Dear Allstat
I have a query regarding the sample weighting scheme when
units at the first stage of a two stage sampling
scheme are sampled with probability proportional to
size.
The data I am analysing comes from a study where
hospitals are sampled from the set all district
general hospitals in the UK with probability in
proportion to their catchment population. Then in each
of the sampled hospitals a number of patients are
sampled at random.
I have read in text that if say the patient population
for all district general hospitals is N and the
catchment population for sampled hospital i is Ni and b
hospitals are selected in total, then the probability
of selection for hospital i (assuming the hospitals
are selected with replacement) is
pi = bNi/N
I cannot however believe this to be correct, since
there is the chance that pi > 1 if Ni is large enough
in comparison to N.
I make the probability of hospital i being selected
pi = 1-(1-Ni/N)^b which is 1- the probability of
hospital i not being selected.
Can anyone clarify this ?
The next question is how do I weight each of the
patients selected in hospital i ?
If there are ni patients selected in hospital i, then
I think that the probability of any individual patient
selected in hospital i is
p1i = pi*ni/Ni
Again can anyone clarify this and possibly be able to
provide some useful references.
Many Thanks
Trevor Mole
Department of Medical Statistics and Evaluation
Imperial College School of Medicine
Hammersmith Hospital
London
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trevor mole
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