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InitValLikelihoodNonMixGamma <- function(data) {
## Calculates initial values for the maximum likelihood estimation
## in the non-mixure model with Gamma type survival, i. e.
## S(t) = c^Gamma^(0)(a, b * t), a > 0, b > 0, 0 < c < 1, t >= 0,
## via method of moments for a and b as the parameters
## in the simple Gamma model (taking into account only
## the patiens who died) and using the relative frequency of survival
## for the estimation of c.
##
## Args:
## data: Data frame which consists of at least three columns with the group
## in the first (all of the same group),
## status (1 = event, 0 = censored) in the second
## and event time in the third column.
##
## Results:
## Returns calculated initial values for the maximum likelihood estimation.
# auxiliary variables
t <- data[, 3][data[, 2] == 1]
n.d <- length(x = t)
m1 <- sum(t) / n.d
m2 <- sum(t^2) / n.d
n.alive <- sum(1 - data[, 2])
n <- length(x = data[, 1])
# initial values...
b.0 <- m1 / (m2 - m1^2)
a.0 <- m1 * b.0
c.0 <- n.alive / n
# ...and if applicable projection into feasible region
eps <- 1e-6
if (a.0 < eps) {
a.0 <- eps
}
if (b.0 < eps) {
b.0 <- eps
}
if (c.0 < eps) {
c.0 <- eps
}
if (c.0 > 1 - eps) {
c.0 <- 1 - eps
}
return(c(a.0, b.0, c.0))
}
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