Package 'EquiSurv' reference manual

Title:	Modeling, Confidence Intervals and Equivalence of Survival Curves
Description:	We provide a non-parametric and a parametric approach to investigate the equivalence (or non-inferiority) of two survival curves, obtained from two given datasets. The test is based on the creation of confidence intervals at pre-specified time points. For the non-parametric approach, the curves are given by Kaplan-Meier curves and the variance for calculating the confidence intervals is obtained by Greenwood's formula. The parametric approach is based on estimating the underlying distribution, where the user can choose between a Weibull, Exponential, Gaussian, Logistic, Log-normal or a Log-logistic distribution. Estimates for the variance for calculating the confidence bands are obtained by a (parametric) bootstrap approach. For this bootstrap censoring is assumed to be exponentially distributed and estimates are obtained from the datasets under consideration. All details can be found in K.Moellenhoff and A.Tresch: Survival analysis under non-proportional hazards: investigating non-inferiority or equivalence in time-to-event data <arXiv:2009.06699>.
Authors:	Kathrin Moellenhoff
Maintainer:	Kathrin Moellenhoff <[email protected]>
License:	GPL (>= 2)
Version:	0.1.0
Built:	2024-10-29 03:15:10 UTC
Source:	https://github.com/cran/EquiSurv

Parametric Bootstrap of time-to-event data following an exponential distribution

Description

Function generating bootstrap data according to an exponential distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_exponential(t0, B = 1000, theta, C, N)
boot_exponential(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the exponential distribution, theta=rate
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

t0<-2
N<-30
C<-1
boot_exponential(t0=t0,theta=1,C=C,N=N)
t0<-2
N<-30
C<-1
boot_exponential(t0=t0,theta=1,C=C,N=N)

Parametric Bootstrap of time-to-event data following a gaussian distribution

Description

Function generating bootstrap data according to a gaussian distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_gaussian(t0, B = 1000, theta, C, N)
boot_gaussian(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the gaussian distribution, theta=(mean,sd)
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

t0<-2
N<-30
C<-1
boot_gaussian(t0=t0,theta=c(1.7,1),C=C,N=N)
t0<-2
N<-30
C<-1
boot_gaussian(t0=t0,theta=c(1.7,1),C=C,N=N)

Parametric Bootstrap of time-to-event data following a logistic distribution

Description

Function generating bootstrap data according to a logistic distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_logistic(t0, B = 1000, theta, C, N)
boot_logistic(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the logistic distribution, theta=(location,scale)
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

t0<-2
N<-30
C<-1
boot_logistic(t0=t0,theta=c(1,0.4),C=C,N=N)
t0<-2
N<-30
C<-1
boot_logistic(t0=t0,theta=c(1,0.4),C=C,N=N)

Parametric Bootstrap of time-to-event data following a loglogistic distribution

Description

Function generating bootstrap data according to a loglogistic distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_loglogistic(t0, B = 1000, theta, C, N)
boot_loglogistic(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the loglogistic distribution, theta=(shape,scale)
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

alpha<-0.05
t0<-2
N<-30
C<-1
boot_loglogistic(t0=t0,theta=c(1,3),C=C,N=N)
alpha<-0.05
t0<-2
N<-30
C<-1
boot_loglogistic(t0=t0,theta=c(1,3),C=C,N=N)

Parametric Bootstrap of time-to-event data following a lognormal distribution

Description

Function generating bootstrap data according to a lognormal distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_lognormal(t0, B = 1000, theta, C, N)
boot_lognormal(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the lognormal distribution, theta=(meanlog,sdlog)
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

t0<-2
N<-30
C<-1
boot_lognormal(t0=t0,theta=c(0.6,1),C=C,N=N)
t0<-2
N<-30
C<-1
boot_lognormal(t0=t0,theta=c(0.6,1),C=C,N=N)

Parametric Bootstrap of time-to-event data following a Weibull distribution

Description

Function generating bootstrap data according to a Weibull distribution (specified by a model parameter $\theta$ ), assuming exponentially distributed right-censoring (specified by a rate C). After data generation again a model is fitted and evaluated at a pre-specified time point $t_0$ yielding the response vector.

