precision              package:twostage              R Documentation

_O_p_t_i_m_a_l _s_a_m_p_l_i_n_g _d_e_s_i_g_n _f_o_r _2-_s_t_a_g_e _s_t_u_d_i_e_s _w_i_t_h _f_i_x_e_d _p_r_e_c_i_s_i_o_n

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

     Optimal design for two-stage-study with fixed variance
 of
     estimates using the Mean Score method 


     BACKGROUND 


     This function calculates the total number of study observations
     and the second-stage sampling fractions that will minimise the
     study cost subject to a fixed variance for a specified
     coefficient. 
 The user must also supply the unit cost of
     observations at the
 first and second stage, and the vector of
     prevalences in each 
 of the strata defined by different levels of
     dependent variable 
 and first stage covariates . 

     Before running this function you should run the `coding' function,
     
 to see in which order you must supply the vector of
     prevalences. For details, type help(`coding')

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



     precision (y=y,x=x,z=z,prev=prev,factor=NULL,var="var",prc=prc,c1=c1,c2=c2)

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

     REQUIRED ARGUMENTS
 

       y: response variable (binary 0-1)

       x: matrix of predictor variables

       z: matrix of the first stage variables which must be categorical
           (can be more than one column)

    prev: vector of estimated prevalences for each (y,z) stratum

     var: the name of the predictor variable whose coefficient is to be
          optimised. 
 See DETAILS if this is a factor variable

     prc: the fixed variance of `var' coefficient

      c1: the cost per first stage observation

      c2: the cost per second stage observation 


          OPTIONAL ARGUMENTS

  factor: the names of any factor variables in the predictor matrix

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

     The response, predictor and first stage variables 
 have to be
     numeric. If you have multiple columns of 
 z, say (z1,z2,..zn),
     these will be recoded into
 a single vector `new.z' 

       z1  z2  z3  new.z
        0   0   0      1
        1   0   0      2
        0   1   0      3
        1   1   0      4
        0   0   1      5
        1   0   1      6
        0   1   1      7
        1   1   1      8

     If some of the value combinations do not exist 
 in your data, the
     function will adjust accordingly. 
 For example if the combination
     (0,1,1) is absent,
 then (1,1,1) will be coded as 7. 


     If you wish to optimise the coefficient of a factor variable, 
     you need to specify which level of the variable to optimise. 
 For
     example, if "weight" is a factor variable with 3 categories
 1,2
     and 3 then var="weight2" will optimise the estimation of the
     coefficient which measures the difference between weight=2 and
     the baseline (weight=1). By default the baseline is always 
 the
     category with the smallest value. 

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

     The following lists will be returned:

       n: the optimal number of observations (first stage sample size)

     var: the variance of estimates achieved by the optimal design

    cost: the minimum study cost 


          and a list called `design' consisting of the following items:

  ylevel: the different levels of response variable

  zlevel: the different levels of first stage covariates z.

    prev: the prevalence of each (`ylevel',`zlevel') stratum

      n2: the sample size of pilot observations for each
          (`ylevel',`zlevel') stratum

    prop: optimal 2nd stage sampling proportion for each
          (`ylevel',`zlevel') stratum

samp.2nd: optimal 2nd stage sample size for each (`ylevel',`zlevel')
          stratum

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

     Reilly,M and M.S. Pepe. 1995. A mean score method for 
 missing
     and auxiliary covariate data in 
 regression models. Biometrika
     82:299-314 


     Reilly,M. 1996. Optimal sampling strategies for 
 two-stage
     studies. Amer. J. Epidemiol. 
 143:92-100

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

     `ms.nprev',`fixed.n',
 `budget',`cass1',
 `cass2',`coding'

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



     This example uses the same CASS dataset (cass2) which is used
     in the example of the "budget" function. The data are in the
     cass2 matrix, which can be loaded using

     data(cass2)
     and a description of the dataset can be seen using

     help(cass2)

     In our example below, we use sex and weight as auxiliary variables. 
     The commands below will calculate the sampling design which will achieve a 
     variance of 0.0472 for the coefficient of SEX subject to 
     minimising the study cost. We assume a first-stage cost of  1/unit
     and second-stage cost of  0.5/unit,

     data(cass2) 
     y_cass2[,1]                  #response variable
     z_cass2[,10]             #auxiliary variable
     x_cass2[,c(2,4:9)]       #predictor variables in the model


     # run CODING function to see in which order we should enter prevalences
     coding(x=x,y=y,z=z)     

     # supplying the prevalence (from Table 5, Reilly 1996)
     prev_c(0.0197823937,0.1339020772,0.6698813056,0.0544015826,
     + 0.0503214639,0.0467359050,0.0009891197,0.0040801187,0.0127349159,
     + 0.0022255193,0.0032146390,0.0017309594)

     # optimise SEX coefficient
     precision(x=x,y=y,z=z,var="sex",prev=prev,prc=0.0472,c1=1,c2=0.5)

     This will give us the following output:

     [1] "please run coding function to see the order in which you"
     [1] "must supply the first-stage sample sizes or prevalences"
     [1] " Type ?coding for details!"
     [1] "For calls requiring n1 or prev as input, use the following order"
           ylevel z new.z n2
      [1,]      0 1     1 10
      [2,]      0 2     2 10
      [3,]      0 3     3 10
      [4,]      0 4     4 10
      [5,]      0 5     5 10
      [6,]      0 6     6 10
      [7,]      1 1     1  8
      [8,]      1 2     2 10
      [9,]      1 3     3 10
     [10,]      1 4     4 10
     [11,]      1 5     5 10
     [12,]      1 6     6 10
     [1] "Check sample sizes/prevalences"
     $n
     [1] 9165

     $design
           ylevel zlevel         prev n2   prop samp.2nd
      [1,]      0      1 0.0197823937 10 0.5230       95
      [2,]      0      2 0.1339020772 10 0.2841      349
      [3,]      0      3 0.6698813056 10 0.0726      446
      [4,]      0      4 0.0544015826 10 0.4488      224
      [5,]      0      5 0.0503214639 10 0.2480      114
      [6,]      0      6 0.0467359050 10 0.4922      211
      [7,]      1      1 0.0009891197  8 1.0000        9
      [8,]      1      2 0.0040801187 10 1.0000       37
      [9,]      1      3 0.0127349159 10 1.0000      117
     [10,]      1      4 0.0022255193 10 1.0000       20
     [11,]      1      5 0.0032146390 10 1.0000       29
     [12,]      1      6 0.0017309594 10 1.0000       16

     $cost
     [1] 9998

     $var
                         [,1]
     (Intercept) 1.424664e+00
     sex         4.719827e-02
     weight      4.514397e-05
     age         2.128650e-04
     angina      6.044365e-02
     chf         5.935923e-03
     lve         1.014436e-04
     surg        3.236426e-02 

     CHECK: 
     Note that the minimum cost obtained is the same as our budget
     in the fixed budget problem (10,000), and all the solutions are 
     the same except for rounding error. 


