coxr                package:coxrobust                R Documentation

_F_i_t _R_o_b_u_s_t_l_y _P_r_o_p_o_r_t_i_o_n_a_l _H_a_z_a_r_d_s _R_e_g_r_e_s_s_i_o_n _M_o_d_e_l

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

     Fits efficiently and robustly Cox proportional hazards regression
     model in its basic form, where explanatory variables are time
     independent with one event per subject.  Method is based on a
     smooth modification of the partial likelihood.

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

     coxr(formula, data, subset, na.action, trunc = 0.95,
          f.weight = c("linear", "quadratic", "exponential"),
          singular.ok = TRUE, model = FALSE)

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

 formula: a formula object, with the response on the left of a '~'
          operator, and the terms on the right.  The response must be a
          survival object as returned by the 'Surv' function.

    data: a data frame in which to interpret the variables named in the
          'formula', or in the 'subset'.

  subset: expression saying that only a subset of the rows of the data
          should be used in the fit.

na.action: a missing-data filter function, applied to the model.frame,
          after any subset argument has been used.

   trunc: roughtly, quantile of the sample T_i exp(beta'Z_i), it
          determines the trimming level for the robust estimator

f.weight: type of weighting function, default is '"quadratic"'

singular.ok: logical value indicating how to handle collinearity in the
          model matrix. If 'TRUE', the program will automatically skip
          over columns of the X matrix that are linear combinations of
          earlier columns.  In this case the coefficients for such
          columns will be 'NA', and the variance matrix will contain
          zeros.  For ancillary calculations, such as the linear
          predictor, the missing coefficients are treated as zeros.

   model: a logical value indicating whether model frame should be
          included as a component of the returned value.

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

     The method consists in maximization of an objective function which
     is a smooth modification of the partial likelihood. Observations
     with excessive values of Lambda(T) exp(beta'Z), where Lambda is
     the cumulated hazard, beta vector of parameters, Z explanatory
     variables and T possibly censored survival time, are
     down-weighted.  Both Lambda and beta are iteratively robustly
     estimated.

     Numerical results are supported by a graphical tool 'plot', which
     in a series of 5 graphs let us compare how well data are explained
     by the estimated proportional hazards model with non-robust (black
     color) and robust method (green color).  The first graph shows
     standardized difference of two estimated survival functions; one
     via the Cox model and the other via Kaplan Meier estimator.  The
     following four graphs show the same differences for four strata,
     defined by the quartiles of the estimated linear predictor.
     Comparison of estimation results along with analysis of the graphs
     leads frequently to a very detailed information about the model
     fit (see examples).

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

     An object of class 'coxr'. See 'coxr.object' for details.

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

     Bednarski, T. (1993). Robust estimation in Cox's regression model.
     Scandinavian Journal of Statistics. Vol. 20, 213-225.

     Bednarski, T. (1989). On sensitivity of Cox's estimator.
     Statistics and Decisions. 7, 215-228.

     Grzegorek, K.(1993). On robust estimation of baseline hazard under
     the Cox model and via Frechet differentiability. Preprint of the
     Institute of Mathematics of the Polish Academy of Sciences.518.

     Minder, C.E. & Bednarski, T. (1996). A robust method for
     proportional hazards regression. Statistics in Medicine Vol. 15,
     1033-1047.

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

     'coxph', 'coxr.object', 'gen_data', 'plot.coxr', 'Surv'

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

     # Create a simple test data set using the attached function gen_data
     a <- gen_data(200, c(1, 0.1, 2), cont = 0.05, p.censor = 0.30)
     result <- coxr(Surv(time, status) ~ X1 + X2 + X3, data = a , trunc = 0.9)
     result
     plot(result)

     #use the lung cancer data at Mayo Clinic to
     #compare results of non-robust and robust estimation
     result <- coxr(Surv(time, status) ~ age + sex + ph.karno + meal.cal + wt.loss, data = lung)
     result
     plot(result)

     #use the Veteran's Administration Lung Cancer Data
     #to compare results of non-robust and robust estimation
     result <- coxr(Surv(time,status) ~ age + trt + celltype + karno + diagtime + prior, data = veteran)
     result
     plot(result)

