| Type: | Package |
| Title: | Win Ratio Analysis of Composite Time-to-Event Outcomes |
| Version: | 1.0 |
| Author: | Lu Mao and Tuo Wang |
| Maintainer: | Lu Mao <lmao@biostat.wisc.edu> |
| URL: | https://sites.google.com/view/lmaowisc/ |
| Description: | Implements various win ratio methodologies for composite endpoints of death and non-fatal events, including the (stratified) proportional win-fractions (PW) regression models (Mao and Wang, 2020 <doi:10.1111/biom.13382>), (stratified) two-sample tests with possibly recurrent nonfatal event, and sample size calculation for standard win ratio test (Mao et al., 2021 <doi:10.1111/biom.13501>). |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| LazyData: | true |
| Depends: | R (≥ 3.5.0) |
| RoxygenNote: | 7.1.2 |
| Imports: | survival, cubature, gumbel |
| Suggests: | knitr, rmarkdown |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-11-26 20:09:50 UTC; lmao |
| Repository: | CRAN |
| Date/Publication: | 2021-11-26 21:20:08 UTC |
Compute the sample size for standard win ratio test
Description
Compute the sample size for standard win ratio test.
Usage
WRSS(xi, bparam, q = 0.5, alpha = 0.05, side = 2, power = 0.8)
Arguments
xi |
A bivariate vector of hypothesized component-wise (treatment-to-control) log-hazard
ratios under the Gumbel–Hougaard copula model described in |
bparam |
A list containing baseline parameters |
q |
Proportion of patients assigned to treatment. |
alpha |
Type I error rate. |
side |
2-sided or 1-sided test. |
power |
Target power. |
Value
A list containing n, the computed sample size.
References
Mao, L., Kim, K. and Miao, X. (2021). Sample size formula for general win ratio analysis. Biometrics, https://doi.org/10.1111/biom.13501.
See Also
Examples
# The following is not run in package checking to save time.
## Not run:
## load the package and pilot dataset
library(WR)
head(hfaction_cpx9)
dat<-hfaction_cpx9
## subset to control group
pilot<-dat[dat$trt_ab==0,]
## get the data ready for gumbel.est()
id<-pilot$patid
## convert time from month to year
time<-pilot$time/12
status<-pilot$status
## compute the baseline parameters for the Gumbel--Hougaard
## copula for death and hospitalization
gum<-gumbel.est(id, time, status)
## get the baseline parameters
lambda_D<-gum$lambda_D
lambda_H<-gum$lambda_H
kappa<-gum$kappa
## set up design parameters and use base()
## to calculate bparam for WRSS()
# max follow-up 4 years
tau<-4
# 3 years of initial accrual
tau_b<-3
# loss to follow-up rate
lambda_L=0.05
# compute the baseline parameters
bparam<-base(lambda_D,lambda_H,kappa,tau_b,tau,lambda_L)
bparam
## sample size with power=0.8 under hazard ratios
## 0.9 and 0.8 for death and hospitalization, respectively.
WRSS(xi=log(c(0.9,0.8)),bparam=bparam,q=0.5,alpha=0.05,
power=0.8)$n
## sample size under the same set-up but with power 0.9
WRSS(xi=log(c(0.9,0.8)),bparam=bparam,q=0.5,alpha=0.05,
power=0.9)$n
## End(Not run)
Generalized win ratio tests
Description
Perform stratified two-sample test of possibly recurrent nonfatal event and death using the recommended last-event assisted win ratio (LWR), and/or naive win ratio (NWR) and first-event assisted win ratio (FWR) (Mao et al., 2022). The LWR and FWR reduce to the standard win ratio of Pocock et al. (2012).
Usage
WRrec(ID, time, status, trt, strata = NULL, naive = FALSE)
Arguments
ID |
A vector of unique patient identifiers. |
time |
A numeric vector of event times. |
status |
A vector of event type variable; 2 = recurrent event, 1 = death, and 0 = censoring. |
trt |
A vector of binary treatment indicators. |
strata |
A vector of categorical variable for strata; Default is NULL, which leads to unstratified analysis. |
naive |
If TRUE, results for NWR and FWR will be provided in addition to LWR; Default is FALSE, which gives LWR only. |
Value
An object of class WRrec, which contains the following
elements.
theta |
A bivariate vector of win/loss fractions by LWR. |
log.WR, se |
Log-win ratio estimate and its standard error by LWR. |
pval |
|
theta.naive |
A bivariate vector of win/loss fractions by NWR. |
log.WR.naive, se.naive |
Log-win ratio estimate and its standard error by NWR. |
theta.FI |
A bivariate vector of win/loss fractions by FWR. |
log.WR.FI, se.FI |
Log-win ratio estimate and its standard error by FWR. |
... |
References
Mao, L., Kim, K. and Li, Y. (2022). On recurrent-event win ratio. Statistical Methods in Medical Research, under review.
