RankRegTest              package:emplik              R Documentation

_T_e_s_t _t_h_e _A_F_T _m_o_d_e_l _R_a_n_k _R_e_g_r_e_s_s_i_o_n _e_s_t_i_m_a_t_o_r _b_y _E_m_p_i_r_i_c_a_l _L_i_k_e_l_i_h_o_o_d

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

     Use the empirical likelihood ratio and Wilks theorem to test if
     the regression coefficient is equal to beta, based on the rank
     estimator for the AFT model.

     The log empirical likelihood been maximized is

        sum_{d=1} log Delta F(e_i) + sum_{d=0} log [1-F(e_i)];

     where e_i are the residuals.

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

     RankRegTest(y, d, x, beta, type="Gehan")

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

       y: a vector of length N, containing the censored responses.

       d: a vector (length N) of either 1's or 0's.  d=1 means y is
          uncensored; d=0 means y is right censored. 

       x: a matrix of size N by q. 

    beta: a vector of length q. the value of the regression 
          coefficient to be tested in the model  y_i = beta x_i  +
          epsilon_i 

    type: default to Gehan type.  The other option is Logrank type.

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

     The estimator of beta can be obtained by function  'rankaft( )' in
     the package 'rankreg'. But here you may test other values of 
     beta. If you test the beta value that is obtained from the
     'rankaft( )', then the -2LLR should be 0 and the p-value should be
     1.

     The above likelihood should be understood as the likelihood of the
      error term, so in the regression model the error e_i should be
     iid.

     The estimation equation used when maximize the  empirical
     likelihood is 

   0 = sum_i phi (e_i)  d_i Delta F(e_i) (x_i - bar x_i  )/(n w_i)

     which was described in detail in the references below.

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

     A list with the following components: 

 "-2LLR": the -2 loglikelihood ratio; should have approximate chisq 
          distribution under H_o.

  logel2: the log empirical likelihood, under estimating equation.

   logel: the log empirical likelihood of the Kaplan-Meier of e's.

    prob: the probabilities that max the empirical likelihood  under
          rank estimating equation.

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

     Mai Zhou.

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

     Kalbfleisch, J. and Prentice, R. (2002) The Statistical Analysis
     of Failure Time Data. 2nd Ed. Wiley, New York.  (Chapter 7)

     Jin, Z., Lin, D.Y., Wei, L. J. and Ying, Z. (2003). Rank-based
     inference for the accelerated failure time model. Biometrika, 90,
     341-53.

     Zhou, M. (2005). Empirical likelihood analysis of the rank
     estimator for the censored accelerated failure time model. 
     Biometrika, 92, 492-98.

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

     if(require("rankreg", quietly = TRUE)) {
     ####library(rankreg)
     data(myeloma)
     RankRegTest(y=myeloma[,1], d=myeloma[,2], x=myeloma[,3], beta= -15.50147)
     # you should get "-2LLR" = 9.050426e-05 (practically zero)
     # The beta value, -15.50147, was obtained by rankaft() from the rankreg package.
     }

