Summary: Can I use non-population information (e.g. representative proportions from another survey) when calculating sampling weights? If so how might one account for the sampling error?
I'm calculating standard errors for a set of mean estimates (cohorts are age, gender and health state).
I can calculate sampling weights using my data and population age, gender information from the census. There is no census information on health state.
I have non-census health status information from a 'large' survey* (from the same population) which also has age-gender information. Presently I assume that the 'large' survey* point estimates for relative proportions of health states (for a given age gender cohort) are sufficiently precise to stand in for the population proportions which I do not observe. I use these alongside census age/gender information to derive population cohort counts and calculate sampling weights as usual. Then I use Stata's svy package for se's via Taylor linearization.
I'm uncomfortable with the stand-in of the the 'large' survey* proportions in place of true population proportions as the imprecision of these is not accounted for in my standard error estimation.
I think the influence of these is small, but how acceptable would you say the above approach is? Are there better ways of going about it?
When I say sampling weights I use the following simple formula: (Npopulation of a given age, gender, health cohort)/Npopulation)/(nsample of a given age, gender, health cohort/nsample)
The larger survey is the National Survey of Mental Health and Welbeing (Australia), which has a stratified, multistage, design. The smaller survey is a simple random sample.