Pocock, S., Ariti, C., Collier, T., and Wang, D. (2012). The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European Heart Journal, 33, 176–182.
See Also
Examples
## load the HF-ACTION trial data
library(WR)
head(hfaction_cpx9)
dat<-hfaction_cpx9
## Comparing exercise training to usual care by LWR, FWR, and NWR
obj<-WRrec(ID=dat$patid,time=dat$time,status=dat$status,
trt=dat$trt_ab,strata=dat$age60,naive=TRUE)
## print the results
obj
Compute the baseline parameters needed for sample size calculation for standard win ratio test
Description
Compute the baseline parameters \zeta_0^2 and \boldsymbol\delta_0
needed for sample size calculation for standard win ratio test (see WRSS).
The calculation is based
on a Gumbel–Hougaard copula model for survival time D^{(a)} and nonfatal event
time T^{(a)} for group a (1: treatment; 0: control):
{P}(D^{(a)}>s, T^{(a)}>t) =\exp\left(-\left[\left\{\exp(a\xi_1)\lambda_Ds\right\}^\kappa+
\left\{\exp(a\xi_2)\lambda_Ht\right\}^\kappa\right]^{1/\kappa}\right),
where \xi_1 and \xi_2 are the component-wise log-hazard ratios to be used
as effect size in WRSS.
We also assume that patients are recruited uniformly over the period [0, \tau_b]
and followed until time \tau (\tau\geq\tau_b), with an exponential
loss-to-follow-up hazard \lambda_L.
Usage
base(lambda_D, lambda_H, kappa, tau_b, tau, lambda_L, N = 1000, seed = 12345)
Arguments
lambda_D |
Baseline hazard |
lambda_H |
Baseline hazard |
kappa |
Gumbel–Hougaard copula correlation parameter |
tau_b |
Length of the initial (uniform) accrual period |
tau |
Total length of follow-up |
lambda_L |
Exponential hazard rate |
N |
Simulated sample size for monte-carlo integration. |
seed |
Seed for monte-carlo simulation. |
Value
A list containing real number zeta2 for \zeta_0^2
and bivariate vector delta for \boldsymbol\delta_0.
References
Mao, L., Kim, K. and Miao, X. (2021). Sample size formula for general win ratio analysis. Biometrics, https://doi.org/10.1111/biom.13501.
See Also
Examples
# see the example for WRSS
A subset of the German Breast Cancer study data
Description
These are a subset of the German Breast Cancer study data.
Usage
gbc
Format
A data frame with 985 rows and 12 variables:
- id
subject IDs
- time
event times (months)
- status
event status; 0:censoring, 1:death, 2:cancer recurrence
- hormone
treatment indicator: 1=Hormone therapy; 2=standard therapy
- age
age at diagnosis (years)
- menopause
menopausal Status; 1=No; 2=Yes
- size
tumor size
- grade
tumor grade, 1-3
- nodes
number of nodes involved
- prog_recp
number of progesterone receptors
- estrg_recp
number of estrogen receptors
References
Sauerbrei, W., Royston, P., Bojar, H., Schmoor, C. and Schumacher, M. (1999). Modelling the effects of standard prognostic factors in node-positive breast cancer. German Breast Cancer Study Group (GBSG). British Journal of Cancer, 79, 1752–1760.
Hosmer, D.W. and Lemeshow, S. and May, S. (2008) Applied Survival Analysis: Regression Modeling of Time to Event Data: Second Edition, John Wiley and Sons Inc., New York, NY
Estimate baseline parameters in the Gumbel–Hougaard model for sample size calculation using pilot data
Description
Estimate baseline parameters in the Gumbel–Hougaard model
described in base for sample size calculation using pilot study data.
Usage
gumbel.est(id, time, status)
Arguments
id |
A vector of unique patient identifiers. |
time |
A numeric vector of event times. |
status |
A vector of event type variable; 2 = nonfatal event, 1 = death, and 0 = censoring. |
Value
A list containing lambda_D for \lambda_D,
lambda_H for \lambda_H, and kappa for \kappa
in the Gumbel–Hougaard model.
