Cluster randomized sampling and subseqent analysis I am currently designing the sampling strategy for a prevalence survey on elderly in long term care facilities (LTCF) in my service, I used the "Limebook" from WHO as a reference. And I would like to see for comment on my design to see if I have done anything wrong here.
Scenario: Let say I am doing a survey in country X, country X can be divided into 3 district A,B,C. I need to do survey in the LTCF in country, there are many types of LTCF and it can be roughly divided into "private" (P) LTCF and "non-private" (NP) LTCF. Since district A,B,C are different in size and population, so the numbers of LTCF are different in the 3 districts. And LTCFs have different number of residents.
I have estimated by prevalence of disease Z, relative precision and the design effect. So the total sample size needed is 4000, with the designed effect to be 4 and cluster size to be 120.
In the first stage of sampling I will determine how many clusters need to be sampled from each of the strata (strata is determined by districts X LTCF type, i.e. A-P, A-NP, B-P, B-NP, C-P, C-NP), proportional to the number of residents found in each strata.) (i.e. strata is sampled with probability proportionate to size)
Let say I need to pick up 2 clusters from A-P, then I created a list of residents living in priate LTCF in district A, and then pick up 2 of them, one from LTCF-R and one from LTCF-S. Then I will sample everyone in LTCF-R and LTCF-S. (i.e. LTCF is sampled with probability proportionate to size)
If LTCF-R is too small (e.g. only 30 rather than 120), its neighboring LTCF (e.g. LTCF-T also a private LTCF) will be selected and included in the LTCF-R cluster.
If LTCF-R is too big (e.g. 300 rather than 120), random sample of 120 residence will be sampled.
Till now I am doing something similar as the "Multi-stage cluster sampling in Nigeria 2011" mentioned in Example 5.4 in the WHO TB prevalence survey handbook.
One thing that worries me quite a bit is that I need to add another LTCF into the original cluster is the residence in the cluster is not enough. This seems not quite like the scenario mentioned by Frerichs R.R in his chapter about cluster sampling. I am not sure if I can still use the formula in his chapter for calculating the disease Z prevalence of my cluster sampled data.
Please feel free to comment or ask question. Thanks in advance.
 A: You are totally right, this is a bad design in terms of selecting the clusters. And targeting the overall sample size with a large number of the SSUs sampled within a PSU is a bad target, too. I would first try to get an idea of the ICC for the variables of interest, and then design the sample to maximize the accuracy given the budget, which will likely lead to more clusters and fewer observations per cluster unless adding more clusters to the sample is prohibitively expensive (travel costs to a given center are prohibitively expensive as compared to the costs of individual interviews). DEFF = 4 really has to be justified by a defensible cost analysis.
If you really need to achieve the cluster size of 120, then you would want to combine the small LTCFs together into a single sampling unit. You would probably want to take as dissimilar centers as possible when combining them, so as to minimize the design effect.
I would also advise to use an appropriate complex survey software, like Stata or R, rather than trying to implement the formula that may not be applicable, anyway. You will have unequal weights because (1) you sample PPS (which is not trivial at all in and of itself, see Brewer and Hanif (1983) and Thompson (1997)); (2) you may have different probabilities of selection within the clusters for larger units, so the probability of selection of the cluster will get multiplied by 300/120. So the formulae from the book you cited would not apply (and relying on free books may be a bad idea, too; you must have some budget for survey design and post-processing, so you'd want to get a solid book on sampling and survey data analysis with this money; if you did not have that budget, then you must be trying to go so cheap that your survey may not meet meet the minimum quality criteria).
