wc.fit                package:survrec                R Documentation

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_e_s_t_i_m_a_t_o_r _d_e_v_e_l_o_p_e_d _b_y _W_a_n_g _a_n_d _C_h_a_n_g.

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

     Estimation of survival function for correlated or i.i.d.
     recurrence  time data by means of the product limit estimator
     (PLE) method developed by Wang and Chang. The resulting object of
     class "survfitr" is plotted by `plot.survfitr', before it is
     returned.

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

     wc.fit(x,tvals) 

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

       x: a survival recurrent event object.

   tvals: vector of times where the survival function can be estimated. 

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

     Wang and Chang (1999) proposed an estimator of the common marginal
     survivor function in the  case where within-unit interrocurence
     times are correlated. The correlation structure  considered by
     Wang and Chang (1999) is quite general and contains, in
     particular,  both the i.i.d. and multiplicative (hence gamma)
     frailty model as special cases. 

     This estimator removes the bias noted for the produc-limit
     estimator developed by  Pea, Strawderman and Hollander (PSH, 2001)
     when interrocurence times are correlated within  units. However,
     when applied to i.i.d. interocurrence times, this estimator is not
     expected  to perform as well as the PSH estimator, especially with
     regard to efficiency.

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

       n: number of unit or subjects observed.

       m: vector of number of recurrences in each subject (length n).

  failed: vector of number of recurrences in each subject (length n*m).
          Vector ordered (e.g. times of first unit, times of second
          unit, ..., times of n-unit)

censored: vector of times of censorship for each subject (length n).

numdistinct: number of distinct failures times.

distinct: vector of distinct failures times.

  AtRisk: matrix of number of persons-at-risk at each distinct time and
          for each subject.

survfunc: vector of survival estimated in distinct times.

   tvals: copy of argument.

PSHpleAttvals: vector of survival estimated in tvals times.

_N_o_t_e:

     The mantainer wishes to thank Professors Chiung-Yu Huang and
     Shu-Hui Chang for their help for providing us with the Fortran
     code which computes standard errors of Wang and Chang's estimator.

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

     Wang, M.-C. and Chang, S.-H. (1999). Nonparametric Estimation of a
     Recurrent Survival Function. _J. Amer. Statist. Assoc_ *94*,
     146-153.

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

     'survfitr' 'Survr'

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

     data(MMC)

     fit<-wc.fit(Survr(MMC$id,MMC$time,MMC$event))
     fit
     plot(fit,conf.int=FALSE)

     # compare with pena-straderman-hollander

     fit<-psh.fit(Survr(MMC$id,MMC$time,MMC$event))
     fit
     lines(fit,lty=2)

     # and with MLE frailty

     fit<-mlefrailty.fit(Survr(MMC$id,MMC$time,MMC$event))
     fit
     lines(fit,lty=3)