References
Mao, L., Kim, K. and Miao, X. (2021). Sample size formula for general win ratio analysis. Biometrics, https://doi.org/10.1111/biom.13501.
See Also
Examples
# see the example for WRSS
A subset of the HF-ACTION study data on high-risk non-ischemic heart failure patients
Description
These are data on a subgroup of 426 high-risk non-ischemic patients in the HF-ACTION study.
Usage
hfaction_cpx9
Format
A data frame with 1,448 rows and 5 variables:
- patid
patient ID
- time
event times (months)
- status
event status; 0:censoring, 1:death, 2:hospitalization
- trt_ab
treatment indicator: 1: exercise training, 0: usual care
- age60
1: 60 years or older, 0: less than 60 years old
References
O'Connor, C. M., Whellan, D. J., Lee, K. L., Keteyian, S. J., Cooper, L. S., Ellis, S. J., Leifer, E. S., Kraus, W. E., Kitzman, D. W., Blumenthal, J. A. et al. (2009). Efficacy and safety of exercise training in patients with chronic heart failure: HF-ACTION randomized controlled trial. Journal of the American Medical Association, 301, 1439–1450.
A subset of the HF-ACTION study data on non-ischemic heart failure patients with full covariate measurement.
Description
These are a subset of the data on 451 non-ischemic patients in the HF-ACTION study will complete baseline covariates.
Usage
non_ischemic
Format
A data frame with 751 rows and 16 variables:
- ID
subject IDs
- time
event times (days)
- status
event status; 0:censoring, 1:death, 2:hospitalization
- trt_ab
treatment indicator: 1=exercise training; 0=usual care
- age
patient age in years
- sex
1=female; 2=male
- Black.vs.White
1=black; 0=otherwise
- Other.vs.White
1=race other than black or white; 0=otherwise
- bmi
body mass index
- bipllvef
(biplane) left-ventricular ejection fraction
- hyperten
indicator for history of hypertension
- COPD
indicator for history of COPD
- diabetes
indicator for history of diabetes
- acei
indicator for current use of ACE inhibitors
- betab
indicator for current use of beta blockers
- smokecurr
indicator for current smoker
References
O'Connor, C. M., Whellan, D. J., Lee, K. L., Keteyian, S. J., Cooper, L. S., Ellis, S. J., Leifer, E. S., Kraus, W. E., Kitzman, D. W., Blumenthal, J. A. et al. (2009). Efficacy and safety of exercise training in patients with chronic heart failure: HF-ACTION randomized controlled trial. Journal of the American Medical Association, 301, 1439–1450.
Plot the standardized score processes
Description
Plot the standardized score processes.
Usage
## S3 method for class 'pwreg.score'
plot(
x,
k,
xlab = "Time",
ylab = "Standardized score",
lty = 1,
frame.plot = TRUE,
add = FALSE,
ylim = c(-3, 3),
xlim = NULL,
lwd = 1,
...
)
Arguments
x |
an object of class |
k |
A positive integer indicating the order of covariate to be plotted. For example, |
xlab |
a title for the x axis. |
ylab |
a title for the y axis. |
lty |
the line type. Default is 1. |
frame.plot |
a logical variable indicating if a frame should be drawn in the 1D case. |
add |
a logical variable indicating whether add to current plot? |
ylim |
a vector indicating the range of y-axis. Default is (-3,3). |
xlim |
a vector indicating the range of x-axis. Default is NULL. |
lwd |
the line width, a positive number. Default is 1. |
... |
further arguments passed to or from other methods |
Value
A plot of the standardized score process for object pwreg.score.
See Also
Examples
# see the example for score.proc
Print the results of the two-sample recurrent-event win ratio analysis
Description
Print the results of the two-sample recurrent-event win ratio analysis.
Usage
## S3 method for class 'WRrec'
print(x, ...)
Arguments
x |
an object of class |
... |
further arguments passed to or from other methods. |
Value
Print the results of WRrec object.
See Also
Examples
# see the example for WRrec
Print the results of the proportional win-fractions regression model
Description
Print the results of the proportional win-fractions regression model.
Usage
## S3 method for class 'pwreg'
print(x, ...)
Arguments
x |
an object of class |
... |
further arguments passed to or from other methods |
Value
Print the results of pwreg object
See Also
Examples
# see the example for pwreg
Print information on the content of the pwreg.score object
Description
Print information on the content of the pwreg.score object
Usage
## S3 method for class 'pwreg.score'
print(x, ...)
