llCoxReg             package:risksetROC             R Documentation

_I_n_c_i_d_e_n_t/_D_y_n_a_m_i_c (_I/_D) _R_O_C _c_u_r_v_e, _A_U_C _a_n_d _i_n_t_e_g_r_a_t_e_d _A_U_C (_i_A_U_C)
_e_s_t_i_m_a_t_i_o_n _o_f _c_e_n_s_o_r_e_d _s_u_r_v_i_v_a_l _d_a_t_a

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

     This function estimates the time-varying parameter estimate
     beta(t) of non-proportional  hazard model using local-linear Cox
     regression as discussed in Heagerty and Zheng, 2005.

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

     llCoxReg(Stime, entry=NULL, status, marker, span=0.40, p=1, window="asymmetric") 

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

   Stime: For right censored data, this is the follow up time. For left
          truncated data, this is the ending time for the interval.

   entry: For left truncated data, this is the entry time of the
          interval. The default is set to \it{NULL} for right censored
          data.

  status: Survival status.

  marker: Marker value.

    span: bandwidth parameter that controls the size of a local
          neighborhood.

       p: 1 if only the time-varying coefficient is of interest and 2 
          if the derivative of time-varying coefficient is also of
          interest, default is 1

  window: Either of "asymmetric" or "symmetric", default is asymmetric.

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

     This function calculates the parameter estimate beta(t) of
     non-proportional hazard model using local-linear Cox regression as
     discussed in Heagerty and Zheng, 2005. This estimation is based on
     a time-dependent Cox  model (Cai and Sun, 2003). For _p=1_, the
     return item _beta_ has two columns, the first column is the
     time-varying parameter estimate, while the second column is the
     derivative. However, if the derivative of the time-varying
     parameter is of interest, then we suggest to use _p=2_. In this
     case, _beta_ has four columns, the first two columns are the same
     when _p=1_, while the last two columns estimates the coefficients
     of squared marker value and its derivative.

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

     Returns a list of following items: 

    time: unique failure times

    beta: estimate of time-varying parameter beta(t) at each unique
          failure time. 

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

     Patrick J. Heagerty

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

     Heagerty, P.J., Zheng Y. (2005) Survival Model Predictive Accuracy
     and ROC curves _Biometrics_, *61*, 92 - 105

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

     data(pbc)
     ## considering only randomized patients
     pbc1 <- pbc[1:312,]
     ## create new censoring variable combine 0,1 as 0, 2 as 1
     survival.status <- ifelse( pbc1$status==2, 1, 0)
     survival.time <- pbc1$fudays
     pbc1$status1 <- survival.status
     fit <- coxph( Surv(fudays,status1) ~ log(bili) +
                                          log(protime) +
                                          edema +
                                          albumin +
                                          age,
                   data=pbc1 )
     eta5 <- fit$linear.predictors
     x <- eta5
     nobs <- length(survival.time[survival.status==1])
     span <- 1.0*(nobs^(-0.2))
     bfnx1 <- llCoxReg(Stime=survival.time, status=survival.status, marker=x,
                        span=span, p=1)
     plot(bfnx1$time, bfnx1$beta[,1], type="l", xlab="Time", ylab="beta(t)")

