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survreg.distributions.s
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survreg.distributions.s
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# SCCS @(#)survreg.distributions.s 4.3 11/19/92
#
# Create the survreg.distributions object
#
# Infinite mean in log logistic courtesy of Victor Moreno
# SERC, Institut Catala d'Oncologia (V.Moreno@ico.scs.es) 9Feb98
# survival package defines basic quantile function ignoring link
# Actual quantile function called Quantile here, for SV4 or R
survreg.auxinfo <- list(
exponential = list(
survival = function(times, lp, parms) exp(-times/exp(lp)),
hazard = function(times, lp, parms) exp(-lp),
quantile = function(p) log(-log(p)),
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) -logb(1-q)*exp(lp)
names(q) <- format(q)
drop(outer(lp, q, FUN=f, parms=parms))
},
mean = function(lp, parms) exp(lp),
latex = function(...) '\\exp(-t/\\exp(X\\beta))'
),
extreme = list(
survival = function(times, lp, parms) {
exp(-exp((times-lp)/exp(parms)))
},
hazard = function(times, lp, parms) {
scale <- exp(parms[1]) #14Jun97
exp((times-lp)/scale)/scale
},
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*logb(-logb(1-q))
names(q) <- format(q)
drop(outer(lp, q, FUN=f, parms=parms))
},
mean = function(lp, parms) {
names(parms) <- NULL
lp-.57722*exp(parms)
},
latex = function(scale) {
yvar <- "t"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("\\exp[-\\exp(",z,")]")
z
}
),
weibull = list(
survival = function(times, lp, parms) {
t.trans <- logb(times)
names(t.trans) <- format(times)
exp(-exp((t.trans-lp)/exp(parms)))
},
hazard = function(times, lp, parms) {
t.trans <- logb(times)
t.deriv <- 1/times
names(t.trans) <- format(times)
scale <- exp(parms[1]) #14Jun97
ifelse(times==0,exp(-lp/scale)/scale,
exp((t.trans-lp)/scale)*t.deriv/scale)
},
quantile = function(p) log(-log(p)),
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*logb(-logb(1-q))
names(q) <- format(q)
drop(exp(outer(lp, q, FUN=f, parms=parms)))
},
mean = function(lp, parms, transform) {
names(parms) <- NULL
exp(lp)*gamma(exp(parms)+1)
},
latex = function(scale) {
yvar <- "\\log(t)"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("\\exp[-\\exp(",z,")]")
z
}
),
logistic = list(
survival = function(times, lp, parms) {
1/(1+exp((times-lp)/exp(parms)))
},
hazard = function(times, lp, parms) {
scale <- exp(parms)
1/scale/(1+exp(-(times-lp)/scale))
},
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*logb(q/(1-q))
names(q) <- format(q)
drop(outer(lp, q, FUN=f, parms=parms))
},
mean = function(lp, parms) lp,
latex = function(scale){
yvar <- "t"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("[1+\\exp(",z,")]^{-1}")
z
}
),
loglogistic = list(
survival = function(times, lp, parms) {
1/(1+exp((logb(times)-lp)/exp(parms)))
},
hazard = function(times, lp, parms) {
t.trans <- logb(times)
t.deriv <- 1/times
scale <- exp(parms)
names(t.trans) <- format(times)
t.deriv/scale/(1+exp(-(t.trans-lp)/scale))
},
quantile = qlogis,
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*logb(q/(1-q))
names(q) <- format(q)
drop(exp(outer(lp, q, FUN=f, parms=parms)))
},
mean = function(lp, parms) {
names(parms) <- NULL
if(exp(parms)>1) rep(Inf,length(lp)) else
exp(lp)*pi*exp(parms)/sin(pi*exp(parms))
},
latex = function(scale) {
yvar <- "\\log(t)"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("[1+\\exp(",z,")]^{-1}")
z
}),
gaussian = list(
survival = function(times, lp, parms) pnorm(- (times-lp)/exp(parms)),
hazard = function(times, lp, parms) {
scale <- exp(parms)
z <- (times-lp)/scale
dnorm(z) / scale / pnorm(- z)
},
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*qnorm(q)
names(q) <- format(q)
drop(outer(lp, q, FUN=f, parms=parms))
},
mean = function(lp, parms) lp,
latex = function(scale) {
yvar <- "t"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("1-\\Phi(",z,")")
z
}
),
lognormal = list(
survival = function(times, lp, parms) {
t.trans <- logb(times)
names(t.trans) <- format(times)
pnorm(- (t.trans-lp)/exp(parms))
},
hazard = function(times, lp, parms) {
t.trans <- logb(times)
t.deriv <- 1/times
scale <- exp(parms)
names(t.trans) <- format(times)
z <- (t.trans-lp)/scale
t.deriv * dnorm(z) / scale / pnorm(- z)
},
quantile = qnorm,
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms)*qnorm(q)
names(q) <- format(q)
drop(exp(outer(lp, q, FUN=f, parms=parms)))
},
mean = function(lp, parms) {
names(parms) <- NULL
exp(lp+exp(2*parms)/2)
},
latex = function(scale) {
yvar <- "\\log(t)"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("1-\\Phi(",z,")")
z
}
),
t = list(
survival = function(times, lp, parms) {
scale <- exp(parms[1])
df <- parms[2]
pt(- (times-lp)/scale,df)
},
hazard = function(times, lp, parms) {
scale <- exp(parms[1])
df <- parms[2]
z <- (times-lp)/scale
dt(z,df) / scale / pt(- z,df)
},
Quantile = function(q=.5, lp, parms) {
names(parms) <- NULL
f <- function(lp, q, parms) lp + exp(parms[1])*qt(q, parms[2])
names(q) <- format(q)
drop(outer(lp, q, FUN=f, parms=parms))
},
mean = function(lp, parms) lp,
latex = function(scale,df) {
yvar <- "t"
z <- if(scale==1) paste(yvar,"-X\\beta") else paste(
"\\frac{", yvar, "-X\\beta}{",format(scale),"}",sep="")
z <- paste("1-T_{",df,"}(",z,")", sep="")
z
}
)
)