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R/baselines.R
In parfm: Parametric Frailty Models
Defines functions
logskewnormal
loglogistic
lognormal
gompertz
exponential
frechet
weibull
################################################################################
# Baseline hazard distributions #
################################################################################
# #
# These are functions with parameters #
# - pars: the vector of parameters #
# - t : the time point #
# - what: the quantity to be returned by the function #
# either "H", the cumulated hazard, #
# or "lh", the log-hazard #
# #
# #
# Date: December 19, 2011 #
# Last modification on: January 25, 2017 #
################################################################################
################################################################################
################################################################################
################################################################################
# #
# Weibull baseline hazard function #
# #
# Parameters: #
# [1] rho > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \rho \lambda t ^ (\rho-1) #
# #
# #
# Date: December, 19, 2011 #
################################################################################
weibull <- function(pars,
t,
what) {
if (what == "H")
return(pars[2] * t ^ (pars[1]))
else if (what == "lh")
return(log(pars[1]) + log(pars[2]) + ((pars[1] - 1) * log(t)))
}
################################################################################
# #
# Fréchet or Inverse Weibull baseline hazard function #
# #
# Parameters: #
# [1] rho > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda \rho t ^ -(\rho + 1) / (exp(\lambda t ^ -\rho) - 1) #
# H(t) = -log[1 - exp{- \lambda t ^ -\rho}] #
# #
# #
# Date: June, 26, 2012 #
# Last modification: January 31, 2017 #
################################################################################
inweibull <- frechet <- function(pars,
t,
what) {
if (what == "H")
return(-log(1 - exp(-pars[2] * (t ^ -pars[1]))))
else if (what == "lh")
return(sum(log(pars[1:2])) - log(t) * (pars[1] + 1) -
log(exp(pars[2] * (t ^ -pars[1])) - 1))
}
################################################################################
# #
# Exponential baseline hazard function #
# #
# Parameters: #
# [1] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda #
# #
# #
# Date: December, 19, 2011 #
################################################################################
exponential <- function(pars,
t,
what) {
if (what == "H")
return(pars * t)
else if (what == "lh")
return(log(pars))
}
################################################################################
# #
# Gompertz baseline hazard function #
# #
# Parameters: #
# [1] gamma > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda exp(\gamma t) #
# #
# #
# Date: December, 19, 2011 #
################################################################################
gompertz <- function(pars,
t,
what) {
if (what == "H")
return(pars[2] / pars[1] * (exp(pars[1] * t) - 1))
else if (what == "lh")
return(log(pars[2]) + pars[1] * t)
}
################################################################################
# #
# Lognormal baseline hazard function #
# #
# Parameters: #
# [1] mu \in \mathbb R #
# [2] sigma > 0 #
# #
# Hazard: #
# h(t) = \frac{ \phi(\log t -\mu \over \sigma) }{ #
# \sigma t [1-\Phi(\log t -\mu \over \sigma)] } #
# #
# with \phi the density and \Phi the distribution function #
# of a standard Normal #
# #
# #
# Date: December, 19, 2011 #
################################################################################
lognormal <- function(pars,
t,
what) {
if (what == "H") #return - log (S)
return(- log(1 - plnorm(t, meanlog = pars[1], sdlog = pars[2])))
else if (what == "lh") #return log(f) - log(S)
return(dlnorm(t, meanlog = pars[1], sdlog = pars[2], log = TRUE) -
log(1 - plnorm(t, meanlog = pars[1], sdlog = pars[2])))
}
