Comparison of survival curves between two groups

Description

Various statistical methods for survival analysis in comparing survival curves between two groups, including overall hypothesis tests described in Li et al. (2015), fixed-point tests in Klein et al. (2007), short-term tests, and long-term tests in Logan et al. (2008). Some commonly used descriptive statistics and plots are also included.

Author(s)

Jingjing Lyu, Zheng Chen, Huimin Li, Jinbao Chen, Xinghui Huang. maintainer: Zheng Chen zheng-chen@hotmail.com

References

[1] Li H, Han D, Hou Y, et al. Statistical inference methods for two crossing survival curves: a comparison of methods. PLoS One, 2015, 10: e116774.

[2] Huang X, Lyu J, Hou Y, et al. A Nonparametric Statistical Method for Two Crossing Survival Curves. Communications in Statistics - Simulation and Computation, 2020. doi: 10.1080/03610918.2020.1753075.

[3] Klein JP, Logan B, Harhoff M, et al. Analyzing survival curves at a fixed point in time. Statistics in Medicine, 2007, 26(24):4505-4519.

[4] Logan BR, Klein JP, Zhang M. Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation. Biometrics, 2008, 64(3): 733-740.

The Data with Survival Curves Crossed

Description

Crossdata is a dataset from simulation, which is violated the proportional hazard ratio assumption.

Usage

data(Crossdata)

Format

A data frame with 200 observations on the following 3 variables.

time

The follow up time for right censored data.

status

The status indicator, normally 1=event, 0=alive or right censored.

group

The group indicator for comparison, 0= control group, 1= treatment group.

Examples

data(Crossdata)

Plot for Cumulative Hazard Function

Description

A function used to plot the curves of cumulative hazard function.

Usage

Cumhazard.plot(time,status,group,col=c(1,4),lwd=c(1,1),lty=c(1,1)
               ,lab.x="",lab.y="",legend=FALSE,local.x=NULL,local.y=NULL
               ,legend.0="",legend.1="")

Arguments

Value

None

See Also

Survival.plot,Hazard.plot

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get cumulative hazard plot
Cumhazard.plot(data1$time, data1$status, data1$group, lab.x='Time', lab.y='Cumulative hazard'
               ,col=c(1,4), lwd=c(3,3), lty=c(1,1), legend=TRUE, local.x=0, local.y=3
               ,legend.0='group0', legend.1='group1')

Summarize Descriptive Statistics Commonly Used in Survival Data

Description

A function used to produce result summaries of the results of various descriptive statistics.

Usage

Descriptive.stat(time, status, group, tau="observed", alpha=0.05)

Arguments

Value

A list containing the following components:

Examples

#get 'Crossdata' from package
data(Crossdata)
data2<-Crossdata
#
#get result of descriptive statistics with tau=the minimum of the largest observed time
Descriptive.stat(data2$time, data2$status, data2$group,tau="observed")
#get result of descriptive statistics with tau=the minimum of the largest event time
Descriptive.stat(data2$time, data2$status, data2$group,tau="event")

Statistical inference methods for testing at a fixed time point

Description

A function used to produce the results of various statistical inference methods for testing at a fixed time point.

Usage

Fixpoint.test(time, status, group, t0)

Arguments

Value

A list containing the following components:

References

[1]Klein JP, Logan B, Harhoff M, et al. Analyzing survival curves at a fixed point in time. Statistics in Medicine, 2007, 26(24):4505-4519.

[2]Anderson JR, Pike LBC. Approximate Confidence Intervals for Probabilities of Survival and Quantiles in Life-Table Analysis. Biometrics, 1982, 38(2):407-416.

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#if there exist differences at 6 months and 12 months
Fixpoint.test(data1$time,data1$status,data1$group,t0=0.5)
Fixpoint.test(data1$time,data1$status,data1$group,t0=1)

Plot for Kernel-Based Hazard Function

Description

A function used to plot the hazard functions. The hazard functions are estimated from right censored data using kernel-based methods.

Usage

Hazard.plot(time,status,group,max.0=NULL,max.1=NULL
            ,col=c(1,4),lwd=c(1,1),lty=c(1,1)
            ,lab.x="",lab.y="",legend=FALSE
            ,local.x=NULL,local.y=NULL,legend.0="",legend.1="")

Arguments

Value

None

Note

In Hazard.plot, the kernel estimates are based on the package "muhaz". Here, the algorithm method is the "same bandwidth for all grid points", and the biquadratic is of the boundary kernel function to be used. More details can be found in package "muhaz", the function of muhaz.

