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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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)

Arguments

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)

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
)

Arguments

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)

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)

Arguments

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)