################################################################################
# #
# Loglogistic baseline hazard function #
# #
# Parameters: #
# [1] alpha \in \mathbb R #
# [2] kappa > 0 #
# #
# Hazard: #
# h(t) = \frac{ \exp(\alpha) \kappa t^{\kappa-1} }{ #
# 1 + \exp(\alpha) t^\kappa } #
# #
# #
# Date: December, 19, 2011 #
################################################################################
loglogistic <- function(pars,
t,
what) {
if (what == "H")
return(log(1 + exp(pars[1]) * t ^ (pars[2])))
else if (what == "lh")
return(pars[1] + log(pars[2]) + (pars[2] - 1) * log(t) -
log(1 + exp(pars[1]) * t ^ pars[2]) )
}
################################################################################
# #
# Log-skewNormal baseline hazard function #
# Azzalini, Adelchi. (1985). A class of distributions which includes #
# the normal ones. Scandinavian Journal of Statistics, 12:171-178 #
# #
# Parameters: #
# [1] xi \in \mathbb R, the location parameter #
# [2] omega > 0, the scale parameter (called omega in original paper) #
# [3] alpha \in \mathbb R, the shape parameter #
# #
# Density: #
# f(t) = 2 / (\omega t) \phi_d((\log(t) - \xi) / \omega) #
# \Phi(\alpha (log(t) - \xi) / \omega) #
# #
# #
# Author: Andrea Callegaro #
# Date: November, 22, 2016 #
################################################################################
logskewnormal <- function(pars,
t,
what) {
# library(sn)
#log-skew normal density
dlsn <- Vectorize(function(t, pars) {
dsn(log(t), xi = pars[1], omega = pars[2], alpha = pars[3]
) / t
}, 't')
#log-skew normal cdf
plsn <- Vectorize(function(t, pars) {
psn(log(t), xi = pars[1], omega = pars[2], alpha = pars[3])
}, 't')
if (what == "H") #return -log(S)
return(-log(1 - plsn(t, pars = pars)))
else if (what == "lh") #return (log(f) - log(S))
return(log(dlsn(t, pars = pars)) -
log(1 - plsn(t, pars = pars)))
}
# setGeneric('basehaz', package = 'survival')
# setClass('parfm')
# setMethod('basehaz', signature(fit = 'parfm'), function(fit, centered = TRUE) {
# return(fit)
# })
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Defines functions logskewnormal loglogistic lognormal gompertz exponential frechet weibull
################################################################################
# Baseline hazard distributions #
################################################################################
# #
# These are functions with parameters #
# - pars: the vector of parameters #
# - t : the time point #
# - what: the quantity to be returned by the function #
# either "H", the cumulated hazard, #
# or "lh", the log-hazard #
# #
# #
# Date: December 19, 2011 #
# Last modification on: January 25, 2017 #
################################################################################
################################################################################
################################################################################
################################################################################
# #
# Weibull baseline hazard function #
# #
# Parameters: #
# [1] rho > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \rho \lambda t ^ (\rho-1) #
# #
# #
# Date: December, 19, 2011 #
################################################################################
weibull <- function(pars,
t,
what) {
if (what == "H")
return(pars[2] * t ^ (pars[1]))
else if (what == "lh")
return(log(pars[1]) + log(pars[2]) + ((pars[1] - 1) * log(t)))
}
################################################################################
# #
# Fréchet or Inverse Weibull baseline hazard function #
# #
# Parameters: #
# [1] rho > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda \rho t ^ -(\rho + 1) / (exp(\lambda t ^ -\rho) - 1) #
# H(t) = -log[1 - exp{- \lambda t ^ -\rho}] #
# #
# #
# Date: June, 26, 2012 #
# Last modification: January 31, 2017 #
################################################################################
inweibull <- frechet <- function(pars,
t,
what) {
if (what == "H")
return(-log(1 - exp(-pars[2] * (t ^ -pars[1]))))