See Also

Survival.plot,Cumhazard.plot

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get kernel smooth hazard plot
Hazard.plot(data1$time, data1$status, data1$group, max.0=NULL,max.1=NULL
            , lab.x='Time', lab.y='Smooth hazard ratio'
            , col=c(1,4), lwd=c(3,3), lty=c(1,1), legend=TRUE, local.x=2.7, local.y=1.25
            , legend.0='group0', legend.1='group1')

Statistical Inference Methods for Testing After a Specified Time Point

Description

A function used to produce the results of statistical inference methods for testing the difference after a specified time point.

Usage

Long.test(time,status,group,t0)

Arguments

Value

A list containing the following components:

Note

The partial log-rank method is different from the log-rank method in overall.test. Here, the "partial" means let all observations left truncated at the cut-point time t0.

References

Logan BR, Klein JP, Zhang M. Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation. Biometrics, 2008, 64(3): 733-740.

See Also

crosspoint,Short.test

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get cross point
crosspoint(data1$time,data1$status,data1$group)
#two survival curves crossing at 1.69 years
#
#get the result after cross point (t0=1.69)
Long.test(data1$time,data1$status,data1$group,t0=1.69)

Statistical Inference Methods for Overall Hypothesis Tests

Description

A function used to produce the results of various statistical inference methods for overall hypothesis testing, along with the test result of proportional hazards assumption.

Usage

Overall.test(time, status, group, tau=NULL, nperm=500, seed=12345)

Arguments

Value

A list containing the following components:

Note

The results of Two-stage is based on the "TSHRC" package, more details can be found in package "TSHRC", the function of twostage.

The results of RMST is based on the "survRM2" package, more details can be found in package "survRM2", the function of rmst2.

References

[1] Li H, Han D, Hou Y, et al. Statistical inference methods for two crossing survival curves: a comparison of methods. PLoS One, 2015, 10: e116774.

[2] Qiu P, Sheng J. A two-stage procedure for comparing hazard rate functions. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 2008, 70: 191-208.

[3] Huang X, Lyu J, Hou Y, et al. A Nonparametric Statistical Method for Two Crossing Survival Curves. Communications in Statistics - Simulation and Computation, 2020. doi: 10.1080/03610918.2020.1753075.

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get result of overall hypothesis testing
Overall.test(data1$time,data1$status,data1$group,nperm=10)

The Data Satisfied Proportional Hazard Assumption

Description

PHdata is a dataset from simulation, which is satisfied the proportional hazard ratio assumption.

Usage

data(PHdata)

Format

A data frame with 200 observations on the following 3 variables.

time

The follow up time for right censored data.

status

The status indicator, normally 1=event, 0=alive or right censored.

group

The group indicator for comparison, 0= control group, 1= treatment group.

Examples

data(PHdata)

Statistical Inference Methods for Testing Before a Specified Time Point

Description

A function used to produce the results of statistical inference methods for testing the difference before a specified time point.

Usage

Short.test(time,status,group,t0)

Arguments

Value

A list containing the following components:

Note

The partial Weighted Kaplan-Meier method and partial log-rank method are different from the Weighted Kaplan-Meier method and the log-rank method in overall.test. Here, the "partial" means let all observations right censored at the cut-point time t0.

See Also

crosspoint,Long.test

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get cross point
crosspoint(data1$time,data1$status,data1$group)
#two survival curves crossing at 1.69 years
#
#get the result before cross point (t0=1.69)
Short.test(data1$time,data1$status,data1$group,t0=1.69)

Plot for Cumulative Survival Function

Description

A function used to plot the survival curves.

Usage

Survival.plot(time,status,group,...)

Arguments

Value

None

Note

Survival.plot is based on the survival package, more details can be found in package "survival", the function of plot.survfit.

See Also

Cumhazard.plot,Hazard.plot

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#
#get survival plot
Survival.plot(data1$time, data1$status, data1$group, xlab = "Time", ylab = "Survival"
              , col = c(1, 4), lwd = c(3, 3), lty= c(1, 1))
legend(2.5, 1, c("group0", "group1"), col = c(1, 4), lwd = c(3, 3), lty= c(1, 1), bty="n")

Produce The Cross Time Point When Two Survival Curves Crossed Each Other

Description

A function used to produce the cross time points in two survival curves.

Usage

crosspoint(time,status,group)

Arguments

Value

A list containing the following components:

Note

The crosspoint function only used to find the cross time point in survival curves.

Examples

#get 'Crossdata' from package
data(Crossdata)
data1<-Crossdata
#get cross point
#two survival curves crossing at 1.69 years or so
crosspoint(data1$time,data1$status,data1$group)
#
#get 'PHdata' from package
data(PHdata)
data2<-PHdata
#when there exists no crossing
#the program will stop "There is no crossing exists"
# Not run: crosspoint(data2$time,data2$status,data2$group)