Censored Poisson Family Function

Description

Family function for a censored Poisson response.

Usage

cens.poisson(link = "loge", imu = NULL)

Arguments

Details

Often a table of Poisson counts has an entry J+ meaning >= J. This family function is similar to poissonff but handles such censored data. The input requires SurvS4. Only a univariate response is allowed. The Newton-Raphson algorithm is used.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Warning

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.

Note

The function poissonff should be used when there are no censored observations. Also, NAs are not permitted with SurvS4, nor is type = "counting".

Author(s)

Thomas W. Yee

References

See survival for background.

See Also

SurvS4, poissonff, Links.

Examples

# 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(ii <- 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(ii <- 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 means 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,
     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)
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 check