CIF {survidm}

Nonparametric estimation of the Cumulative Incident Functions in the illness-death model

Description

This function is used to obtain nonparametric estimates of the cumulative incidence probabilities in the illness-death model. They represent the probability of one individual's being or having been in state j at time t.

Usage

CIF(
  formula,
  s,
  data,
  conf = FALSE,
  n.boot = 199,
  conf.level = 0.95,
  z.value,
  bw = "dpik",
  window = "gaussian",
  method.weights = "NW",
  cluster = FALSE,
  ncores = NULL,
  presmooth = FALSE
)

Arguments

formula

A formula object, which must have a survIDM object as the response on the left of the ~ operator and, if desired, a term on the right. The term may be a qualitative or quantitative variable. Without covariates, the right hand side should be ~ 1.

s

The first time for obtaining estimates for the cumulative incidence functions. If missing, 0 will be used.

data

A data.frame including at least four columns named time1, event1, Stime and event, which correspond to disease free survival time, disease free survival indicator, time to death or censoring, and death indicator, respectively.

conf

Provides pointwise confidence bands. Defaults to FALSE.

n.boot

The number of bootstrap replicates to compute the variance of the estimator. Default is 199.

conf.level

Level of confidence. Defaults to 0.95 (corresponding to 95%).

z.value

The value of the covariate on the right hand side of formula at which the cumulative incidence probabilities are computed. For quantitative covariates, i.e. of class integer and numeric.

bw

A single numeric value to compute a kernel density bandwidth. Use "dpik" for the KernSmooth package based selector or "np" for the 'npudensbw' function of the np package.

window

A character string specifying the desired kernel. See details below for possible options. Defaults to "gaussian" where the gaussian density kernel will be used.

method.weights

A character string specifying the desired weights method. Possible options are "NW" for the Nadaraya-Watson weights and "LL" for local linear weights. Defaults to "NW".

cluster

A logical value. If TRUE (default), the bootstrap procedure for the confidence intervals is parallelized. Note that there are cases (e.g., a low number of bootstrap repetitions) that R will gain in performance through serial computation. R takes time to distribute tasks across the processors also it will need time for binding them all together later on. Therefore, if the time for distributing and gathering pieces together is greater than the time need for single-thread computing, it does not worth parallelize.

ncores

An integer value specifying the number of cores to be used in the parallelized procedure. If NULL (default), the number of cores to be used is equal to the number of cores of the machine - 1.

presmooth

A logical value. If TRUE, the presmoothed landmark estimator of the cumulative incidence function is computed.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

An object of class "survIDM" and one of the following two classes: "CIF" (Cumulative Incidence Function), and "cifIPCW" (Inverse Probability of Censoring Weighting for the Cumulative Incidence Function). Objects are implemented as a list with elements:

est

data.frame with estimates of the cumulative incidence probabilities.

CI

data.frame with the confidence intervals of the cumulative incidence probabilities.

conf.level

Level of confidence.

s

The first time for obtaining estimates for the cumulative incidence probabilities.

t

The time for obtaining the estimates of cumulative incidence probabilities.

conf

logical; if FALSE (default) the pointwise confidence bands are not given.

callp

The expression of the estimated probability.

Nlevels

The number of levels of the covariate. Provides important information when the covariate at the right hand side of formula is of class factor.

levels

The levels of the qualitative covariate (if it is of class factor) on the right hand side of formula.

formula

A formula object.

call

A call object.

Author(s)

Luis Meira-Machado, Marta Sestelo and Gustavo Soutinho.

References

Geskus, R.B. (2011). Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics, 67, 39–49.

Kalbeisch, J. D. and Prentice R. L. (1980) The statistical analysis of failure time data. John Wiley & Sons, New York.

Examples

# Cumulative Incidence Function (CIF)
res <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE)
res
summary(res, time=365*1:7)
plot(res, ylim=c(0, 0.6))

res01 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
conf = FALSE, presmooth = TRUE)
res01
summary(res01, time=365*1:7)
plot(res01, ylim=c(0, 0.6))


# CIF for those in State 1 at time s=365, Y(s)=0
res1 <- CIF(survIDM(time1, event1, Stime, event) ~ 1, data = colonIDM,
s = 365, conf = FALSE)
summary(res1, time=365*1:7)
plot(res1, ylim=c(0, 0.6))


# Conditional CIF (with a factor)
res2 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),
data = colonIDM, s = 365, conf = FALSE)
summary(res2, time=365*1:5)
plot(res2)

res2.1 <- CIF(survIDM(time1, event1, Stime, event) ~ factor(sex),  #new
data = colonIDM, s = 365, conf = FALSE, presmooth = TRUE)
summary(res2.1, time=365*1:5)
plot(res2.1)


# Conditional CIF (with continuous covariate)
res3 <- CIF(survIDM(time1, event1, Stime, event) ~ age, data = colonIDM,
z.value = 56, conf = FALSE)
summary(res3, time=365*1:6)
plot(res3)