Usage

boot_weibull(t0, B = 1000, theta, C, N)
boot_weibull(t0, B = 1000, theta, C, N)

Arguments

`t0`	time point of interest
`B`	number of bootstrap repetitions. The default is B=1000
`theta`	parameter of the Weibull distribution, theta=(shape,scale)
`C`	rate of the exponential distribution specifiying the censoring
`N`	size of the dataset = number of observations

Value

A vector of length B containing the estimated survival at t0

Examples

t0<-2
N<-30
C<-1
boot_weibull(t0=t0,theta=c(1,3),C=C,N=N)
t0<-2
N<-30
C<-1
boot_weibull(t0=t0,theta=c(1,3),C=C,N=N)

Lower and upper confidence bounds for the difference of two parametric survival curves

Description

Function fitting parametric survival curves $S_1$ , $S_2$ to two groups and yielding lower and upper (1- $\alpha$ )-confidence bounds for the difference $S_1-S_2$ of these two curves at a specific time point, based on approximating the variance via bootstrap. For the bootstrap exponentially distributed random censoring is assumed and the parameters estimated from the datasets. $m_1$ and $m_2$ are parametric survival models following a Weibull, exponential, gaussian, logistic, log-normal or log-logistic distribution. For the generation of the bootstrap data exponentially distributed right-censoring is assumed and the rates estimated from the datasets. See Moellenhoff and Tresch <arXiv:2009.06699> for details.

Usage

confint_diff(alpha, t0, m1, m2, B = 1000, data_r, data_t, plot = TRUE)
confint_diff(alpha, t0, m1, m2, B = 1000, data_r, data_t, plot = TRUE)

Arguments

`alpha`	confidence level
`t0`	time point of interest
`m1`, `m2`	type of parametric model. Possible model types are "weibull", "exponential", "gaussian", "logistic", "lognormal" and "loglogistic"
`B`	number of bootstrap repetitions. The default is B=1000
`data_r`, `data_t`	datasets containing time and status for each individual (have to be referenced as this)
`plot`	if TRUE, a plot of the two survival curves will be given

Value

A list containing the difference $S_1(t_0)-S_2(t_0)$ , the lower and upper (1- $\alpha$ )-confidence bounds and a summary of the two model fits. Further a plot of the curves is given.

References

K.Moellenhoff and A.Tresch: Survival analysis under non-proportional hazards: investigating non-inferiority or equivalence in time-to-event data <arXiv:2009.06699>

Examples

data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
confint_diff(alpha=alpha,t0=t0,m1="weibull",m2="weibull",data_r=veteran_r,data_t=veteran_t)
data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
confint_diff(alpha=alpha,t0=t0,m1="weibull",m2="weibull",data_r=veteran_r,data_t=veteran_t)

Lower and upper confidence bounds for the difference of two Kaplan-Meier curves

Description

Function fitting Kaplan-Meier curves $S_1$ , $S_2$ to two groups and yielding lower and upper (1- $\alpha$ )-confidence bounds for the difference $S_1-S_2$ of these two curves at a specific time point by using Greenwood's formula.

Usage

confint_km_diff(alpha, t0, data_r, data_t, plot = TRUE)
confint_km_diff(alpha, t0, data_r, data_t, plot = TRUE)

Arguments

`alpha`	confidence level
`t0`	time point of interest
`data_r`, `data_t`	datasets containing time and status for each individual
`plot`	if TRUE, a plot of the two Kaplan Meier curves will be given

Value

A list containing the difference $S_1(t_0)-S_2(t_0)$ and the lower and upper (1- $\alpha$ )-confidence bounds. Further a plot of the curves is given.

Examples

data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
confint_km_diff(alpha=alpha,t0=t0,data_r=veteran_r,data_t=veteran_t)
data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
confint_km_diff(alpha=alpha,t0=t0,data_r=veteran_r,data_t=veteran_t)

Non-inferiority and equivalence test for the difference of two parametric survival curves

Description

Function for fitting and testing two parametric survival curves $S_1$ , $S_2$ at $t_0$ concerning the hypotheses of non-inferiority

$H_0:S_1(t_0)-S_2(t_0)\geq \epsilon\ vs.\ H_1: S_1(t_0)-S_2(t_0)< \epsilon$

or equivalence

$H_0:|S_1(t_0)-S_2(t_0)|\geq \epsilon\ vs.\ H_1: |S_1(t_0)-S_2(t_0)|< \epsilon.$

$m_1$ and $m_2$ are parametric survival models following a Weibull, exponential, gaussian, logistic, log-normal or log-logistic distribution. The test procedure is based on confidence intervals obtained via bootstrap. For the generation of the bootstrap data exponentially distributed random censoring is assumed and the rates estimated from the datasets. See Moellenhoff and Tresch <arXiv:2009.06699> for details.

