Censored Poisson Family Function
Family function for a censored Poisson response.
cens.poisson(link = "loglink", imu = NULL,
biglambda = 10, smallno = 1e-10)link |
Link function applied to the mean;
see |
imu |
Optional initial value;
see |
biglambda, smallno |
Used to help robustify the code when |
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as
vglm and
vgam.
As the response is discrete,
care is required with Surv, especially with
"interval" censored data because of the
(start, end] format.
See the examples below.
The examples have
y < L as left censored and
y >= U (formatted as U+) as right censored observations,
therefore
L <= y < U is for uncensored and/or interval censored
observations.
Consequently the input must be tweaked to conform to the
(start, end] format.
A bit of attention has been directed to try robustify the code
when lambda is very large, however this currently works
for left and right censored data only, not interval
censored data. Sometime the fix involves an approximation,
hence it is a good idea to set trace = TRUE.
Thomas W. Yee
See survival for background.
# Example 1: right censored data
set.seed(123); U <- 20
cdata <- data.frame(y = rpois(N <- 100, exp(3)))
cdata <- transform(cdata, cy = pmin(U, y),
rcensored = (y >= U))
cdata <- transform(cdata, status = ifelse(rcensored, 0, 1))
with(cdata, table(cy))
with(cdata, table(rcensored))
with(cdata, table(print(SurvS4(cy, status)))) # Check; U+ means >= U
fit <- vglm(SurvS4(cy, status) ~ 1, cens.poisson, data = cdata,
trace = TRUE)
coef(fit, matrix = TRUE)
table(print(depvar(fit))) # Another check; U+ means >= U
# Example 2: left censored data
L <- 15
cdata <- transform(cdata,
cY = pmax(L, y),
lcensored = y < L) # Note y < L, not cY == L or y <= L
cdata <- transform(cdata, status = ifelse(lcensored, 0, 1))
with(cdata, table(cY))
with(cdata, table(lcensored))
with(cdata, table(print(SurvS4(cY, status, type = "left")))) # Check
fit <- vglm(SurvS4(cY, status, type = "left") ~ 1, cens.poisson,
data = cdata, trace = TRUE)
coef(fit, matrix = TRUE)
# Example 3: interval censored data
cdata <- transform(cdata, Lvec = rep(L, len = N),
Uvec = rep(U, len = N))
cdata <-
transform(cdata,
icensored = Lvec <= y & y < Uvec) # Not lcensored or rcensored
with(cdata, table(icensored))
cdata <- transform(cdata, status = rep(3, N)) # 3 == interval censored
cdata <- transform(cdata,
status = ifelse(rcensored, 0, status)) # 0 means right censored
cdata <- transform(cdata,
status = ifelse(lcensored, 2, status)) # 2 means left censored
# Have to adjust Lvec and Uvec because of the (start, end] format:
cdata$Lvec[with(cdata,icensored)] <- cdata$Lvec[with(cdata,icensored)]-1
cdata$Uvec[with(cdata,icensored)] <- cdata$Uvec[with(cdata,icensored)]-1
# Unchanged:
cdata$Lvec[with(cdata, lcensored)] <- cdata$Lvec[with(cdata, lcensored)]
cdata$Lvec[with(cdata, rcensored)] <- cdata$Uvec[with(cdata, rcensored)]
with(cdata, # Check
table(ii <- print(SurvS4(Lvec, Uvec, status, type = "interval"))))
fit <- vglm(SurvS4(Lvec, Uvec, status, type = "interval") ~ 1,
cens.poisson, data = cdata, trace = TRUE)
coef(fit, matrix = TRUE)
table(print(depvar(fit))) # Another check
# Example 4: Add in some uncensored observations
index <- (1:N)[with(cdata, icensored)]
index <- head(index, 4)
cdata$status[index] <- 1 # actual or uncensored value
cdata$Lvec[index] <- cdata$y[index]
with(cdata, table(ii <- print(SurvS4(Lvec, Uvec, status,
type = "interval")))) # Check
fit <- vglm(SurvS4(Lvec, Uvec, status, type = "interval") ~ 1,
cens.poisson, data = cdata, trace = TRUE, crit = "c")
coef(fit, matrix = TRUE)
table(print(depvar(fit))) # Another checkPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.