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PersMonNonMixWei <- function(lambda, k, c, n.alive, new.pat, cont.time) {
## Calculates the further person months
## in the non-mixture model with Weibull type survival, i. e.
## S(t) = c^[1 - exp(- lambda * t^k)], lambda > 0, k > 0, 0 < c < 1, t >= 0,
## from the interim analysis until the end of time of continuation.
##
## Args:
## lambda: Parameter.
## k: Parameter.
## c: Parameter.
## n.alive: Number of patients still alive.
## new.pat: Number of patients who will be recruited each time unit.
## cont.time: Period of time of continuing the trial.
##
## Results:
## Further person months.
# auxiliary functions / integrands
Integrand1 <- function(x) {
c^(1 - exp(- lambda * x^k))
}
Integrand2 <- function(x) {
c^exp(- lambda * x^k)
}
Integrand3 <- function(x) {
(stats::integrate(f = Integrand2,
lower = 0,
upper = x)$value * c^(1 - exp(- lambda * x^k)))
}
# calculation of further person months
O.star <- (n.alive * stats::integrate(f = Integrand1,
lower = 0,
upper = cont.time)$value
+ new.pat / c * stats::integrate(f = Vectorize(Integrand3),
lower = 0,
upper = cont.time)$value)
return(O.star)
}
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