Is there any necessity to segment the large area to conduct multiple SMART survey instead of doing 1 SMART?

If you think that the prevalences in the two registered camps is likely to be similar (did you see this in the first round of surveys?) then you could combine these into a single survey. It seems, from what you write, that you will only be able to a good survey in one of the registered camps.

You are assuming that a single estimate for all "makeshift" camps is reasonable and useful. I am not sure that is likely as these camps may be very different from each other in terms of populations and/or the presence, coverage, and quality of services that might act to control malnutrition. I'd be tempted to make strata for camps based on levels of service available, or by TFP and SFP workload, or by upazila and perform separate surveys in each stratum or upazila.

I am not much in favour of wide-area surveys without spatial sampling and small area estimates because I think that it is unlikely that the resulting estimate will apply over the whole survey area and the survey may leave pockets of worryingly high prevalence undetected.

I hope this is of some use.

SMART surveys almost always use populations to locate clusters proportional to population size (PPS). This is a broadly accepted method.

I think that you mean using the total population aged 6-59 months in sample size calculations.

I had a quick look at the SMART METHODOLOGY (2006) manual which covers sampling in considerable detail. This does not mentions adjusting sample sizes to account for population sizes. I also looked at the ENA for SMART manual (2012) and see that the calculated sample size is adjusted (corrected) for population size as an option in the ENA software and suggests that his should be doen when the population is less than 10,000 children.

The term "small population" needs some definition. Sample size calculations often assume that n observations are taken from a population of size = N with replacement. We usually violate this assumption be sampling without replacement. This violation is not usually considered important if:

    Sampling proportion = n / N

is below about 0.1. Since we tend to sample from large populations we do not usually need to worry about small population sizes. We typically sample from a population of N = 100,000 adults (n ≈ 20,000 children) so would only worry if the sample size was above:

    n = 20000 * 0.1 = 2000

Most sample sizes calculations assume a very large population. If you have a small population (e.g. <= 2,000 people) then the calculated sample size will be slightly larger than is needed. This is OK as the sample size will be more than sufficient to meet the desired precision.

The uncorrected sampel size will be something like:

    n = p(1 - p) / (e / 1.96)^2

where n is the sampel size, p is the expected prevalence, and e is the desired precision. Using an example from Table 3 on page 46 of the SMART METHODOLOGY (2006) manual:

    n = (0.1(1 - 0.1)) / (0.03 / 1.96)^2 = 384

which is the same sample size as is given in the SMART manual.

For a small population we can correct this using a "finite population correction" (FPC):

    n = (n * N) / (n + (N - 1))

where n is the uncorrected sampel size and N is the total population size. Continuing the example above with a population of N = 2,000 children ... the sampling prportion is:

    Sampling proportion = 384 / 2000 = 0.192

so we have a small population and should use

    n = (384 * 2000) / (384 + (2000 - 1)) = 322

If we sampled n = 384 children we would have a sample size of at least n = 322.

We don't often bother with using a FPC with SMART surveys because (i) we seldom sample from small populations, (ii) we need to apply a sparate FPC during data analysis which can complicate data analysis, and (iii) the uncorrected sample size works well enough. It is, however, common to use an FPC for SQUEAC and SLEAC coverage surveys as there a usually small numbers of SAM cases (i.e. a very small population) in any population.

I hope this is of some help.