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"), longer.terminal=TRUE)        

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

    time: time points of concentration assessments. 

    conc: levels of concentrations. 

  points: minimum number of data points in the terminal phase. 

    prev: pre-dosing value. 

  method: method of model fitting. 

longer.terminal: requesting a longer terminal than inital half-life.

_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 seperate 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 corresponding
     half-life 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
     using the function 'optim', where OLS regression parameters are
     used as starting 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 for the 'npr' method (see Birkes and Dodge (page 115,
     1993)). 


     When 'longer.terminal=TRUE', the best two-phase model where
     terminal half-life >= inital half-life is selected. When
     'longer.terminal=FALSE', the best two-phase model among all
     possible tuples of regression is selected which can result in
     longer inital half-life than terminal half-life. 


     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:

     A list of S3 class '"halflife"' containing the following
     components: 


   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 concentration values below or
     equal to zero are omitted.

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

     Martin J. Wolfsegger and Thomas Jaki

_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, longer.terminal=TRUE)
     print(result1$parms)
     plot(result1)
     plot(result1, log='y')

     ## 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)
     result2 <- lee(conc=conc, time=time, method='ols', points=2, longer.terminal=FALSE)
     print(result2$parms)
     plot(result2)
     plot(result2, log='y')

     ## 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)
     result3 <- lee(conc=conc, time=time, method='ols', points=2, longer.terminal=FALSE)
     print(result3$parms)
     plot(result3)
     plot(result3, log='y')

     ## advanced plots 
     xlim <- c(0,30)
     ylim <- c(1,80)
     ylab <- 'Log Concentration'
     xlab <- 'Time [hours]'

     text1 <- paste('Initial half-life:', round(result2$parms[1,1],2), 
     '   Terminal half-life:', round(result2$parms[1,2],2))
     text2 <- paste('Initial half-life:', round(result3$parms[1,1],2), 
     '   Terminal half-life:', round(result3$parms[1,2],2))

     split.screen(figs=c(2,1)) 
     screen(1)
     plot(result2, ylab=ylab, xlab=xlab, main='Half-life: Preparation 1', 
     xlim=xlim, ylim=ylim, log='y', sub=text1)
     screen(2)
     plot(result3, ylab=ylab, xlab=xlab, main='Half-life: Preparation 2', 
     xlim=xlim, ylim=ylim, log='y', sub=text2)
     close.screen(all=TRUE)

