W1.4                   package:drc                   R Documentation

_T_h_e _f_o_u_r-_p_a_r_a_m_e_t_e_r _W_e_i_b_u_l_l _f_u_n_c_t_i_o_n_s

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

     'W1.4' and 'W2.4' provide the four-parameter Weibull functions,
     self starter function and  names of the parameters.

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

       W1.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
       
       W2.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

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

   fixed: numeric vector. Specifies which parameters are fixed and at
          what value they are fixed.  NAs for parameter that are not
          fixed.

   names: a vector of character strings giving the names of the
          parameters. The default is reasonable.

     ...: additional arguments to be passed from the convenience
          functions.

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

     The equations for the mean functions are given at 'weibull1'.

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

     See 'weibull1'.

_N_o_t_e:

     This function is for use with the model fitting function 'drm'.

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

     Christian Ritz

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

     Seber, G. A. F. and Wild, C. J (1989) _Nonlinear Regression_, New
     York: Wiley & Sons (pp. 330-331).

     Ritz, C (2009) Towards a unified approach to dose-response
     modeling in ecotoxicology _To appear in Environ Toxicol Chem_.

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

     Setting c=0 yields 'W1.3'. A more flexible function, allowing 
     fixing or constraining parameters, is available through
     'weibull1'.

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

     ## Fitting a four-parameter Weibull (type 1) model
     terbuthylazin.m1 <- drm(rgr~dose, data = terbuthylazin, fct = W1.4())
     summary(terbuthylazin.m1)

     ## Fitting a first-order multistage model
     ## to data from BMDS by EPA
     ## (Figure 3 in Ritz (2009))
     bmds.ex1 <- data.frame(ad.dose=c(0,50,100), dose=c(0, 2.83, 5.67), num=c(6,10,19), total=c(50,49,50))

     bmds.ex1.m1<-drm(num/total~dose, weights=total, data=bmds.ex1, fct=W2.4(fixed=c(1,NA,1,NA)), type="binomial")

     modelFit(bmds.ex1.m1)  # same as in BMDS

     summary(bmds.ex1.m1)  # same background estimate as in BMDS

     logLik(bmds.ex1.m1)

     ## BMD estimate identical to BMDS result
     ## BMDL estimate differs from BMDS result (different method)
     ED(bmds.ex1.m1, 10, ci="delta")

     ## Better fit

     bmds.ex1.m2<-drm(num/total~dose, weights=total, data=bmds.ex1, fct=W1.4(fixed=c(-1,NA,1,NA)), type="binomial")
     modelFit(bmds.ex1.m2)
     summary(bmds.ex1.m2)

     ED(bmds.ex1.m2, 50, ci = "delta")

     ## Creating Figure 3 in Ritz (2009)
     bmds.ex1.m3 <- drm(num/total~dose, weights=total, data=bmds.ex1, fct=LL.4(fixed=c(-1,NA,1,NA)), type="binomial")

     plot(bmds.ex1.m1, ylim = c(0.05, 0.4), log = "", lty = 3, lwd = 2, xlab = "Dose (mg/kg/day)", ylab = "",
     cex=1.2, cex.axis=1.2, cex.lab=1.2)

     mtext("Tumor incidence", 2, line=4, cex=1.2)  # tailored y axis label

     plot(bmds.ex1.m2, ylim = c(0.05, 0.4), log = "", add = TRUE, lty = 2, lwd = 2)

     plot(bmds.ex1.m3, ylim = c(0.05, 0.4), log = "", add = TRUE, lty = 1, lwd = 2)

     arrows(2.6 , 0.14, 2, 0.14, 0.15, lwd=2)
     text(2.5, 0.14, "Weibull-1", pos=4, cex=1.2)

