is obtained by setting indCorr = TRUE, but the amount of correlation is not dependent on a single parameter.

Value

A data.frame with columns

trialref

the trial reference
trt

the treatment arm (-0.5 or 0.5)
id

the patient id
timeT

the value of the true endpoint T
statusT

the censoring/event (0/1) indicator of the true endpoint T
timeS

the value of the surrogate endpoint S
statusS

the censoring/event (0/1) indicator of the surrogate endpoint S

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

References

Burzykowski T, Cortinas Abrahantes J (2005). Validation in the case of two failure-time endpoints. In The Evaluation of Surrogate Endpoints (pp. 163-194). Springer, New York.

Rotolo F, Paoletti X, Burzykowski T, Buyse M, Michiels S. A Poisson approach for the validation of failure time surrogate endpoints in individual patient data meta-analyses. Statistical Methods in Medical Research 2017; In Press. doi:10.1177/0962280217718582

Shi Q, Renfro LA, Bot BM, Burzykowski T, Buyse M, Sargent DJ. Comparative assessment of trial-level surrogacy measures for candidate time-to-event surrogate endpoints in clinical trials. Computational Statistics & Data Analysis 2011; 55: 2748–2757.

Examples

set.seed(1)
  simData.re(N = 2, ni = 5)
  simData.cc(N = 2, ni = 5)
  simData.mx(N = 2, ni = 5)

Surrogate threshold effect

Description

The function ste() computes the surrogate threshold effect (STE) of a .

Usage

ste(x, models = names(x), exact.models)

## S3 method for class 'steSurrosurv'
print(x, digits = 2, ...)

Arguments

x

The fitted models, an object of class surrosurv

models, exact.models

Which models should be fitted (see surrosurv())

digits

the number of digits

...

Further parameters to be passed to the generic print() function

Value

An object of class steSurrosurv

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

References

Burzykowski T, Buyse M. Surrogate threshold effect: an alternative measure for meta-analytic surrogate endpoint validation. Pharm Stat. 2006;5(3):173-86. doi:10.1002/pst.207

Examples

## Not run: 
  # Possibly long computation time!
  data('gastadv')
  mod <- surrosurv(gastadv, 'Clayton')
  ste(mod)
  
## End(Not run)

Fit and print the models for evaluating the surrogacy strength of a candidate surrogate endpoint

Description

The function surrosurv fits (all or a subset of) statistical models to evaluate a surrogate endpoint S for a given true endpoint T, using individual data from a meta-analysis of randomized controlled trials.

Usage

surrosurv(data,
          models = c('Clayton', 'Plackett', 'Hougaard',
                     'Poisson I', 'Poisson T', 'Poisson TI', 'Poisson TIa'),
          intWidth = NULL,  nInts = 8,
          cop.OPTIMIZER = "bobyqa",
          poi.OPTIMIZER = "bobyqa",
          verbose = TRUE,
          twoStage = FALSE,
          keep.data = TRUE)

## S3 method for class 'surrosurv'
predict(object, models = names(object), exact.models, ...)

## S3 method for class 'surrosurv'
print(x, silent = FALSE, 
      digits = 2, na.print = "-.--", ...)
          
## S3 method for class 'predictSurrosurv'
print(x, n = 6, ...)
          
## S3 method for class 'surrosurv'
plot(x, ...)

## S3 method for class 'predictSurrosurv'
plot(x, models = names(x), exact.models,
                      pred.ints = TRUE,
                      show.ste = TRUE,
                      surro.stats = TRUE, 
                      xlab, ylab, 
                      xlim, ylim, mfrow, main, ...)

Arguments

data

A data.frame with columns

  • trialref, the trial reference

  • trt, the treatment arm (-0.5 or 0.5)

  • id, the patient id

  • timeT, the value of the true endpoint T

  • statusT, the censoring/event (0/1) indicator of the true endpoint T

  • timeS, the value of the surrogate endpoint S

  • statusS, the censoring/event (0/1) indicator of the surrogate endpoint S

models

For surrosurv(), the models should be fitted/plotted/predicted. Possible models are: Clayton copula (unadjusted and adjusted), Plackett copula (unadjusted and adjusted), Hougaard copula (unadjusted and adjusted), Poisson (with individual-level heterogeneity only, with trial-level heterogeneity only, with both individual- and trial-level heterogeneity, with both individual- and trial-level heterogeneity and with random per-trial intercept).

exact.models

If TRUE, plots or predictions are generated only for the elements of x which match exactly any of models. If exact.models = TRUE, partial matching is used. By default, exact.models = TRUE if all the models match exactly any of the names(x) (or names(object)) and exact.models = FALSE otherwise.

