SI                    package:drc                    R Documentation

_C_o_m_p_a_r_i_n_g _s_e_l_e_c_t_i_v_i_t_y _i_n_d_i_c_e_s _a_c_r_o_s_s _c_u_r_v_e_s

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

     'SI' compares selectivity indices for arbitrary dosage across
     curves. The selectivity is the ratio between effective dosages
     from different curves.

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

       SI(object, percVec, compMatch = NULL, od = FALSE, reverse = FALSE, 
       interval = c("none", "delta", "fieller", "fls"), 
       level = ifelse(!(interval == "none"), 0.95, NULL),
       reference = c("control", "upper"),  
       type = c("relative", "absolute"),
       display = TRUE, pool = TRUE, logBase = NULL, ...)
       
       relpot(object, plotit = TRUE, compMatch = NULL, percVec = NULL, interval = "none", 
       type = c("relative", "absolute"), scale = c("original", "percent", "unconstrained"), ...)

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

  object: an object of class 'drc'.

 percVec: a numeric vector of dosage values.

compMatch: an optional character vector of names of assays to be
          compared. If not specified all comparisons are supplied.

      od: logical. If TRUE adjustment for over-dispersion is used. This
          argument only makes a difference for binomial data.

 reverse: logical. If TRUE the order of comparison of two curves is
          reversed.

interval: character string specifying the type of confidence intervals
          to be supplied. The default is "none".  Use "delta" for
          asymptotics-based confidence intervals (using the delta
          method and the t-distribution). Use "fieller" for confidence
          intervals based on Fieller's theorem (with help from the
          delta method). Use "fls" for from-logarithm-scale-based
          confidence intervals (in case the parameter in the model fit
          is  log(ED50) as is the case for the 'logistic' or
          'llogistic2' models); currently the argumetn 'logBase' then
          also needs to be specified.

   level: numeric. The level for the confidence intervals. Default is
          0.95.

reference: character string. Is the upper limit or the control level
          the reference?

    type: character string specifying whether absolute or relative
          response levels are supplied.

 logBase: numeric. The base of the logarithm in case logarithm
          transformed dose values are used.

 display: logical. If TRUE results are displayed. Otherwise they are
          not (useful in simulations).

    pool: logical. If TRUE curves are pooled. Otherwise they are not.
          This argument only works for models with independently fitted
          curves as specified in 'drm'.

     ...: In 'SI': additional arguments to the function doing the
          calculations.  For instance the upper limit for the bisection
          method  needs to be larger than the ED values used in the
          required relative pontency. In 'relpot': additional graphical
          parameters.

  plotit: logical. If TRUE the relative potencies are plotted as a
          function of the response level.

   scale: character string indicating the scale to be used on the x
          axis: original or percent response level (only having an
          effect for type="relative").

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

     The function 'relpot' is a convenience function, which is useful
     for assessing how the relative potency changes as a function of
     the response level (eg for plotting as outlined in Ritz _et al_
     (2006)).

     Fieller's theorem is incorporated using the formulas Kotz and
     Johnson (1983) and Finney (1978).

     For objects of class 'braincousens' or 'mlogistic' the additional
     argument may be the 'upper' argument or the 'interval' argument.
     The 'upper' argument specifies the upper limit of the bisection
     method.  The upper limits needs to be larger than the EDx level to
     be calculated. The default limit is 1000. The 'interval' argument
     should specify a rough interval in which the dose yielding the
     maximum hormetical response lies. The default interval is
     'c(0.001, 1000)'.  Notice that the lower limit should not be set
     to 0 (use something like 1e-3, 1e-6, ...).

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

     A matrix with columns containing the estimates, estimated standard
     errors,  t-statistics for testing indices equal to 1 and the
     corresponding p-values.

_N_o_t_e:

     This function is only implemented for the following built-in
     functions available in the package _drc_:  'braincousens',
     'cedergreen', 'ucedergreen', 'llogistic' and 'weibull1'.

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

     Christian Ritz

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

     Finney, D. J. (1978) _Statistical method in Biological Assay_,
     London: Charles Griffin House,  3rd edition (pp. 80-82).

     Kotz, S. and Johnson, N. L. (1983) _Encyclopedia of Statistical
     Sciences Volume 3_,  New York: Wiley & Sons (pp. 86-87).

     Ritz, C. and Cedergreen, N. and Jensen, J. E. and Streibig, J. C.
     (2006)  Relative potency in nonsimilar dose-response curves, _Weed
     Science_, *54*, 407-412.

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

     A related functions 'ED.drc' (for calculating effective doses) and
      'relpot' (for displaying relative potencies).

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

     m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4())

     SI(m1, c(50,50))
     SI(m1, c(10,50))
     SI(m1, c(10,50), reverse = TRUE)

     ## Relative potency of two herbicides
     m2 <- drm(DryMatter~Dose, Herbicide, 
     data = S.alba, fct = LL.3())

     SI(m2, c(50, 50))  
     SI(m2, c(50, 50), ci = "delta")
     SI(m2, c(50, 50), ci = "fieller")

     ## Comparison based on absolute
     ##  response level

     m3 <- drm(SLOPE~DOSE, CURVE,
     data = spinach, fct = LL.4())

     SI(m3, c(0.5,0.5), c(2,4), type="a", ci="fieller")

     SI(m3, c(55,80), c(2,4))  
     # same comparison using a relative response level

     ## Relative potency transformed from log scale
     m4 <- drm(drymatter~log(dose), treatment, data=G.aparine[-c(1:40), ], 
     pmodels = data.frame(treatment,treatment,1,treatment), fct = LL2.4())

     SI(m4, c(50,50), ci="fls", logBase=exp(1))

