adaptTest-package         package:adaptTest         R Documentation

_A_d_a_p_t_i_v_e _t_w_o-_s_t_a_g_e _t_e_s_t_s

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

     The functions defined in this program serve for implementing
     adaptive two-stage tests.

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


       Package:   adaptTest
       Type:      Package
       Version:   1.0
       Date:      2009-10-14
       License:   GPL (version 2 or later)
       LazyLoad:  yes

     An adaptive two-stage test can be considered as a family of
     decreasing functions f[c](p1) in the unit square. Each of these
     functions is a conditional error function, specifying the type I
     error conditional on the p-value p1 of the first stage. For
     example, f[c](p1) = min(1, c/p1) corresponds to Fisher's
     combination test (Bauer and Koehne, 1994). Based on this function
     family, the test can be put into practice by specifying the
     desired overall level alpha, stopping bounds alpha1 <= alpha0 and
     a parameter alpha2. After computing p1, the test stops with or
     without rejection of the null hypothesis if p1 <= alpha1 or p1 >
     alpha0, respectively. Otherwise, the null hypothesis is rejected
     if and only if p2 <= f[c](p1) holds for the p-value p2 of the
     second stage, where c is such that the local level of this latter
     test is alpha2 (e.g., c = c(alpha2) = exp(-chi2_{4,alpha2}/2) for
     Fisher's combination test).

     This package provides functions for handling conditional error
     functions, performing calculations among the different parameters
     (alpha, alpha0, alpha1, alpha2 and c) and computing overall
     p-values, in addition to graphical visualization routines.
     Currently, four predefined tests are included: Bauer and Koehne
     (1994), Lehmacher and Wassmer (1999), Vandemeulebroecke (2006),
     and the horizontal conditional error function. User-defined tests
     can also be implemented.

     This package contains the following functions:

        *  Key functions are 'CEF', 'plotCEF', 'tsT', 'ovP'.

        *  Further functions are 'a1Table', 'getpar', 'parconv',
           'pathCEF', 'plotBounds', 'eq', 'ne', 'ge', 'gt', 'le', 'lt'.

     The functions 'a1Table', 'getpar', 'parconv' and 'tsT' can handle
     the four predefined tests mentioned above. The functions 'CEF',
     'plotCEF', 'pathCEF' and 'ovP' can also handle these, and
     user-defined tests in addition. The functions 'plotBounds', 'eq',
     'ne', 'ge', 'gt', 'le' and 'lt' do not directly handle tests.

_N_o_t_e:

     Note that a family of conditional error functions can be
     parameterized in two alternative ways: more "traditionally" by
     some parameter c that, in turn, depends on the local level alpha2
     of the test after the second stage, or - perhaps more conveniently
     - by alpha2 itself.

     In this implementation, early stopping bounds are _not_ part of
     the conditional error function. Rather, they are specified
     separately and "imposed" on it.

     I want to thank Niklas Hack for technical support.

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

     Marc Vandemeulebroecke

     Maintainer: Marc Vandemeulebroecke
     <marc.vandemeulebroecke(at)novartis.com>

_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.

     Brannath, W., Posch, M., Bauer, P. (2002). Recursive combination
     tests. _J. Amer. Statist. Assoc._ 97, 236-244.

     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.

     Vandemeulebroecke, M. (2006). _A general approach to two-stage
     tests._ Doctoral thesis, Otto-von-Guericke-Universitaet Magdeburg,
     'http://www.dissertation.de'.

     Vandemeulebroecke, M. (2008). Group sequential and adaptive
     designs - a review of basic concepts and points of discussion.
     _Biometrical Journal_ 50, 541-557.

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

     'CEF', 'tsT'

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

     ## Example from Bauer and Koehne (1994)
     alpha  <- 0.1
     alpha2 <- 0.1
     alpha0 <- 0.5
     alpha1 <- tsT(typ="b", a=alpha, a0=alpha0, a2=alpha2)
     plotCEF(typ="b", a2=alpha2, add=FALSE)
     plotBounds(alpha1, alpha0)
     CEF(typ="b", a2=alpha2)

