aj {changeLOS}R Documentation

Aalen-Johansen estimator

Description

computes the Aalen-Johansen estimator for the matrix of transition probabilities P(s,t). The entry (l,m) of the matrix denotes the estimated probability that state m has been reached by time t given state l has been occupied by time s.

Usage

aj(tr, s, t)

Arguments

tr an object of 'trans'
s begin of the time interval
t end of the time interval

Details

The Aalen-Johansen estimator is considered in detail by Andersen et al. (1993). Usually, the process describing movements between states is considered to be Markovian; this assumption may be relaxed, cf. Datta and Satten (2001).

The Aalen-Johansen estimator is a finite matrix product, one matrix for every observed transition time in the time interval (s,t]. These matrices can be obtained from trans.

Value

An object of class 'aj'. The object is a list of:

matrix the matrix of transition probabilities P(s,t)
start the beginning s of the time interval (s,t]
end the end t of the time interval (s,t]
times the transition times in the interval (s,t]
matrices array of estimators for P(s,u) for all transition times u in (s,t]

Author(s)

Matthias Wangler mw@imbi.uni-freiburg.de

References

P Andersen, O Borgan, R Gill, and N Keiding (1993). Statistical models based on counting processes. New York: Springer

S Datta, and G Satten (2001). Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics and Probability Letters 55 (4), 403–411.

Andersen and Keiding (2002). Multi-state models for event history analysis. Statistical Methods in Medical Research 11 (2), 91–115.

See Also

trans

Examples

data(los.data)
my.observ <- prepare.los.data(x=los.data)
my.model <- msmodel(c("0","1","2","3"),cens.name="cens")
my.trans <- trans(model=my.model,observ=my.observ)
my.aj <- aj(my.trans,s=0,t=80)

[Package changeLOS version 2.0.9-2 Index]