What should I do while designing stratified cluster randomized sampling survey if cluster size is large/smaller than I expect?

Question

I am design a sampling strategy for a health survey in long-term care facilities (LTCFs). I refer to the article here and want to ask question about the cluster size.

I am thinking of doing a stratified cluster randomized sample (addition question, if I sample everyone in a single LTCF, is it still a 2-stage sampling? or just 1-stage? Is that I need to sample some LTCF, and then sample some resident in the sampled LTCF, then this can be called as 2-stage sampling? I am getting lost in the terminology jungle), something like this one I asked before. After reading a few books and articles, I think I need to use both stratification and clustering so to have better balance on inflating/deflating the standard error for my measurement.

I have assigned the size of a cluster to be 60 and then do a sample size estimation (approx. 3000), my question is as follow:

Say if I sampled a "small" LTCF, only 20 residents inside, I need 40 more, what should I do? To sample additional cluster?

In another way round, if I sampled a "large" LTCF, with 400 residents inside, I only need 60, should I only do a simple random sampling to pick up the 60 residents I need?

The "unequal cluster size" has been a nightmare to me for quite sometime, right now I have no clue how to process this kind of data appropriately (as I can't do it as if the data is collected by simple random sampling, right?).

I am reading Sharon L. Lor's Sampling - Design and Analysis; and Steven G. Herringa's Applied Survey Data Analysis. Can anyone give me some clue, perhaps in the 2 books, that can give me some insight on getting out of the nightmare? Recommendation of other books/articles is also welcomed. Thanks.

Answer 1

It is techincally only a one-phase study design when you do not select at random your ultimate sampling units from within your primary sampling units. This Amstat article has some info about that:

http://www.amstat.org/sections/srms/proceedings/y2008/Files/301835.pdf

However, you're getting into deep water when you do this pseudo random sampling within units. Without appropriate weighting, you will obtain an unrepresentative sample. For instance, suppose small LTCF are fundamentally different, less staff, less residents, etc. If you sample exhaustively from these PSUs whereas other PSUs with larger measures-of-size (MOSs) are sampled at a fraction (say 5-20% as you mentioned), your smaller LTCFs will be overrepresented. Hence, by virtue of random sampling within PSUs, you make it into a 2-phase design, hence you'll need either reweighting or homogeneous sampling frequencies within PSUs to ensure your estimates are unbiased.