aj                 package:changeLOS                 R Documentation

_A_a_l_e_n-_J_o_h_a_n_s_e_n _e_s_t_i_m_a_t_o_r

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     aj(tr, s, t)

_A_r_g_u_m_e_n_t_s:

      tr: an object of 'trans'

       s: begin of the time interval

       t: end of the time interval

_D_e_t_a_i_l_s:

     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'.

_V_a_l_u_e:

     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]

_A_u_t_h_o_r(_s):

     Matthias Wangler mw@imbi.uni-freiburg.de

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

     'trans '

_E_x_a_m_p_l_e_s:

     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)

