popower                package:Hmisc                R Documentation

_P_o_w_e_r _a_n_d _S_a_m_p_l_e _S_i_z_e _f_o_r _O_r_d_i_n_a_l _R_e_s_p_o_n_s_e

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

     'popower' computes the power for a two-tailed two sample
     comparison of ordinal outcomes under the proportional odds ordinal
     logistic model.  The power is the same as that of the Wilcoxon
     test but with ties handled properly.  'posamsize' computes the
     total sample size needed to achieve a given power.  Both functions
     compute the efficiency of the design compared with a design in
     which the response variable is continuous.  'print' methods exist
     for both functions.  Any of the input arguments may be vectors, in
     which case a vector of powers or sample sizes is returned.  These
     functions use the methods of Whitehead (1993).

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

     popower(p, odds.ratio, n, n1, n2, alpha=0.05)
     ## S3 method for class 'popower':
     print(x, ...)
     posamsize(p, odds.ratio, fraction=.5, alpha=0.05, power=0.8)
     ## S3 method for class 'posamsize':
     print(x, ...)

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

       p: a vector of marginal cell probabilities which must add up to
          one. The 'i'th element specifies the probability that a
          patient will be in response level 'i', averaged over the two
          treatment groups. 

odds.ratio: the odds ratio to be able to detect.  It doesn't matter
          which group is in the numerator. 

       n: total sample size for 'popower'.  You must specify either 'n'
          or 'n1' and 'n2'.  If you specify 'n', 'n1' and 'n2' are set
          to 'n/2'. 

      n1: for 'popower', the number of subjects in treatment group 1 

      n2: for 'popower', the number of subjects in group 2 

   alpha: type I error 

       x: an object created by 'popower' or 'posamsize'

fraction: for 'posamsize', the fraction of subjects that will be
          allocated to group 1 

   power: for 'posamsize', the desired power (default is 0.8) 

     ...: unused

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

     a list containing 'power' and 'eff' (relative efficiency) for
     'popower', or containing 'n' and 'eff' for 'posamsize'.

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

     Frank Harrell 
      Department of Biostatistics 
      Vanderbilt University School of Medicine 
      f.harrell@vanderbilt.edu

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

     Whitehead J (1993): Sample size calculations for ordered
     categorical data.  Stat in Med 12:2257-2271.

     Julious SA, Campbell MJ (1996): Letter to the Editor.  Stat in Med
     15: 1065-1066.  Shows accuracy of formula for binary response
     case.

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

     'bpower', 'cpower'

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

     #For a study of back pain (none, mild, moderate, severe) here are the
     #expected proportions (averaged over 2 treatments) that will be in
     #each of the 4 categories:

     p <- c(.1,.2,.4,.3)
     popower(p, 1.2, 1000)   # OR=1.2, total n=1000
     posamsize(p, 1.2)
     popower(p, 1.2, 3148)

