The first integrate function
f1(t, survdist, k, lambda0)time variable
survival distribution of uncured patients. It can be "exp" or "weib".
if survdist = "weib", the shape parameter k needs to be specified. By default k = 1, which refers to the exponential distribution.
the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm.
The density function of Weibull distribution with shape parameter k and scale parameter \(\lambda_{0}\) is given by
$$f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),$$ for \(t > 0\),
and the corresponding survival distribution is
$$S(t)=\exp(-(\lambda_0 t)^k).
$$