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 intervalcensored 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
1 2 3 4 5 6 7 8 
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 h for each covariate (default = equation 7 of Dehghan and Duchesne (2011)). 
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 
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 xaxis, by defaut 
ylab 
A label for the yaxis, by defaut 
xleg 
x location for legend, "bottomleft" by default (see 
yleg 
y location for legend, NULL by default (see 
... 
Further arguments to be passed to 
Details
For intervalcensored 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 intervalcensored data. Lifetime Data Analysis, 17, 234255.
See Also
Surv
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  data(simul)
## 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")
