| Type: | Package |
| Title: | Generalized Turnbull's Estimator |
| Version: | 1.2-4 |
| Date: | 2025-08-25 |
| Description: | Generalized Turnbull's estimator proposed by Dehghan and Duchesne (2011). |
| License: | GPL-2 |
| LazyData: | true |
| Depends: | survival |
| Suggests: | interval |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | yes |
| Packaged: | 2025-08-25 14:06:13 UTC; Sophie |
| Author: | Mohammad Hossein Dehghan [aut], Thierry Duchesne [aut, cre], Sophie Baillargeon [aut] |
| Maintainer: | Thierry Duchesne <thierry.duchesne@mat.ulaval.ca> |
| Repository: | CRAN |
| Date/Publication: | 2025-08-25 16:00:02 UTC |
Generalized Turnbull's Estimator
Description
The gte function computes the generalized Turnbull's estimator proposed by Dehghan and Duchesne (2011).
It is a nonparametric estimator of a conditional survival function given a vector of continuous covariates
that can handle interval-censored lifetimes.
Details
| Package: | gte |
| Type: | Package |
| Version: | 1.2-4 |
| Date: | 2025-08-25 |
| License: | GPL-2 |
Author(s)
Mohammad Hossein Dehghan, Thierry Duchesne and Sophie Baillargeon
Maintainer: Thierry Duchesne <thierry.duchesne@mat.ulaval.ca>
References
Dehghan, M. H. and Duchesne, T. (2011). A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data. Lifetime Data Analysis, 17, 234-255.
Generalized Turnbull's Estimator
Description
The gte function computes the generalized Turnbull's Estimator (GTE) proposed by Dehghan and Duchesne (2011).
It is a nonparametric estimator of a conditional survival function given a vector of continuous covariates
that can handle interval-censored lifetimes.
The print method for objects obtained from gte only prints the output value surv.summary.
The plot method for objects obtained from gte plots the estimate of the conditional survival
function, by default overlaying curves if more than one estimate is present and shading the innermost interval,
in which the GTE is indeterminate.
Usage
gte(formula, data, z, h = NULL, itermax = 1e+05, tole = 5e-04)
## S3 method for class 'gte'
print(x, ...)
## S3 method for class 'gte'
plot(
x,
overlay = TRUE,
shade = TRUE,
xlab = "time",
ylab = "survival",
xleg = "bottomleft",
yleg = NULL,
...
)
Arguments
formula |
A formula object with the response on the left of a ~ operator, and the covariates on the right.
The response must be a survival object as returned by the |
data |
An optional data frame, list or environment
containing the variables in the model formula. If not found in data, the variables are taken from
|
z |
A matrix: each row contains the values of a covariate vector at which an estimate of the conditional survival function is requested. If there is only one covariate, it can be a vector (possibly of length 1). |
h |
A vector: the values of the bandwidth parameter |
itermax |
maximal number of iterations for the algorithm (default=100000). |
tole |
maximal distance between successive iterations tolerated before declaring convergence (default=0.0005). |
x |
An object, produced by the |
... |
Further arguments to be passed to |
overlay |
A logical: Should the curves be overlayed when there is more than one estimate
of the conditional survival function in the |
shade |
A logical: Should the rectangles of indeterminate NPMLE (innermost interval)
be shaded? (default= |
xlab |
A label for the x-axis, by defaut |
ylab |
A label for the y-axis, by defaut |
xleg |
x location for legend, "bottomleft" by default (see |
yleg |
y location for legend, NULL by default (see |
Details
For interval-censored data, the Surv function should be called with the argument
type="interval" or type="interval2". If type="interval", the event argument
is mandatory. Therefore, in addition to the left and right endpoints of the censoring interval (called, respectively,
left and right for illustrative purpose), one would need a third variable (status) taking the value 0
for right censored data, 1 for an event at exact time, 2 for left censored data and 3 for interval censored data.
The Surv function would be called as follows:
Surv(time=left, time2=right, event=status, type="interval").
If type="interval2", the event argument cannot be given.
The value of event is derived from the time and time2 argument as follows:
if time takes the value NA, event=2 (left censored data);
if time2 takes the value NA, event=0 (right censored data);
if time=time2, event=1 (exact time);
otherwise, event=3 (interval censored data).
See the help page of the Surv function for more details.
In the gte function, the data must be given through the Surv function
but it is internally transformed in two vectors : L and R for the left and right endpoints of
the censoring interval, respectively.
If event=0 (right censored data), then L=time and R=Inf;
if event=1 (exact time), then L=time and R=time;
if event=2 (left censored data), then L=0 and R=time;
and if event=3 (interval censored data), then L=time and R=time2;
If one has vectors L and R respecting this convention, they can be given directly to gte
by calling Surv as follows:
Surv(L, R, type="interval2").
Value
time |
A vector: the ordered distinct values of the left and right endpoints of the censoring interval (omitting the smallest value, but always including time 0). |
surv |
A matrix: the estimates of the conditional survival function at time |
intmap |
A matrix : The intervals of the potential steps in the conditional survival function,
called innermost interval, over which the GTE is indeterminate. The left endpoints of
the intervals are in the first row, and the rigth endpoints in the second. The object
attribute LRin denotes whether to include each of the endpoints or not. This matrix
is computed with an internal function derived from function |
surv.summary |
A summary of |
Call |
The function call. |
Author(s)
Mohammad Hossein Dehghan, Thierry Duchesne and Sophie Baillargeon
References
Dehghan, M. H. and Duchesne, T. (2011). A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data. Lifetime Data Analysis, 17, 234-255.
See Also
Examples
## Calling Surv() with type="interval2"
Fit <- gte(Surv(L, R, type="interval2") ~ Z, data=simul, z=c(10, 20))
Fit
## Calling Surv() with type="interval"
event <- ifelse(is.na(simul$R), 0,
ifelse(is.na(simul$L), 2,
ifelse(simul$R==simul$L, 1, 3)))
time <- ifelse(event==2, simul$R, simul$L)
time2 <- ifelse(event==3, simul$R, NA)
simul_event <- cbind(simul, time, time2, event)
Fit_event <- gte(Surv(time, time2, event, type="interval") ~ Z, data=simul_event, z=c(10, 20))
Fit_event
# The results are the same
all.equal(Fit_event$time, Fit$time)
all.equal(Fit_event$surv, Fit$surv)
## Plotting the results
plot(Fit, xleg="topright")
Simulated Data
Description
Simulated Interval-censored data
Usage
simul
Format
A data frame with 100 observations on the following 3 variables.
- L
the left endpoints of the censoring interval
- R
the right endpoints of the censoring interval
- Z
a continuous covariate
Details
The value R = NA means that the observation is right censored (occurs 2 times).
If L = NA, then the observation is left censored (occurs 26 times).
An observation with R = L means that the time of occurence of the event
is known exactly (occurs 3 times).
References
Dehghan, M. H. and Duchesne, T. (2011). A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data. Lifetime Data Analysis, 17, 234-255.
Examples
Fit <- gte(Surv(L, R, type="interval2") ~ Z, data=simul, z=15)
plot(Fit)