test_diff {EquiSurv}

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

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)