transIPCW {TPmsm} | R Documentation |
Inverse probability censoring weighted transition probabilities
Description
Provides estimates for the transition probabilities based on inverse probability censoring weighted estimators, IPCW.
Usage
transIPCW(object, s, t, x, bw="dpik", window="normal", method.weights="NW",
state.names=c("1", "2", "3"), conf=FALSE, n.boot=1000, conf.level=0.95,
method.boot="percentile", method.est=1, ...)
Arguments
object |
An object of class ‘survTP’. |
s |
The first time for obtaining estimates for the transition probabilities. If missing, 0 will be used. |
t |
The second time for obtaining estimates for the transition probabilities.
If missing, the maximum of |
x |
Covariate values for obtaining estimates for the conditional transition probabilities. If missing, unconditioned transition probabilities will be computed. |
bw |
A character string indicating a function to compute a kernel density bandwidth. Defaults to “dpik” from package KernSmooth. Alternatively a single numeric value can be specified. |
window |
A character string specifying the desired kernel. See details below for possible options. Defaults to “normal” 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”. |
state.names |
A vector of characters giving the state names. |
conf |
Provides pointwise confidence bands. Defaults to |
n.boot |
The number of bootstrap samples. Defaults to 1000 samples. |
conf.level |
Level of confidence. Defaults to 0.95 (corresponding to 95%). |
method.boot |
The method used to compute bootstrap confidence bands. Possible options are “percentile” and “basic”. Defaults to “percentile”. |
method.est |
The method used to compute the estimate. Possible options are 1 or 2. |
... |
Further arguments.
Typically these arguments are passed to the function specified by argument |
Details
If bw="dpik"
then possible options for argument window
are “normal”, “box”, “epanech”, “biweight” or “triweight”.
When argument bw
is numeric then argument window
accepts the same options as when bw="dpik"
plus one of “tricube”, “triangular” or “cosine”.
If method.est=1
then p_{11}(s,t|X)
, p_{12}(s,t|X)
and p_{22}(s,t|X)
are estimated according to the following expressions:
p_{11}(s,t|X)=\frac{1-P(Z \leq t|X)}{1-P(Z \leq s|X)}
,
p_{12}(s,t|X)=\frac{P(Z \leq t|X)-P(Z \leq s|X)-P(s<Z \leq t, T \leq t|X)}{1-P(Z \leq s|X)}
,
p_{22}(s,t|X) =\frac{P(Z \leq s|X)-P(Z \leq s,T \leq t|X)}{P(Z \leq s|X)-P(T \leq s|X)}
.
Then, p_{13}(s,t|X)=1-p_{11}(s,t|X)-p_{12}(s,t|X)
and p_{23}(s,t|X)=1-p_{22}(s,t|X)
.
If method.est=2
then p_{11}(s,t|X)
, p_{12}(s,t|X)
and p_{22}(s,t|X)
are estimated according to the following expressions:
p_{11}(s,t|X)=\frac{P(Z>t|X)}{P(Z>s|X)}
,
p_{12}(s,t|X)=\frac{P(s<Z \leq t,T>t|X)}{P(Z>s|X)}
,
p_{22}(s,t|X) =\frac{P(Z \leq s,T>t|X)}{P(Z \leq s, T>s|X)}
.
Then, p_{13}(s,t|X)=1-p_{11}(s,t|X)-p_{12}(s,t|X)
and p_{23}(s,t|X)=1-p_{22}(s,t|X)
.
Value
If argument x
is missing or if argument object
doesn't contain a covariate,
an object of class ‘TPmsm’ is returned. There are methods for contour
, image
, print
and plot
.
‘TPmsm’ objects are implemented as a list with elements:
method |
A string indicating the type of estimator used in the computation. |
est |
A matrix with transition probability estimates. The rows being the event times and the columns the 5 possible transitions. |
inf |
A matrix with the lower transition probabilities of the confidence band. The rows being the event times and the columns the 5 possible transitions. |
sup |
A matrix with the upper transition probabilities of the confidence band. The rows being the event times and the columns the 5 possible transitions. |
time |
Vector of times where the transition probabilities are computed. |
s |
Start of the time interval. |
t |
End of the time interval. |
h |
The bandwidth used. If the estimator doesn't require a bandwidth, it's set to |
state.names |
A vector of characters giving the states names. |
n.boot |
Number of bootstrap samples used in the computation of the confidence band. |
conf.level |
Level of confidence used to compute the confidence band. |
If argument x
is specified and argument object
contains a covariate,
an object of class ‘TPCmsm’ is returned. There are methods for print
and plot
.
‘TPCmsm’ objects are implemented as a list with elements:
method |
A string indicating the type of estimator used in the computation. |
est |
A 3 dimensional array with transition probability estimates. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. |
inf |
A 3 dimensional array with the lower transition probabilities of the confidence band. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. |
sup |
A 3 dimensional array with the upper transition probabilities of the confidence band. The first dimension being the event times, the second the covariate values and the last one the 5 possible transitions. |
time |
Vector of times where the transition probabilities are computed. |
covariate |
Vector of covariate values where the conditional transition probabilities are computed. |
s |
Start of the time interval. |
t |
End of the time interval. |
x |
Additional covariate values where the conditional transition probabilities are computed, which may or may not be present in the sample. |
h |
The bandwidth used. |
state.names |
A vector of characters giving the states names. |
n.boot |
Number of bootstrap samples used in the computation of the confidence band. |
conf.level |
Level of confidence used to compute the confidence band. |
Author(s)
Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado
References
Araújo A, Meira-Machado L, Roca-Pardiñas J (2014). TPmsm: Estimation of the Transition Probabilities in 3-State Models. Journal of Statistical Software, 62(4), 1-29. doi:10.18637/jss.v062.i04
Meira-Machado L., de Uña-Álvarez J., Datta S. (2011). Conditional Transition Probabilities in a non-Markov Illness-death Model. Discussion Papers in Statistics and Operation Research n 11/03. Department of Statistics and Operations Research, University of Vigo (ISSN: 1888-5756, Deposito Legal VG 1402-2007). https://depc05.webs.uvigo.es/reports/12_05.pdf
Meira Machado L. F., de Uña-Álvarez J., Cadarso-Suárez C. (2006). Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Anal, 12(3), 325-344. doi:10.1007/s10985-006-9009-x
Davison, A. C., Hinkley, D. V. (1997). Bootstrap Methods and their Application, Chapter 5, Cambridge University Press.
See Also
transAJ
,
transKMPW
,
transKMW
,
transLIN
,
transLS
,
transPAJ
.
Examples
# Set the number of threads
nth <- setThreadsTP(2);
# Create survTP object with age as covariate
data(heartTP);
heartTP_obj <- with( heartTP, survTP(time1, event1, Stime, event, age=age) );
# Compute unconditioned transition probabilities
transIPCW(object=heartTP_obj, s=33, t=412);
# Compute unconditioned transition probabilities with confidence band
transIPCW(object=heartTP_obj, s=33, t=412, conf=TRUE, conf.level=0.9,
method.boot="basic", method.est=2);
# Compute conditional transition probabilities
transIPCW(object=heartTP_obj, s=33, t=412, x=0);
# Compute conditional transition probabilities with confidence band
transIPCW(object=heartTP_obj, s=33, t=412, x=0, conf=TRUE, conf.level=0.95,
n.boot=100, method.boot="percentile", method.est=2);
# Restore the number of threads
setThreadsTP(nth);