Usage

test_diff(
  epsilon,
  alpha,
  t0,
  type,
  m1,
  m2,
  B = 1000,
  plot = TRUE,
  data_r,
  data_t
)
test_diff(
  epsilon,
  alpha,
  t0,
  type,
  m1,
  m2,
  B = 1000,
  plot = TRUE,
  data_r,
  data_t
)

Arguments

`epsilon`	non-inferiority/equivalence margin
`alpha`	significance level
`t0`	time point of interest
`type`	type of the test. "ni" for non-inferiority, "eq" for equivalence test
`m1`, `m2`	type of parametric model. Possible model types are "weibull", "exponential", "gaussian", "logistic", "lognormal" and "loglogistic"
`B`	number of bootstrap repetitions. The default is B=1000
`plot`	if TRUE, a plot of the two survival curves will be given
`data_r`, `data_t`	datasets containing time and status for each individual (have to be referenced as this)

Value

A list containing the difference $S_1(t_0)-S_2(t_0)$ , the lower and upper (1- $\alpha$ )-confidence bounds, the summary of the two model fits, the chosen margin and significance level and the test decision. Further a plot of the curves is given.

References

K.Moellenhoff and A.Tresch: Survival analysis under non-proportional hazards: investigating non-inferiority or equivalence in time-to-event data <arXiv:2009.06699>

Examples

data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
epsilon<-0.15
test_diff(epsilon=epsilon,alpha=alpha,t0=t0,type="eq",m1="weibull",m2="weibull",
data_r=veteran_r,data_t=veteran_t)
data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
epsilon<-0.15
test_diff(epsilon=epsilon,alpha=alpha,t0=t0,type="eq",m1="weibull",m2="weibull",
data_r=veteran_r,data_t=veteran_t)

Non-inferiority and equivalence test for the difference of two Kaplan-Meier curves

Description

Function for fitting and testing two Kaplan Meier curves $S_1$ , $S_2$ at $t_0$ concerning the hypotheses of non-inferiority

$H_0:S_1(t_0)-S_2(t_0)\geq \epsilon\ vs.\ H_1: S_1(t_0)-S_2(t_0)< \epsilon$

or equivalence

$H_0:|S_1(t_0)-S_2(t_0)|\geq \epsilon\ vs.\ H_1: |S_1(t_0)-S_2(t_0)|< \epsilon.$

Usage

test_nonpar(epsilon, alpha, t0, type, data_r, data_t, plot = TRUE)
test_nonpar(epsilon, alpha, t0, type, data_r, data_t, plot = TRUE)

Arguments

`epsilon`	non-inferiority/equivalence margin
`alpha`	significance level
`t0`	time point of interest
`type`	type of the test. "ni" for non-inferiority, "eq" for equivalence test
`data_r`, `data_t`	datasets containing time and status for each individual
`plot`	if TRUE, a plot of the two Kaplan Meier curves will be given

Value

A list containing the difference $S_1(t_0)-S_2(t_0)$ , the lower and upper (1- $\alpha$ )-confidence bounds, the chosen margin and significance level and the test decision. Further a plot of the curves is given.

Examples

data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
epsilon<-0.15
test_nonpar(epsilon=epsilon,alpha=alpha,t0=t0,type="eq",data_r=veteran_r,data_t=veteran_t)
data(veteran)
veteran_r <- veteran[veteran$trt==1,]
veteran_t <- veteran[veteran$trt==2,]
alpha<-0.05
t0<-80
epsilon<-0.15
test_nonpar(epsilon=epsilon,alpha=alpha,t0=t0,type="eq",data_r=veteran_r,data_t=veteran_t)

Package 'EquiSurv'

Help Index

Parametric Bootstrap of time-to-event data following an exponential distribution

Description

Usage

Arguments

Value

Examples

Parametric Bootstrap of time-to-event data following a gaussian distribution

Description

Usage

Arguments

Value

Examples

Parametric Bootstrap of time-to-event data following a logistic distribution

Description

Usage

Arguments

Value

Examples

Parametric Bootstrap of time-to-event data following a loglogistic distribution

Description

Usage

Arguments

Value

Examples

Parametric Bootstrap of time-to-event data following a lognormal distribution

Description

Usage

Arguments

Value

Examples

Parametric Bootstrap of time-to-event data following a Weibull distribution

Description

Usage

Arguments

Value

Examples

Lower and upper confidence bounds for the difference of two parametric survival curves

Description

Usage

Arguments

Value

References

Examples

Lower and upper confidence bounds for the difference of two Kaplan-Meier curves

Description

Usage

Arguments

Value

Examples

Non-inferiority and equivalence test for the difference of two parametric survival curves

Description

Usage

Arguments

Value

References

Examples

Non-inferiority and equivalence test for the difference of two Kaplan-Meier curves

Description

Usage

Arguments

Value

Examples