lee                    package:PK                    R Documentation

_T_w_o-_P_h_a_s_e _H_a_l_f-_L_i_f_e _E_s_t_i_m_a_t_i_o_n _b_y _L_i_n_e_a_r _F_i_t_t_i_n_g

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

     Estimation of inital and terminal half-life by two-phase linear
     regression fitting.

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

     lee(time, conc, points=3, prev=0, method=c("lad", "ols", "hub", "npr"))              

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

    time: time points of concentration assessments. 

    conc: levels of concentrations. 

  points: minimum data points in the terminal phase. 

    prev: pre-dosing value. 

  method: method of model fitting. 

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

     Estimation of inital and terminal half-life based on the method of
     Lee et al. (1990). This method uses a two-phase linear regression
     approach to break down the model into two straight lines based on
     the selection of the log10 transformed concentration values. For
     two-phase models the initial and terminal half-life were
     determined from the slopes of the regression lines. If a
     single-phase model is selected by this method, the half-life so
     determined is utilized as both initial and terminal phase
     half-life. Half-life is determined only for decreasing inital and
     terminal phases. 


     The method 'ols' uses the ordinary least squares regression (OLS)
     to fit regression lines. 


     The method 'lad' uses the absolute deviation regression (LAD) to
     fit regression lines by using the algorithm as described in Birkes
     and Dodge (chapter 4, 1993) for calculation of regression
     estimates.  


     The method 'hub' uses the Huber M regression to fit regression
     lines. Huber M-estimates are calculated by non-linear estimation
     by function 'optim', where OLS regression parameters are used as
     start values. The function that is minimized involved k =
     1.5*1.483*MAD, where MAD is defined as the median of absolute
     deviation of residuals obtained by a least absolute deviation
     (LAD) regression based on the observed data. The initial value of
     MAD is used and not updated during iterations (Holland and Welsch,
     1977). 


     The method 'npr' uses the nonparametric regression to fit
     regression lines by using the algorithm as described in Birkes and
     Dodge (chapter 6, 1993) for calculation of regression estimates. 


     The selection criteria for the best tuple of regression lines is
     the sum of squared residuals for the 'ols' method, the sum of
     Huber M residuals for the 'hub' method, the sum of absolute
     residuals for the 'lad' method and the sum of a function on ranked
     residuals suggest by Birkes and Dodge (page 115, 1993) for the
     'npr' method. 



     If the pre-dosing value indicating the intrinsinc level is greater
     than 0, the pre-dosing value is subtracted from all concentration
     levels before calculation of inital and terminal half-life.

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

   parms: half-life and model estimates.

   chgpt: changepoint between inital and terminal phase. 

    time: time points of concentration assessments. 

    conc: levels of concentrations. 

  method: "lee". 

_N_o_t_e:

     Records including missing values and values below or equal to zero
     are omitted.

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

     Martin Wolfsegger

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

     Birkes D. and Dodge Y. (1993). Alternative Methods of Regression.
     Wiley, New York, Chichester, Brisbane, Toronto, Singapore.  

      Holland P. W. and Welsch R. E. (1977). Robust regression using
     iteratively reweighted least-squares. Commun. Statist.-Theor.
     Meth. A6(9):813-827. 

      Lee M. L., Poon Wai-Yin, Kingdon H. S. (1990). A two-phase linear
     regression model for biologic half-life data. Journal of
     Laboratory and Clinical Medicine. 115(6):745-748. 


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

     ## example for preparation 1 from Lee et. al (1990)
     time <- c(0.5, 1.0, 4.0, 8.0, 12.0, 24.0)
     conc <- c(75, 72, 61, 54, 36, 6)
     result1 <- lee(conc=conc, time=time, method='ols', points=2)
     print(result1$parms)
     plot(result1)

     ## example for preparation 2 from Lee et. al (1990)
     time <- c(0.5, 1.0, 2.0, 6.5, 8.0, 12.5, 24.0)
     conc <- c(75, 55, 48, 51, 39, 9, 5)
     result2 <- lee(conc=conc, time=time, method='ols', points=2)
     print(result2$parms)
     plot(result2)

     ## advanced plots 
     xlim <- c(0,30)
     ylim <- c(1,80)
     ylab <- 'Log Concentration'
     text1 <- paste('Initial half-life:', round(result1$parms[1,1],3), '   Terminal half-life:', round(result1$parms[1,2],3))
     text2 <- paste('Initial half-life:', round(result2$parms[1,1],3), '   Terminal half-life:', round(result2$parms[1,2],3))
     split.screen(figs=c(2,1)) 
     screen(1)
     plot(result1, ylab=ylab, main='Half-life: Preparation 1', xlim=xlim, ylim=ylim, log='y', sub=text1)
     screen(2)
     plot(result2, ylab=ylab, main='Half-life: Preparation 2', xlim=xlim, ylim=ylim, log='y', sub=text2)
     close.screen(all=TRUE)