Arguments
x |
A object of class pwreg.score. |
... |
further arguments passed to or from other methods. |
Value
Print the results of pwreg.score object.
See Also
Examples
# see the example for score.proc
Fit a standard proportional win-fractions (PW) regression model
Description
Fit a standard proportional win-fractions (PW) regression model.
Usage
pwreg(
ID,
time,
status,
Z,
rho = 0,
strata = NULL,
fixedL = TRUE,
eps = 1e-04,
maxiter = 50
)
Arguments
ID |
a vector of unique subject-level identifiers. |
time |
a vector of event times. |
status |
a vector of event type labels. 0: censoring, 1:death and 2: non-fatal event. |
Z |
a matrix or a vector of covariates. |
rho |
a non-negative number as the power of the survival function used
in the weight. Default ( |
strata |
a vector of stratifying variable if a stratified model is desired. |
fixedL |
logical variable indicating which variance estimator to be used. If 'TRUE', the type I variance estimator (for a small number strata) is used; otherwise the type II variance estimator (for a large number strata) is used. |
eps |
precision for the convergence of Newton-Raphson algorithm. |
maxiter |
maximum number of iterations allow for the Newton-Raphson algorithm. |
Value
An object of class pwreg with the following components.
beta:a vector of estimated regression coefficients. Var:estimated
covariance matrix for beta. conv: boolean variable indicating
whether the algorithm converged within the maximum number of iterations.
References
Mao, L. and Wang, T. (2020). A class of proportional win-fractions regression models for composite outcomes. Biometrics, 10.1111/biom.13382
Wang, T. and Mao, L. (2021+). Stratified Proportional Win-fractions Regression Analysis.
See Also
Examples
library(WR)
head(non_ischemic)
id_unique <-unique(non_ischemic$ID)
# Randomly sample 200 subjects from non_ischemic data
set.seed(2019)
id_sample <- sample(id_unique, 200)
non_ischemic_reduce <- non_ischemic[non_ischemic$ID %in% id_sample, ]
# Use the reduced non_ischemic data for analysis
nr <- nrow(non_ischemic_reduce)
p <- ncol(non_ischemic_reduce)-3
ID <- non_ischemic_reduce[,"ID"]
time <- non_ischemic_reduce[,"time"]
status <- non_ischemic_reduce[,"status"]
Z <- as.matrix(non_ischemic_reduce[,4:(3+p)],nr,p)
## unstratified analysis
pwreg.obj <- pwreg(time=time,status=status,Z=Z,ID=ID)
print(pwreg.obj)
## Not run:
## stratified PW by sex
sex<-Z[,3]
## take out sex from the covariate matrix
Z1<-Z[,-3]
pwreg.obj1 <- pwreg(time=time,status=status,Z=Z1,ID=ID,strata=sex)
print(pwreg.obj1)
## End(Not run)
Computes the standardized score processes
Description
Computes the standarized score processes for the covariates.
Usage
score.proc(obj, t = NULL)
Arguments
obj |
an object of class pwreg. |
t |
a vector containing times. If not specified, the function will use all unique event times from the data. |
Value
An object of class pwreg.score consisting of t:
a vector of times; and score: a matrix whose rows are the standardized score processes
as a function of t.
References
Mao, L. and Wang, T. (2020). A class of proportional win-fractions regression models for composite outcomes. Biometrics, 10.1111/biom.13382
See Also
Examples
library(WR)
head(non_ischemic)
# Randomly sample 200 subjects from non_ischemic data
id_unique <-unique(non_ischemic$ID)
set.seed(2019)
id_sample <- sample(id_unique, 200)
non_ischemic_reduce <- non_ischemic[non_ischemic$ID %in% id_sample, ]
# Use the reduced non_ischemic data for analysis
nr <- nrow(non_ischemic_reduce)
p <- ncol(non_ischemic_reduce)-3
ID <- non_ischemic_reduce[,"ID"]
time <- non_ischemic_reduce[,"time"]
status <- non_ischemic_reduce[,"status"]
Z <- as.matrix(non_ischemic_reduce[,4:(3+p)],nr,p)
pwreg.obj <- pwreg(time=time,status=status,Z=Z,ID=ID)
score.obj <- score.proc(pwreg.obj)
#plot the standardized score process for the first covariate
plot(score.obj, k = 1)