transKMPW | R Documentation |
Provides estimates for the transition probabilities based on presmoothed Kaplan-Meier weighted estimators, KMPW.
transKMPW(object, s, t, state.names=c("1", "2", "3"), conf=FALSE, n.boot=1000, conf.level=0.95, method.boot="percentile", method.est=3)
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 |
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, 2, 3 or 4. |
If method.est=1
then p_{11}(s,t), p_{12}(s,t) and p_{22}(s,t) are estimated according to the following expressions:
p_{11}(s,t)=\frac{1-P(Z ≤q t)}{1-P(Z ≤q s)},
p_{12}(s,t)=\frac{P(Z ≤q t)-P(Z ≤q s)-P(s<Z ≤q t, T ≤q t)}{1-P(Z ≤q s)},
p_{22}(s,t) =\frac{P(Z ≤q s)-P(Z ≤q s,T ≤q t)}{P(Z ≤q s)-P(T ≤q s)}.
Then, p_{13}(s,t)=1-p_{11}(s,t)-p_{12}(s,t) and p_{23}(s,t)=1-p_{22}(s,t).
If method.est=2
then p_{11}(s,t), p_{12}(s,t) and p_{22}(s,t) are estimated according to the following expressions:
p_{11}(s,t)=\frac{P(Z>t)}{P(Z>s)},
p_{12}(s,t)=\frac{P(s<Z ≤q t,T>t)}{P(Z>s)},
p_{22}(s,t) =\frac{P(Z ≤q s,T>t)}{P(Z ≤q s,T>s)}.
Then, p_{13}(s,t)=1-p_{11}(s,t)-p_{12}(s,t) and p_{23}(s,t)=1-p_{22}(s,t).
If method.est=3
then p_{11}(s,t), p_{13}(s,t) and p_{23}(s,t) are estimated according to the following expressions:
p_{11}(s,t)=\frac{1-P(Z ≤q t)}{1-P(Z ≤q s)},
p_{13}(s,t)=\frac{P(Z>s,T ≤q t)}{1-P(Z ≤q s)},
p_{23}(s,t) =\frac{P(Z ≤q s,s<T ≤q t)}{P(Z ≤q s)-P(T ≤q s)}.
Then, p_{12}(s,t)=1-p_{11}(s,t)-p_{13}(s,t) and p_{22}(s,t)=1-p_{23}(s,t).
If method.est=4
then p_{11}(s,t), p_{13}(s,t) and p_{23}(s,t) are estimated according to the following expressions:
p_{11}(s,t)=\frac{P(Z>t)}{P(Z>s)},
p_{13}(s,t)=\frac{P(Z>s,T ≤q t)}{P(Z>s)},
p_{23}(s,t) =\frac{P(Z ≤q s,s<T ≤q t)}{P(Z ≤q s,T>s)}.
Then, p_{12}(s,t)=1-p_{11}(s,t)-p_{13}(s,t) and p_{22}(s,t)=1-p_{23}(s,t).
An object of class ‘TPmsm’. 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. |
Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado
Amorim A. P., de Uña-Álvarez J., Meira Machado L. F. (2011). Presmoothing the transition probabilities in the illness-death model. Statistics and Probability Letters, 81(7), 797-806. doi: 10.1016/j.spl.2011.02.017
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
Davison, A. C., Hinkley, D. V. (1997). Bootstrap Methods and their Application, Chapter 5, Cambridge University Press.
transAJ
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transPAJ
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# Set the number of threads nth <- setThreadsTP(2) # Create survTP object data(heartTP) heartTP_obj <- with(heartTP, survTP(time1, event1, Stime, event)) # Compute transition probabilities transKMPW(object=heartTP_obj, s=33, t=412) # Compute transition probabilities with confidence band transKMPW(object=heartTP_obj, s=33, t=412, conf=TRUE, conf.level=0.9, method.boot="percentile", method.est=4) # Restore the number of threads setThreadsTP(nth)
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