M integrate function
m(t, beta0, gamma0, pi0, survdist, k, lambda0)time variable
log hazard ratio of uncured patients
log odds ratio of cure rates between two arms
cure rate for the control arm, which is between 0 and 1.
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
$$S(t)=\exp(-(\lambda_0 t)^k).
$$