transKMW {TPmsm}

Kaplan-Meier weighted transition probabilities

Description

Provides estimates for the transition probabilities based on Kaplan-Meier weighted estimators, KMW.

Usage

transKMW(object, s, t, state.names=c("1", "2", "3"), conf=FALSE, n.boot=1000,
conf.level=0.95, method.boot="percentile", method.est=3)

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 Stime will be used.

state.names

A vector of characters giving the state names.

conf

Provides pointwise confidence bands. Defaults to FALSE.

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.

Details

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 \leq t)}{1-P(Z \leq s)},

p_{12}(s,t)=\frac{P(Z \leq t)-P(Z \leq s)-P(s<Z \leq t, T \leq t)}{1-P(Z \leq s)},

p_{22}(s,t) =\frac{P(Z \leq s)-P(Z \leq s,T \leq t)}{P(Z \leq s)-P(T \leq 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 \leq t,T>t)}{P(Z>s)},

p_{22}(s,t) =\frac{P(Z \leq s,T>t)}{P(Z \leq 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 \leq t)}{1-P(Z \leq s)},

p_{13}(s,t)=\frac{P(Z>s,T \leq t)}{1-P(Z \leq s)},

p_{23}(s,t) =\frac{P(Z \leq s,s<T \leq t)}{P(Z \leq s)-P(T \leq 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 \leq t)}{P(Z>s)},

p_{23}(s,t) =\frac{P(Z \leq s,s<T \leq t)}{P(Z \leq 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).

Value

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 NULL.

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. 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, transIPCW, transKMPW, transLIN, transLS, transPAJ.

Examples

# 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
transKMW(object=heartTP_obj, s=33, t=412);

# Compute transition probabilities with confidence band
transKMW(object=heartTP_obj, s=33, t=412, conf=TRUE, conf.level=0.9,
method.boot="basic", method.est=2);

# Restore the number of threads
setThreadsTP(nth);