intWidth

the width of time intervals for data Poissonization (see poissonize)

nInts

the number of time intervals for data Poissonization (see poissonize)

cop.OPTIMIZER

the optimizer for copula models (see optimx)

poi.OPTIMIZER

the optimizer for Poisson models (see optimx)

verbose

should the function print out the model being fitted

twoStage

should the parameters of the baseline hazard functions fixed to their marginal estimates (Shih and Louis, 1995)

keep.data

should the data object be kept as attribute of the returned results? (this is needed for confint.surrosurv())

x, object

The fitted models, an object of class surrosurv

silent

Should the results be return for storing without printing them?

digits, na.print, xlab, ylab, xlim, ylim, main, ...

other parameters for print or plot

mfrow

the number of rows and columns for displaying the plots (see par). If missing, the default is computed using the function n2mfrow

n

the number of rows to print

pred.ints

Should the prediction intervals be plotted?

show.ste

Should the surrogate threshold effect be showed?

surro.stats

Should the surrogacy statistics be showed?

Details

Three copula models can be fit: Clayton (1978), Plackett (1965), and Hougaard (1986). For all of them the linear regression at the second step is computed both via simple LS regression and via a linear model adjusted for measurement error of the log-hazard ratios estimated at the first step. This adjusted model is the one described by Burzykowski et al. (2001), which relies on the results by van Houwelingen et al. (2002).

The mixed Poisson models that can be fit are used to estimate parameters of mixed proportional hazard models, as described for instance by Crowther et al (2014). The statistical details are provided in Rotolo et al (WP).

The function predict() returns the estimated values of the log-hazard ratios on the true and the surrogate endpoints. The list of the prediction functions (for all the models) is available as attr(predict.surrosurv(...), 'predf').

Value

The fitted models, an object of class surrosurv.

Author(s)

Federico Rotolo [aut] (<https://orcid.org/0000-0003-4837-6501>), Xavier Paoletti [ctb], Marc Buyse [ctb], Tomasz Burzykowski [ctb], Stefan Michiels [ctb] (<https://orcid.org/0000-0002-6963-2968>), Dan Chaltiel [cre] (<https://orcid.org/0000-0003-3488-779X>)

References

Burzykowski T, Molenberghs G, Buyse M et al. Validation of surrogate end points in multiple randomized clinical trials with failure time end points. Journal of the Royal Statistical Society C 2001; 50:405–422. doi:10.1111/1467-9876.00244

Clayton DG. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 1978; 65:141–151. doi:10.1093/biomet/65.1.141

Crowther MJ, Riley RD, Staessen JA, Wang J, Gueyffier F, Lambert PC. Individual patient data meta-analysis of survival data using Poisson regression models. BMC Medical Research Methodology 2012; 12:34. doi:10.1186/1471-2288-12-34.

Gasparrini A, Armstrong B, Kenward MG. Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine 2012; 31:3821–39. doi:10.1002/sim.5471

Hougaard P. A class of multivariate failure time distributions. Biometrika 1986; 73:671–678. doi:10.1093/biomet/73.3.671

Plackett RL. A class of bivariate distributions. Journal of the America Statistical Association 1965; 60:516–522. doi:10.1080/01621459.1965.10480807

Rotolo F, Paoletti X, Burzykowski T, Buyse M, Michiels S. A Poisson approach for the validation of failure time surrogate endpoints in individual patient data meta-analyses. Statistical Methods in Medical Research 2017; In Press. doi:10.1177/0962280217718582

Shih JH, Louis TA. Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics 1995; 51:1384–1399. doi:10.2307/2533269

van Houwelingen HC, Arends LR, Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression. Statistics in Medicine 2002; 21:589–624. doi:10.1002/sim.1040

Examples

set.seed(150)
  data <- simData.re(N = 20, ni = 250,
                     R2 = 0.8, kTau = 0.4,
                     alpha = log(0.95), beta = log(0.85),
                     censorA = 15 * 365.25)
  library(survival)
  par(mfrow = 1:2)
  plot(survfit(Surv(timeS, statusS) ~ trt, data = data), lty = 1:2, 
       xscale = 365.25, main = 'Progression-Free Survival\n(S)', col = 2)
  plot(survfit(Surv(timeT, statusT) ~ trt, data = data), lty = 1:2,
       xscale = 365.25, main = 'Overall Survival\n(T)')
       
  ## Not run: 
    # Long computation time!
    surrores <- surrosurv(data, verbose = TRUE)
    convergence(surrores)
    surrores
  
## End(Not run)
  
  # Advanced GASTRIC data
  ## Not run: 
    # Long computation time!
    data('gastadv')
    allSurroRes <- surrosurv(gastadv, c('Clayton', 'Poisson'), verbose = TRUE)
    convergence(allSurroRes)
    allSurroRes
    predict(allSurroRes)
    plot(allSurroRes)
  
## End(Not run)