CEF                package:adaptTest                R Documentation

_F_u_n_c_t_i_o_n _t_o _s_p_e_c_i_f_y _a _c_o_n_d_i_t_i_o_n_a_l _e_r_r_o_r _f_u_n_c_t_i_o_n

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

     This function returns a conditional error function.

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

     CEF(typ = NA, fun = NA, dis = NA, a2 = NA, c = NA, p1 = NA, p2 = p1)

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

     typ: type of test: '"b"' for Bauer and Koehne (1994), '"l"' for
          Lehmacher and Wassmer (1999), '"v"' for Vandemeulebroecke
          (2006) and '"h"' for the horizontal conditional error
          function

       c: the parameter c

      a2: alpha2, the local level of the test after the second stage

      p1: the p-value p1 of the test after the first stage

      p2: the p-value p2 of the test after the second stage, defaults
          to 'p1'

     fun: a conditional error function

     dis: a distortion method for a supplied conditional error function
          (see details): '"pl"' for power lines, '"vt"' for vertical
          translation

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

     There are two alternative ways of specifying the desired
     conditional error function:

        *  through a type 'typ', and either a parameter (either 'a2' or
           'c') or a point '(p1,p2)', OR

        *  through an initial conditional error function 'fun', and
           possibly a distortion method 'dis' together with either the
           parameter 'a2' or a point '(p1,p2)'

     Most people will only need the first of these two ways; the second
     leads to user-defined non-standard tests.

     If 'typ' is specified, a parameter 'a2' or 'c' or the point
     '(p1,p2)' must be provided. In this case, 'CEF' returns the
     conditional error function of the chosen type with the given
     parameter or running through the given point.

     If 'typ' is not specified, a conditional error function (i.e., a
     nonincreasing function defined on [0,1] with values in [0,1])
     'fun' must be provided. If no distortion method is selected ('dis
     = NA'), 'fun' is returned unchanged. Otherwise, the function is
     distorted using the chosen distortion method, either to match a
     desired second stage level 'a2' or to run through a specified
     point '(p1,p2)' (one of which must be provided). Currently, two
     distortion methods are implemented:

        *  'dis = "pl"', Power lines: For an initial function f, define
           f[r](x) = (f(x^r))^(1/r), r>0. Note that if f is a
           conditional error function of type '"b"' (Bauer and Koehne,
           1994), so is f[r].

        *  'dis = "pl"', Vertical translation: The initial function is
           shifted vertically.

     See 'parconv' for more information on the two alternative
     parameterizations by alpha2 and c.

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

     These functions return a conditional error _function_ (see
     details).

_N_o_t_e:

     Provide either 'typ' or 'fun', not both! If 'typ' is provided,
     then also specify 'a2', 'c', or 'p1' (and possibly 'p2'). If 'fun'
     is provided, then also specify 'dis' and 'a2', or 'dis' and 'p1'
     (and possibly 'p2'), or none of these.

     Warning: Values of 'a2' close to 0 or 1 may not work for 'dis =
     "pl"'. 

     Note that in this implementation of adaptive two-stage tests,
     early stopping bounds are _not_ part of the conditional error
     function. Rather, they are specified separately (see also 'tsT').

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

     Marc Vandemeulebroecke

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

     Bauer, P., Koehne, K. (1994). Evaluation of experiments with
     adaptive interim analyses. _Biometrics_ 50, 1029-1041.

     Lehmacher, W., Wassmer, G. (1999). Adaptive sample size
     calculations in group sequential trials. _Biometrics_ 55,
     1286-1290.

     Vandemeulebroecke, M. (2006). An investigation of two-stage tests.
     _Statistica Sinica_ 16, 933-951.

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

     'adaptTest' package description, 'parconv', 'plotCEF', 'tsT'

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

     ## Plot two conditional error functions of the Lehmacher-Wassmer (1999) type:
     ## one to the local level alpha2=0.1, and one that runs through (p1,p2)=(0.3,0.7)
     foo1 <- CEF(typ="l", a2=0.1)
     foo2 <- CEF(typ="l", p1=0.3, p2=0.7)
     plot(foo1, xlim=0:1)
     plot(foo2, add=TRUE)

     ## A different way of doing the same
     plotCEF(typ="l", a2=0.1, add=FALSE)
     plotCEF(typ="l", p1=0.3, p2=0.7, plt.pt=FALSE)

