aj {changeLOS} | R Documentation |
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.
aj(tr, s, t)
tr |
an object of 'trans' |
s |
begin of the time interval |
t |
end of the time interval |
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
.
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] |
Matthias Wangler mw@imbi.uni-freiburg.de
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.
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)