Algorithm to sample groups to match expected proportions

Question

I need to find a way to sample groups so that the observed proportions match the expected ones. I would like to keep as many of the observations in each group as possible.

Simple example: Group A = 302 (60.3%) Group B = 199 (39.7%)

The proportions I expect are 46.6% and 53.4%, so in this instance I would keep all the observations in Group B and sample Group A by 0.576 to get 174 observations. Is this correct?

Is there anyway to write a rule in SAS or R that would give you the appropriate sampling rate for n groups? My actual problem involves 14 groups with counts ranging from 2 to 77:

Group A = 77 , observed = 21.51%, expected = 15.10%

Group B = 5 , observed = 1.4%, expected = 0.54%

Group C = 2, observed = 0.56%, expected = 1.62%

etc.

Many thanks for your help.

Answer 1

I believe you can use PROC SURVEYSELECT to achieve this. You need to store the expected sampling rate per group in a separate dataset, then apply the the option "SAMPRATE=SAS data set" in the PROC SURVEYSELECT statement. See the online documentation on this procedure for more information.

Answer 2

Here is a dodgy little function to play with:

minsamp <- function(obs,expect) {

  ## get the groups where the number of people available
  ## isn't enough to simply multiply it out
  underrep <- obs[which(obs - expect * sum(obs) < 0)]

  # name of the smallest underrepresented group
  urname <- names(which.min(underrep))

  # get the final result
  round(expect * (obs[urname]/expect[urname]))

}

And an example (based on your simple example:

obs <- c(a=302,b=199)
expect <- c(a=0.466,b=0.534)

> minsamp(obs,expect)
  a   b 
174 199 

And you can see it worked:

> prop.table(minsamp(obs,expect))
        a         b 
0.4664879 0.5335121