else if (what == "lh")
return(sum(log(pars[1:2])) - log(t) * (pars[1] + 1) -
log(exp(pars[2] * (t ^ -pars[1])) - 1))
}
################################################################################
# #
# Exponential baseline hazard function #
# #
# Parameters: #
# [1] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda #
# #
# #
# Date: December, 19, 2011 #
################################################################################
exponential <- function(pars,
t,
what) {
if (what == "H")
return(pars * t)
else if (what == "lh")
return(log(pars))
}
################################################################################
# #
# Gompertz baseline hazard function #
# #
# Parameters: #
# [1] gamma > 0 #
# [2] lambda > 0 #
# #
# Hazard: #
# h(t) = \lambda exp(\gamma t) #
# #
# #
# Date: December, 19, 2011 #
################################################################################
gompertz <- function(pars,
t,
what) {
if (what == "H")
return(pars[2] / pars[1] * (exp(pars[1] * t) - 1))
else if (what == "lh")
return(log(pars[2]) + pars[1] * t)
}
################################################################################
# #
# Lognormal baseline hazard function #
# #
# Parameters: #
# [1] mu \in \mathbb R #
# [2] sigma > 0 #
# #
# Hazard: #
# h(t) = \frac{ \phi(\log t -\mu \over \sigma) }{ #
# \sigma t [1-\Phi(\log t -\mu \over \sigma)] } #
# #
# with \phi the density and \Phi the distribution function #
# of a standard Normal #
# #
# #
# Date: December, 19, 2011 #
################################################################################
lognormal <- function(pars,
t,
what) {
if (what == "H") #return - log (S)
return(- log(1 - plnorm(t, meanlog = pars[1], sdlog = pars[2])))
else if (what == "lh") #return log(f) - log(S)
return(dlnorm(t, meanlog = pars[1], sdlog = pars[2], log = TRUE) -
log(1 - plnorm(t, meanlog = pars[1], sdlog = pars[2])))
}
################################################################################
# #
# Loglogistic baseline hazard function #
# #
# Parameters: #
# [1] alpha \in \mathbb R #
# [2] kappa > 0 #
# #
# Hazard: #
# h(t) = \frac{ \exp(\alpha) \kappa t^{\kappa-1} }{ #
# 1 + \exp(\alpha) t^\kappa } #
# #
# #
# Date: December, 19, 2011 #
################################################################################
loglogistic <- function(pars,
t,
what) {
if (what == "H")
return(log(1 + exp(pars[1]) * t ^ (pars[2])))
else if (what == "lh")
return(pars[1] + log(pars[2]) + (pars[2] - 1) * log(t) -
log(1 + exp(pars[1]) * t ^ pars[2]) )
}
################################################################################
# #
# Log-skewNormal baseline hazard function #
# Azzalini, Adelchi. (1985). A class of distributions which includes #
# the normal ones. Scandinavian Journal of Statistics, 12:171-178 #
# #
# Parameters: #
# [1] xi \in \mathbb R, the location parameter #
# [2] omega > 0, the scale parameter (called omega in original paper) #
# [3] alpha \in \mathbb R, the shape parameter #
# #
# Density: #
# f(t) = 2 / (\omega t) \phi_d((\log(t) - \xi) / \omega) #
# \Phi(\alpha (log(t) - \xi) / \omega) #
# #
# #
# Author: Andrea Callegaro #
# Date: November, 22, 2016 #
################################################################################
logskewnormal <- function(pars,
t,
what) {
# library(sn)
#log-skew normal density
dlsn <- Vectorize(function(t, pars) {
dsn(log(t), xi = pars[1], omega = pars[2], alpha = pars[3]
) / t
}, 't')
#log-skew normal cdf
plsn <- Vectorize(function(t, pars) {
psn(log(t), xi = pars[1], omega = pars[2], alpha = pars[3])
}, 't')
if (what == "H") #return -log(S)
return(-log(1 - plsn(t, pars = pars)))
else if (what == "lh") #return (log(f) - log(S))
return(log(dlsn(t, pars = pars)) -
log(1 - plsn(t, pars = pars)))
}
# setGeneric('basehaz', package = 'survival')
# setClass('parfm')
# setMethod('basehaz', signature(fit = 'parfm'), function(fit, centered = TRUE) {
# return(fit)
# })
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