seqmon                package:seqmon                R Documentation

_S_e_q_u_e_n_t_i_a_l _M_o_n_i_t_o_r_i_n_g _o_f _C_l_i_n_i_c_a_l _T_r_i_a_l_s

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

     A program that computes the probabilities of crossing boundaries
     in a group sequential clinical trial. It implements the
     Armitage-McPherson and Rowe (1969) algorithm using the method
     described in Schoenfeld D. (2001). Assume that there is a sequence
     of test statistics  z1,...zm in a clinical trial. Each statistic
     has a standard normal distribution under the null hypothesis. Let
     a1,...,am and b1,...,bm be a lower and an upper boundary and let 
     t1,...,tm be the amount of information that was used to calculate
     each statistic. The function calculates the probability that
     zj<aj, j<=i and bj<zj, j<=i for  i=1,...,m. Probabilities for an
     alternative hypothesis can be found by adding an offset to
     a1,...,am and    b1,...,bm equal to the expected value of the
     statistic.

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

     seqmon(a,b,t,int)

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

       a: A vector of the lower boundaries at information time
          t1,t2,...,tm

       b: A vector of the upper boundaries at the information times
          t1,t2,...tm

       t: A vector of the information times, usually 1:m

     int: A vector of the number of intervals to divide up (a[k],b[k]),
          500 should be adequate

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

     A m x 2 matrix giving the the cumulative probabilities of crossing
     the lower boundary and the probabilities of crossing the upper
     boundary.

_N_o_t_e:

     The test statistic is assumed to be standardized so that it's
     value at any point in time is normally distributed random variable
     with mean zero and variance one. The numerator of the test 
     statistic is assumed to be a gaussian process with independent
     increments.

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

     Armitage, P., McPherson, C. K. and Rowe, B. C. (1969)  ``Repeated
     significance tests on accumulating data''  _Journal of the Royal
     Statistical Society, Series A, General_, 132, 235-244 

     Schoenfeld D. (2001) ``A simple Algorithm for Designing Group
     Sequential Clinical Trials'' _Biometrics_ 27 , pp, 972-974. 

     O'Brien, Peter C. , and Fleming, Thomas R.  (1979),  ``A multiple
     testing procedure for clinical trials'', _Biometrics_, 35 ,
     549-556

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

     ##The following gives the probablility of crossing 
     ##the boundaries for a O'Brien Flemming (1979) lower and upper bound
     ##with five looks at the data under the null hypothosis.
     z<-2.04
     a<- -z*sqrt(5/(1:5))
     b<- +z*sqrt(5/(1:5))
     t<- 1:5
     int<- 500* array(c(1),5)
     seqmon(a,b,t,int)
     ##This gives the probabilities under the alternative hypothesis if the expected value of the mean difference over it's
     ##standard error for one group is 1.5
     u<-1.5
     seqmon(a+u*sqrt(1:5),b+u*sqrt(1:5),t,int)

